algorithm that so new hasn't even been published. In fact it's in review as we speak. It's David's work and it's pretty cool stuff but to get to it I need to describe for you where we are with regard to the problem of learning and the state estimation framework that I've been describing. So we describe the problem of learning from a common filter perspective. We said that the objective of the learner is to estimate the state of the environment. In his mind he has a generative model in which he describes how the data that he's collecting is generated. Based on that generative model he estimates he or she estimates the parameter that makes up the hidden state of that of that environment. And then we talked about how using the hidden state approach where we estimate the hidden state we can take observations and compare it to predictions and then compute a change in our belief about the hidden state of the system. Now let me begin by giving you a brief review of what we would predict regarding what the learner should do in a situation where noises are altered and state estimation says how he should learn more or learn less from a particular prediction error. So in a scenario where this is going to be chapter 7 by the way. The material today will be chapter 7. The material that I'm going to be describing with regard to this new work, David's work, is not in anything. So it's not in the book, it's not in any published work. You're just going to have to listen to me and pay attention to it and write it down. You're going to have a homework based on that that David just put up on the website tonight. So we'll give you an opportunity to think about it. Alright. So suppose that we have the state state estimation problem. We have x hat of trial n is equal to a x hat of sorry x of trial n minus 1 plus some state update noise epsilon x which we're going to have as variance sigma squared x with mean 0 and we have an observation y of n say it's equal to x of n plus epsilon y where epsilon y is normal 0 sigma squared y this variance. Now when we describe the problem of learning here we say that well we're going to have some belief about x hat a trial n given n so this is our posterior belief and that depends on our prior belief x hat of n n minus 1 plus this thing that we call the common gain the relationship between our uncertainties in our beliefs and our uncertainty in our observation times the difference between what we observed and what we predicted and we wrote that in the case of a scalar system like this the common gain is going to be equal to the ratio between my prior uncertainty and my observation uncertainty which in this case is going to be just p of n n minus 1 plus sigma squared y. So if you look at this equation k of n is really what we might say is my sensitivity to error. It tells me how much I'm going to learn from error. So if I make a prediction and I don't observe what I thought I should observe I'm going to learn something about my prediction and I'm going to improve my belief but how much I learn from that error is this gain which we've been calling the common gain the sensitivity to error and today's lecture is about this gain k and I'm going to show you that our theories associated with the state estimation only takes us so far when we begin to look at how biological systems learn humans learn we're going to see that it begins to fail and we're going to need something else and we're going to come up with a different way of thinking about things but the state of the art is more or less here that there is an objective way to modulate your sensitivity to error and that has to do with the common gain and what is this common gain is the relationship between your prior belief that has uncertainty in it P and your observation so in 2008 people began to test this theory to see if indeed in biological systems their sensitivity to error was modulated by the relationship between their uncertainty about what they believed and the uncertainty about what they observed so just to give you a sense of what that means just to stepping back basically if I'm uncertain about my prediction I'm going to say tomorrow it's going to rain but it turns out that I'm a pretty bad predictor I don't really have a whole lot of confidence in my prediction so therefore if tomorrow comes and it's sunny I'm going to change my predictions I'm going to learn something from my error and I'm going to learn a lot because I was very uncertain about my prediction on the other hand if I'm pretty darn certain about it from you know George Bush and I made prediction that there's going to be weapons of mass destruction in Iraq by God there's going to be those things and I'm going to be pretty darn hard pressed to believe that there isn't because I'm pretty certain about my belief so I don't mean to say anything wrong about George Bush he's a fine president only that he was pretty certain about his predictions and of course you have to be in these scenarios okay so in 2008 people began using these kinds of formulations to ask whether the way individuals learned from error could be thought about in the framework of uncertainty meaning that there's an uncertainty of the learner have something to do with the way they learn okay so the easy way to manipulate things is down here with regard to sigma squared y right so if I make it so that your observations are associated with a lot of noise then what you should do is to not learn right because the denominator here becomes large and so that means that K should become small so the easy thing to do is to make it so that the learner when they observe stimuli when they observe the consequences they just makes it so that it's very noisy so their sensors are bad so that makes it so that you know I'm not going to learn very much from my errors so just to be concrete about things suppose that we look at K of n as a function of n and you know we know that K of n is going to converge to some value as you iterate and this convergence is going to be dependent on these noises the noise is associated with my uncertainties and the noise is associated with my observation and so if I have a scenario where K squared y sigma squared y is 2 whereas sigma squared x is 1 suppose that my uncertainty associated with this noise here this this noise in the in the state equation is small my observation noise is high what's going to happen is that in this case K is going to be pretty close if I have the opposite scenario or if I have my observation noise is so here I have sigma squared y is equal to 1 whereas sigma squared x is equal to 2 there my K is going to be larger because I'm uncertain about my predictions here the state equation has more noise in it than the observation equation so therefore I'm going to be more receptive to my learning errors I'm going to learn more from my errors so if the state equation has noise that's large that's going to make me uncertain about my predictions if the observation equation has more noise it's going to make me uncertain about my observations either of these two can change the common game any questions okay that's the theory Rudolph Coleman who's still alive would say that's obvious so what the heck is new well what was new is that people in the world of learning thought that oh well that's really cool should we try it on people to see how they learn and see if they modulate their learning based on things like this so they began doing experiments where they try to manipulate things like sigma squared y and sigma squared x and so the first experiment that wasn't that was done similar to this was in 2008 and the way they manipulated sigma squared y the observation noise is by having people make movements but then giving them feedback that was like a blur so suppose you're asked to move and hit a target but I'm not going to show you your hand what I'm going to show you is this like a blur that's supposed to represent your hand and sometimes the blur is going to be tight sometimes it's going to be wide so when it's tight that gives you a small variance about what you're seeing when it's wide you're going to be very uncertain about what you're seeing and what they saw was that indeed in scenarios where the feedback was blur a wide blur individuals didn't really learn much from their error whereas when the feedback was a you know a bright representation of their consequence interaction they learn more from there so seems pretty obvious right that that should happen now is that because the common gain well we don't know maybe if you just give a you know sort of a cruddy feedback to people they say well what I don't know what's going on here why should I learn anything but nevertheless that was the first example of this scenario where by changing the feedback in terms of making it more noisy individuals became less less willing to learn from it so more interesting approach was does that make sense it just make to make the feedback more blurry so it's effectively making it so that your sensory system is not very good like putting on glasses that you know fuzzify the environment around you you just are not going to learn as much about your errors as as if you could see things clearly going back to the weapons of mass destruction thing maybe he thought that their sensors weren't very good they just couldn't find it that's why he wasn't learning from there maybe it wasn't because of his priors maybe it was because his observation was noisy or he just didn't believe the people that reported the results to that could also be one could make these judgments okay all right so let's suppose now we want to change the state state noise here let me tell you about the experiment that was done along those lines so again these are movements that individuals are making and what we have is that we have some state that depends on the previous one plus and then we're going to have a perturbation I'm going to call it r that's going to be equal to r0 plus the state x and r is the perturbation so there's a state x that depends that that that alters my perturbation and so in some cases you know the large amount of noise sigma x is going to be large in some other cases the sigma x is going to have small amount and on any given trial the perturbation is going to change from trial to trial and what this what the subject sees is where their hand went plus this perturbation plus some sensory noise signal so then you know the objective is that you know they're going to predict what the r is r hat they're going to have r hat which depends on what they believe to x to be and what they did in this experiment is that they manipulated the sigma x and they considered two scenarios they considered when sigma y was equal to four where sigma x was equal to one and another condition where sigma y was equal to four and sigma x was equal to I think two and a half or something like that so what they did is that they tried to make the perturbation follow a change in in its value from trial to trial that depended on some noise sigma x and that was highly noisy in one condition it changed a lot whereas it was fairly persistent in another condition and what they found was very small evidence for for large so if this is trial number and this is error on the first trial the two groups have the same error but what happens is that in this scenario when sigma x is one presumably you would have an uncertainty here the prior uncertainty that would tend to have a smaller number than in this condition with what it's what sigma x is two and a half and so in the condition where you're more uncertain you should learn this is this this is this oh sorry no I did it backwards because my uncertainty is higher my prior uncertainty is going to be higher when sigma x is two and a half so therefore I'm going to learn more from error my prior uncertainty is lower here so I'm going to learn less from the error my learning rate is going to be slower if my prior uncertainty P is smaller if mom if I'm more certain about the dynamics of the stimulus I'm going to learn less from my error than if I am less certain so just to be clear there was a small bit of evidence suggesting that if the dynamics of the perturbation are described by a state update equation that has large noise the large noise implies more uncertainty about what's going to happen in my belief P is going to be higher that translates into a larger K which translates into a larger sensitivity to error and this turned out in that paper is the 2008 paper there wasn't significant difference between these two lines but it was in the right direction questions yeah yeah it's more complicated right because so let's let's remember what is the posterior uncertainty so so P of n plus one given n is equal to P of n given n times a squared plus sigma squared x so you see a also is important here you know in our equation right but but so is the sigma squared x and then the sigma squared y comes into here so the evolution of the prior answer that the uncertainty depends on sigma x it's always being divided by this number that says add to it sigma y yeah yeah good question okay yeah yeah yeah yeah oh because the error is unrelated to my uncertainty it depends on my prediction right so it depends on the mean not the variance and so if on average these two groups are the same of the of have you know have the same mean in their prediction which is that if I move if I move like this the cursor is gonna go here but it actually goes here the error has the same mean so it starts out basically error being equal to the perturbation I generate this movement I get this error now the question is how much do I learn from that error and the amount that I learned depends on my how uncertain how much do I believe this error that I see as compared to my own belief about what should happen does it make sense so because error is controlled on the first trial by the environment not by my uncertainty about the environment so you know I throw the ball it doesn't matter how uncertain I was about I make a prediction about tomorrow's weather what actually happens in tomorrow's weather is independent of my right so that I will just have some error that depends on my prediction the mean of my prediction and the actual observation okay all right so the the next thing that was done along these lines was to try to see how people can manipulate these these errors and the uncertainty and and the and the this K which is basically what what what goes to our error sensitivity and I want to just mention to you what what worked and what really didn't work so well so what didn't work very well were these attempts to make people better learners so they could make people so they learn worse by adding noise to their observations but they didn't really make them any better in their learning so it was very hard to make the learner so that they learned more from the error than they would normally under reasonable circumstances a couple of places where they succeeded were scenarios where basically they made it so that they thought they were making the person uncertain and the way they did it where as follows so a couple of things that was successful in 2009 where as follows so one of them was to have people sit in darkness before testing them and the idea was as follows that's maybe my uncertainty matrix associated with the sensory consequences of my motor commands becomes large if I haven't been able to see the consequences of my motor commands so if you've made a prediction but you don't know what happened maybe you become more uncertain about your predictions and so what they did is that they had people sit in scenarios where so say they're measuring K this learning from error and how much do you change your belief about the world as a function of the error that you saw and what they saw was that if you move with feedback so suppose that there are three conditions move with normal feedback and you know you have some some valley this is how much I how sensitive I am to error now if I make it so that I move without feedback so maybe I make you know a hundred movements and you'd never show me anything now all of a sudden you show me the result of one of them what they found was that the person seems to learn a little bit more from that error and if they made it so that you just sat silently in a room for like you know a few minutes before you were tested to make no movements at all don't move for a few minutes and that made it increase as well so it wasn't clear why these things were working it wasn't clear you know why why why doesn't matter that the individual sits there for a while before they allowed to make a movement this process of waiting does us does us somehow make people uncertain but it was interpreted in this framework that I've been telling you that they're learning more from the error it must be because they were made more uncertain about the prediction and that resulted in the particular actions that you saw so the more systematic way to approach this problem was something that puts aside the common filter approach and asks in principle what should a good learner do in a certain circumstances and this has to do with the following if your environment is one where it is changing rapidly from trial to trial as compared to it is changing slowly from trial to trial maybe it matters that that rate so maybe I should be able to do you know to be able perhaps do better if my world is somehow consistent and stable if I make predictions on that world whereas in a world that seems to be flipping and flopping from trial to trial maybe in that kind of scenario it makes no sense for me to try to learn anything from air anyway so in 2004 there was a student in my lab his name is Murray Smith he did a kind of a nifty experiment he imagined a scenario like this that basically you have an environment and you know you make observations as before but what he did is that he manipulated this parameter a and the way he did it is based on the following so if I if I make an estimate now if I'm say x hat of n given n is equal to x hat of n given n minus 1 plus k of n y of n minus y hat of n then x my prior on the next trial x hat of n plus 1 given n is going to be a times x hat of n given n which is equal to a times x hat of n and minus 1 plus a times k of n y of n minus y hat of n so we see that a is a modulator of how much I learned from air so if you look at my guess on the next trial and you compare it to my guess in the previous trial you see that if I'm coming from a world where a is large close to 1 I should learn more than if a is 0 so if a is 0 then x hat of n plus 1 given n is going to be equal to has no relationship to anything in the past that's going to be 0 it's expected value right so I'm not going to learn anything from my error if on the other hand a is equal to 1 then my prior on trial n plus 1 is going to be x hat plus k of n times y minus y hat so now in this case the amount that I learned from error is going to be this whereas the amount that I learned from error if a is equal to 0 not going to be it's going to be nothing so the idea was if the perturbation is such that it's controlled by this parameter a so we're going to compare a perturbation that is generated by a random walk in which a is close to 1 versus when it's close to 0 versus where it's close to minus 1 and the idea is that in these three scenarios the learner should behave differently in case where a is close to 1 we should see a lot of learning from error in the case where a is equal to 0 we should see almost no learning from error and if case for a is equal to minus 1 if this theory is right what should happen is that when they see an error to the right instead of learning from that error by moving to the left they should actually move further to the right because they expect a to be negative so this was the basic idea let me show you what this means in terms of generating perturbations so suppose that you want to generate a perturbation in which a is equal to 0.9 what does that mean that means that the perturbation that you're giving is basically a signal that is is a random walk and it moves slowly because the state on the next trial is highly correlated to the state in the previous trial you can't jump very far on the other hand when a is equal to 0 what you have is basically you know a random walk that looks like this when a is equal to minus 0.9 almost minus 1 now you have even a higher frequency it's flipping back and forth and Maurice what he did is that he had people sit in environments in which the distribution of the perturbation was drawn from these kinds of random walks one where a was equal to almost 1 highly correlated the perturbation on one trial was highly correlated to the previous trial one where it was 0 there was no correlation between the current perturbation and the last perturbation and one where it was negative one if you got perturbed to the right you're very likely to get perturbed to the left on the next trial so what he saw was that in this condition the k how much people learn from error went like this so when a is equal to minus 0.9 a is equal to 0 a is equal to plus 0.9 what he saw was that first of all k never became negative people could not make their learning opposite to what one would want you know to the opposite of the error but what they did is that they learned less little bit more little bit more here so this was learning from error how much they changed their belief on one trial versus from the error that they had learned to the next trial this was the first indication that one could alter their learning rate based on the dynamics of the perturbation yeah so I'm going to give you examples from hidden Markov models where there's a state in the environment and the probability of staying in that environment versus changing to another state so I don't know if there's a it would be a flip basically right it would be a system that that has two states and if it's in the current state is very likely for it to change versus one that's likely to stay okay so what we're going with today's lecture is a way to understand how in principle a system could change its learning rate so that if indeed the world is like that it would become negative so how does this so this is David's work this is work that he's done in the last year and we're going to come up with an algorithm and what's cool about this algorithm is that it's going to be able to help us understand a number of problems that exist in learning theory from the perspective of how we remember to do things and and why is it that with the second time we do a task we're better at it and so forth and I'm going to I'm going to tell you about those things more when we talk about problems like this in the next lecture but today it's just going to be the basic algorithm where does it come from and recently we discovered that this basic algorithm that I'm going to tell you about was something that was described with regard to the systems that were used to learn from air in neural networks in the early 90s and we're going to see that the basic rule is very similar to that but it has this this interesting property that it has it is associated with errors themselves so the basic idea in David's algorithm is that if you look at that way we've been doing things this K here is independent of error so the gain how much I'm going to learn from error is unrelated to the error itself it's a modulator of error so what this means is that in the common filter approach if your gain has been increased it's increased for all errors right so we can make you a better learner in the world of the common gain independent of any error that you might see so we're going to see evidence that that is not true that when you are a better learner you are a better learner for a specific kinds of errors you just aren't going to become a better learner for all errors only certain kinds of errors and the question is why what's so special about those errors okay so the point let me go over this again in the mathematics that we've described so far K is a modulator it says that I'm going to learn more or learn less from air which depends on my uncertainty but it does not depend on the error itself it doesn't say for these errors I'm going to learn more for these errors I'm going to learn less it's going to do it for everything okay so yeah because your current state uncertainty does depend on your previous history of errors yes absolutely no it doesn't depend on previous history of errors it depends on history of trials it depends on the X's that you saw not not errors P doesn't depend on Y right P depends on the last P right okay yeah K depends on Y you know K depends on this noise yeah actually in these linear models it makes no difference what errors happened right so okay let me show you let me show you why this the thinking began to change so David began doing experiments whereas follows so he said suppose we are living in a world in which there can be two kinds of perturbation suppose there's a minus one perturbation and there's a plus one perturbation and there's a probability associated with staying in this state or changing so Z is my probability of staying in a plus one per so that means that if I'm in a perturbation state plus one there's some probability that's going to continue but there's also some probability that's going to change so for example suppose that my Z is point nine what does that mean that means that if I'm going to draw for you now the state of the perturbation let me call R R is equal to plus or minus one that's the perturbation you know if Z is equal to point nine if I'm going to say I'm going to start at minus one I'm likely to stay that I'm going to switch stay switch stay so forth on the other hand if I have a scenario where Z is equal to a small number like point one then what's going to happen is that so I'm going to put now Z is equal to point one that means that if I'm at plus one I'm very likely to change so now it's going to look like this I'm not going to stay very long so forth does that make sense okay now now now what should the learner do learner makes a prediction on a particular trial that prediction is associated with the actions that he does as well as this perturbation so if the world is stable meaning that if Z is close to point nine then what I learn is going to help me for the next trial it's good because the world is the same right but if the world is going to change what I learn is going to actually hurt me so in the case where Z is equal to point one you know I should stop learning in the case where Z is equal to point nine I should increase my learning and the Z is equal to point five it's my neutral state so what David did is that he you know put people in these kinds of experiments and he measured learning from error so of course what you have to do is to now regulate error because these are perturbations these are not errors perturbations are things that are added to actions to produce error errors difference between y and y hat that's what we call error so learning from error look like this if you take trials so say this is 500 trials and you look at how people learn from error what happens is that they had they start out by learning by some amount people that have Z is equal to point nine start learning more from error people that have Z is equal to point one they start learning less from error and people that have Z is equal to point five they live in an environment in which the probability of staying is about the same as a probability of changing they don't change how much they learn from error so learning from error could be modulated by this probability associated with the state of the environment if we predict something and we are wrong then we know that the world will change we predict again and it's correct so the maximum certainty should be when the world might or might not change the future probability right so what they say is that if we know that the world will remain the same yeah then we learn a lot yes because it's going to help me the next time if we know for sure that the world will change then I should but in the opposite direction yes exactly exactly exactly so that's exactly right so what you're saying is that in this world when as Z is equal to point one this really should continue on down here not go to zero but it should become negative yeah yeah yeah yeah right right we're gonna get there we'll get there yeah nobody's ever shown that but that would be that would be reasonable okay the second experiment that David did was that all right this is different people so there are some people that are in this group that can increase their learning from error there's some people in this group which they can decrease their learning from error so can the same person do both and what he did is that he did an experiment where we began with Z is equal to point nine then Z changed to point five and then Z changed to point one and then there was another group that started at Z is equal to point one went to point five and then went to point nine and then he's measured again this is trial number and this is learning from error and what he saw is that this group you know starts out high like this comes down like this this group starts down like this and goes up like that okay so people seem to be changing how much they learn from error depending on the state in which the world is changing if the world is changing based on this Markov model that says I'm likely to stay then it makes it so that they up regulate their air sensitivity and then when they down when when the world is changing such that one time you get one perturbation next time you get the opposite perturbation it makes it so that the learning from air seems to go down so what was interesting about this result is that when he looked at the amount of learning that was taking place as a function of error so learning from error as a function of error so errors zero here positive here negative here big positive errors big negative errors he could test between two important hypotheses is it the case that in this world I am a better learner for all errors or is it some errors that I'm particularly good at and is it in this world that I'm a poor learner for all errors or is it again some errors and what he saw was a function that looked like this so it seemed like over some range the errors had resulted in a modulation of the sensitivity so for these range of errors there was this up regulation or down regulation of this sensitivity to error whereas for these range for these larger errors they didn't seem to be a whole lot of change so it wasn't the case that people were changing their sensitivity for all errors they seem to be changing it for some specific errors and it certainly wasn't clear you know why was it those errors it turns out those errors were the most likely errors yeah well this that's interesting yeah that's interesting right right so what's what what is that about yeah it just turned out that those errors were the most likely errors so if you look at the probability of error it had a peak here this is probability of error so it just happens to be these were the errors that they actually experienced the most and they modulated the error sensitivity for those errors in particular okay so then he came up with an algorithm he said what we want to know is there a principled way by which we should change how much we're willing to learn from error and here's what he said so suppose that we have a very simple learning rule where we say we're going to have a state estimator x and our state estimate x hat of n plus 1 is going to be equal to x hat of n plus you know what we call our learning rate eta like you've seen before and we're going to imagine that this eta depends on error times y minus y hat of n where e of n is equal to y of n minus y hat of n and what we want to know is that is there a principle this is a function now this is a function not this is not multiplied by 8 by e so I want to know is there a way for me to change my sensitivity to error this eta function as a function of this this thing here and how should I do it and and that this thought was as follows so suppose that you are behaving as follows so suppose that on trial n minus 1 I generate a command you it produces some consequence here and here's my target here so this is my error now in trial n the next trial I make a better you like this I get a little bit closer so now what I have is that the sign of e of n minus 1 times e of n is a positive number if that's the case then what I should do is that I generate an action I generate another action and I got a little bit closer so if I were to look at what happened in my errors these two errors have the same sign this world is stable I should up regulate my sensitivity to error on the other hand so I should increase my my eta here if I had a scenario where I generated a command I got x here's what I should have done and now I generate another command and I get a different kind of an error so here the sign switch this wasn't good my world changed on this trial so I should down-regulate my error so the algorithm goes as follows suppose that you represent eta as a function of your error as follows there's some set of weights where it encodes error so suppose that there is a mechanism by which your nervous system encodes errors so this is a basis set that's going to encode error there's a basis set for small that prefers small errors and there's a basis set that prefers largest basically it's encoding of the error space am I getting a small error or am I getting a larger and what is this gi gi of e of n is equal to some exponential you're basically a Gaussian centered on some location e of i so this is preferred error size it just basically says I want to encode my error I want to I want to encoding of this error if I get an error here it's going to activate a basis set and if it's going to get an error that's larger it's going to activate a different basis function now the algorithm for changing eta goes as follows so these weights are going to change as follows w the set of weights that describe this error is going to be plus sine of e of n e of n minus one so this is my error now this is this is the rule that I'm going to use to change my sensitivity to error times g of e of n minus one divided by g of e of n minus one transpose so what this means let me give you an intuition about what this means so suppose that I'm going to plot for you now learning from error as a function of error and suppose that I begin with just some sensitivity that says I'm equally sensitive to large errors and smaller so what this says is that if I have an error that's negative if I have an error that's positive I'm going to learn from it move in the other direction if I have an error that's negative I'm going to learn from it move in this direction so I'm going to learn from error and in this case this learning from error is uniform I'm going to learn the same from every error now suppose I get an error here e of n minus one if the next trial has the same sign of an error this is positive what this means is going to increase the weight which means that I'm going to do this I'm going to learn a little bit more on the next trial you see it increased my learning at this location if I saw an error and I saw that error again if e of n minus one and e of e of n are of the same sign they're in the same direction what this algorithm does is that it increases the sensitivity at this particular location if on the other hand the two errors were in the opposite sign then this is what it's going to do it's going to reduce the sensitivity yeah how much do I change my estimate on the next trial given that I saw this error in the previous trial so this is a local rule all you need to know is what happened in the last error and the current error were they of the same sign if they are then you should increase your error sensitivity at the particular error that you saw if they're an opposite sign then should reduce your sensitivity and this rule reproduces these kinds of behaviors but it makes a nice prediction and the predictions as follows it says that if I change sensitivity to error I will have done so for a particular error size I will not be a better learner everywhere I will be just better for those errors that I saw and here's the test of that prediction so here's the idea so the experiment that David did was as follows so he said suppose that I give you perturbations that look like this so first I give you a perturbation that say it goes to plus 8 and then I measure your response to a minus 4 and so here's trial number so I you move I give you a plus 8 perturbation I notice how much you learn from it and then sometime later I give you a minus 4 perturbation and I notice how much you learn from it and that's your baseline then what I'm going to do is I'm going to make you reduce your sensitivity for plus 8 errors and increase simultaneously your sensitivity to a minus 4 error so the idea is can I make it so that for one kind of an error you're going to learn a lot from it but for a different kind of an error you're going to learn nothing from it can I make you so that for certain errors you become very sensitive you learn very much from it but for other errors you become so that you you will refuse to learn from it so because you know that's the prediction of this model this model says that I represent my error space using a basis set I'm sensitive to specific errors so the experiment goes as follows measure the sensitivity to a plus 8 perturbation and then also measure it to a minus 4 perturbation now I'm going to make you so that you reduce your sensitivity to plus 8 errors how am I going to make you so that you make you reduce your sensitivity to plus 8 errors how am I going to do that so now what I should do is give you that environment right plus 8 minus 8 so they're switching back and forth if that if I make your Z equal to 0.1 in that world you should say oh these errors when I see a plus 8 I'm very likely on the next try I'm going to see a minus 8 why the hell should I learn from that right so what he does is that he does this this makes sense so now a plus 8 minus 8 plus 8 minus 8 it gives me a scenario where error has a plus value in one side one trial it has a negative value in the opposite trial I should reduce my sensitivity because the sign is going to be negative but it's going to be negative for that particular error size plus and minus 8 next what he does is that he now gives you these perturbations look what happens here so now when you get a plus 4 perturbation you're going to have an error and it's going to be sustained so you're going to you know they'll learn these things this is giving you errors that are sustaining it's coming from an environment in which Z is almost one it is one it's staying but those errors are half the size of these errors so for plus and minus 8 I should reduce my sensitivity for plus here's a plus 4 error here's a minus 4 error I should increase my sensitivity simultaneously I should increase my sensitivity to plus or minus 4 errors and reduce my sensitivity to plus or minus 8 errors so how do we do that we test for that again here we again give you these two perturbations and what you should see is that here I'm going to learn a lot from this because I've seen these errors before and they were stable here I should ignore that it's going to go away that's what happens people simultaneously increase their sensitivity for plus or minus 4 errors decrease their sensitivity for plus or minus 8 errors which comes we think from something like this all it needs is the history of the errors and it says when the history of the errors suggests that the environment is stable I'm willing to up regulate my sensitivity for those errors and if the history of errors suggests that the environment is transient I'm going to down regulate my sensitivity for those errors okay what's their homework David okay one trial or many trials many trials okay okay so you're going to get a chance to try the algorithm and see if it works for you if it's if it's if it'll help you guys we can send you the paper so you can see it in in detail because you don't have any text to read this on I don't know it's up to you David if you want to send it to them yeah yeah don't submit it all right guys see you Wednesday


So many of you commented on yesterday's video right there about an inspirational story that you shared your stories about YouTube, and I hope everyone will be motivated by reading each other's comments in today's video. And we're going to do it in dark mode. That is going to make it easier for us to watch, for those of us who are watching YouTube late at night. What is dark mode? It's a feature of heartbeat that you can just turn YouTube into a dark theme. And where do you get heartbeat? Just go to www.heartbeat.tm. It's a Google Chrome extension that we, Freedom, built for you that does a lot more than just turn on dark mode. So check out Heartbeat if you don't know. 70,000 people have already installed it, and let's get going. So the first comment, which is also a story and an inspiration, is from RedofJ. He only has 123 subscribers, and he started with Freedom just a year ago. And he did gaming, sometimes doesn't work. But what I want to say is that he made it one day at a time. He made it 120 plus subs, and soon he will make it to 1,000, 10,000, 100,000, and so on. He's got the spirit. I hope you do too. And he also made another comment that for anyone who's having trouble doing vids in gaming or wrestling, the key is to be yourself. That's a great comment. Don't try to be someone you're not. Just be yourself, and your fan base will build around you. Be honest. Be genuine. That's who I am. I'm honest. This is the real me. I'm not putting on an act. And we have quite a following for the George show. This will happen to you too. Just be yourself.  I hear stuff all the time about freedom, not helping their small channels. But honestly, the tools you guys offer us has been great. The collaboration section, the tips for making a good channel. So if you feel we can improve, tell us how in the comments below. And if you really like some of our tools, also tell us so other people can discover those tools who may not know about them yet. So thank you for that comment. And of course, it continues on. So the key to this comment is that while his current audience is great, he wants to aim for 1,000 to 2,000 subscribers before he reaches college. How many of you are not in college yet? How many of you are doing YouTube while still in high school? Tell me in the comments below. I'm really curious to see what age demographic we have in freedom. So it's not your fault that ad block, that's the ad blocker's fault. If the ad revenue could be better. But we also have a new revenue stream which ad blockers can't block. Say it with me, YouTube Red. What is it? Click the I up there in case you don't know. YouTube Red is a subscription revenue that you will always get even if someone has an ad blocker if they have a YouTube Red subscription. So he ended up by saying I've invited two friends who joined late last year and they haven't looked back. One thing would be really cool is if he and I discuss would be make a freedom CS Go team and a freedom league team. Great idea. Why don't you make that suggestion on MGM, our multi-gaming network. What's MGM? Click that I. That'll take you to the MGM official channel, youtube.com slash MGM. Let's move on to game and madness time to play. Well for me too, it's been two years. I started back in 2014 and yes things back then were so tough. That's true. I know because I've been around since then, even before then. I didn't know anyone. I didn't know how it works and from there I got friends and the hell I even got Deceptra as my friend as we all know Deceptra comments on every single video here and on MGM and everyone helped me till I now have reached 265 subs. The point here is it doesn't matter how many subscribers you have. The way you grow faster is by collaborating, cross promoting, finding friends, work together, give each other shout outs, do videos together, cross promote, playlist for playlist. What is that? Click that I. That will tell you all about how to do a playlist for playlist which is far better than sub for sub. Don't do sub for sub. It doesn't work. Playlist for playlist works. All right, let's continue on. The real D.Lo flow said, doing YouTube is a great thing. I love making people laugh and I enjoy doing what I do but not just for I but for you. Freedom does spark me up a lot. So he's a poet. Maybe he didn't even know it. I struggle a lot with what I want to do or what type of content I want to do. You guys are amazing and hope we all grow together. Great attitude. Two thumbs up. Let's show more. All right. And the person who was featured in yesterday's video is All Games Must Die. And you can see he's actively commenting on these videos so he's actively sharing his inspiration with you. So thank you for doing that. All Games Must Die. To be 100% honest, this video has really spoken to me. I've been trying to do YouTube for about two years now, well up until about two or three months ago when I saw that I was getting fewer and fewer views as well as fluctuating at around 80 subscribers, constantly gaining and losing the same amount. Then I had finally started to realize that I was getting nowhere and I began to get depressed. And every time I sat down to do a video with my friends I actually started to blame myself for the channel not growing. So this is a great example of someone who felt like giving up and when he found a role model, something to inspire him, what did he do? He didn't give up. Hashtag never give up. Is giving up is the worst thing you can do. It's the guaranteed way to fail. Do not give up. Keep looking for that inspiration, those people to cross-promote with, to work with. You'll find them in the Freedom Family because we do help each other grow together. We have a collaboration section. We have a community forum. If you haven't already, introduce yourself at www.community.tm. We have over 110,000 members on these forums, guys. Look, 100, I'm going to hide myself, 113,172 members. This is where you go to find people to collaborate with. This is right here. Introduce yourself. Where's the Introduce Yourself section? Uh-oh, we've moved it. Somewhere, introductions. This is where you go to introduce yourself. Look, people are introducing themselves all day long. Let's look at the latest introduction. Hello from the other side. So, hello from the other side said, he's 16 years old. He has hobbies for graphic design. His favorite food is pizza. Here's his channel, 34 subscribers. And he's already got tons of comments. Welcome to the Freedom Forums. Thank you for writing up such an appropriate introduction. Hi, Shakar. Welcome to the Freedom Family. You will get the same warm welcome. If you haven't already, create an account, log in. It's all free. And once you're in, you can post on these community forums, help yourself, find friends, get collaborators, get reviews for your content. And you will grow faster. I promise. Let's move on. Jesse Navy123 said, hello, my name is Jesse. I'm 20 years old. I work part-time. I run a YouTube channel. The reason I decided to make a YouTube channel is because when I was 15, I was hospitalized for four months due to, I don't know how to pronounce that. I'll take a stab, ghee and bear. Two months in, my therapist's nurse started asking if I could motivate other patients. And so I was always working hard and pushing. So he never gave up. That's a great story. So when he was discharged, he thought he could help patients at the hospital, maybe even help those on the internet, even if it is just eight to 10 minutes, hopefully all of us here at Freedom can get along. Thank you for having time to read. Well, thank you for sharing that wonderful inspirational story, Jesse Navy123. Hi, George said, no mania. I'm a Freedom partner and I run a growing entertainment channel that features pro-wrestling and also have a working relationship with a pro-wrestling website. That's great. You're cross-promoting off YouTube. Everyone who can try to do that, bring audiences from other places, try to use your Facebook, your friend's website, the Freedom forums at www.community.tm, anywhere that you can find a home to meet new people, promote your content. Don't spam it, but promote it in places you're encouraged to promote it. Then you will grow faster. The extreme undead said, George, did you read my comment on your previous Georgia video? I hope you'll increase my revenue share since I'm partnered with Freedom for a year and a half. The extreme undead, if you think you've earned an increase in revenue share, simply open a ticket on our ticketing system. How do you do that?  When you click Open a Ticket, it'll take you to our new fresh desk.com. The reason it's Freedom2.support.tm is because it's our second version, 2.0, of our support system. And you can log in and create a ticket and say, hi, Freedom family. I've been with you exactly what you wrote here. I've been with you for a year and a half, and I feel I've earned a raise. Can you give me 70% revenue share or whatever you feel you've earned? And support will get back to you. So let's see how many comments we have here. Pace ourselves, shall we? There's a lot of comments, and of course, there's even more. Now, you'll notice some of these comments I have replied to already and gotten replies to my reply. That's great. Now, guys, I do read every single comment. I make it a point in my day to set aside many hours to keep checking back on videos and looking at the comments. I can't reply to everything, but you can be sure that whatever you write, I personally do read. I don't have an assistant that reads these for me and tells me the highlights. No, I read them myself, because it's important. I feel it's important to be in touch with you guys, to know exactly what you're thinking, and I do that by reading your comments. So if you have thoughts to share with George, write them down in any episode of The George Show in the comments. We have a lot of comments here, guys, almost as many as we had in the previous video. I mean, each episode of The George Show gets something on the order of 300, 200, to 300 comments. So there's quite a few. OK, there we go. That's the end. So where do we leave off? We left off. Uh-oh. There was the wobbly captain. I think we was a little bit before that. Ah, here we go. LongboardstuffZeland said, hey, George, we're a small YouTube channel from Holland. Welcome. We're working to improve our video, but we don't know exactly what to improve. We've got good camera gear, and I can edit good. Well, you can edit well, a little bit of English grammar. That's what our subs say in the comments. For two years, we're making longboard videos every week, one video, and sometimes a special. We put a lot of time in the video, because if it's raining, we can't make a video. We try to get every week a video. OK, they try. So can you help us improve or host one playlist on the channel? I love to see it, because we're a freedom family. So longboard stuff, we actually had a video where we announced winners, and the winners got a playlist for playlist on YouTube.com slash Freedom, Freedom Central. Now, we will do that contest again, and here are still the winners. I'm just going to Freedom Central. You can see the featured on Freedom. This was the winner, and these are the runner-ups. The people who didn't win, but we're still featuring them. And these were exceptional videos in the non-gaming category. Now, you gave us a lot of suggestions. You gave me a lot of suggestions. Not you longboard stuff, but you Freedom Family gave me a lot of suggestions on how we can do another video like this. One suggestion was, don't make it a sausage party. What that means is the winners of the previous contest were all men. Sausage party, man, you get it? So one suggestion was, make the next contest only women. That's a good idea, to be fair. But longboard stuff, Zila, and just look out for future contests for the featured on Freedom that if you win, you will get a playlist on our central channel. And that goes for every channel, everybody out there in the Freedom Family. So random upload said, can you make an updated version on how to get partnered? Because I've been having troubles on how to know if I've been partnered. Please reply or make a video. Thank you so much and have a nice day. Well, there's two steps to partnering. One is you have to go to www.freedom.tm and click Sign Up, which I imagine you've done. And the second is you need to accept an invitation on YouTube. You have to go to youtube.com. slash dashboard, which is your YouTube dashboard and click Learn More. There's a video explaining that right there in the eye. If you click that, it'll tell you how to accept partnership on YouTube. And once you've done both those steps, you're partnered. So I may make another video updating everyone on that, but it isn't that complicated. So two steps, sign up on freedom.tm and then click the Learn More link and accept the partnership on YouTube in your YouTube dashboard. You're right, George. You always have a smile when you speak. Whatever happens. Good work with the freedom. Good work with freedom and I'm a big fan and you're one of the people who have inspired me and cheer me up. Well, thank you, ZA7 for sharing that. I get motivated when I hear that people get happier, inspired based on what I do. That makes what I do meaningful and I'll keep doing it as long as I keep having that effect. So thank you for sharing. And he also asked, oh, someone else asked can someone check if my intro is good and if my channel is good, accept the vids. All right, let's check out your intro because you asked so nicely. Nam's Kazi. Here's your intro. That's very energetic, very upbeat, very exciting. The only suggestion I would make is add your voice. It can be at the end, but tell people about your channel. Give them a reason to subscribe and you'll find your channel will grow a lot faster if you tell people what kind of content they can expect if they subscribe. A great intro. Oh, we lost our spot in the comments. All right, let's wait till we come back. Oh, by the way, did you notice pro tip? This wasn't there before, the right side. How did I get rid of it? So if you're using Chrome, all you do is you right click, inspect element, and then you find the container, which is right there, and do visibility hidden. And it's gone. It makes videos cleaner if you happen to be doing the style of video that I'm doing with me here and YouTube there. I still have to learn how to point because it's all backwards in the camera. I'm actually pointing away from the screen. It takes a little bit of training. Mental training.  So we were on ZA7, yes. Moving on, blur music. Oh, wait, I changed the sort order. Sorry, guys. Go back to newest first and we get to do show more again. Yay. Okay, where were we? I think we were now on wobbly captain. No, I think we missed someone. Who did we miss? There was ZA7. Now, here we go. CGP, can you help me to the goal of 400 subs? Okay, well, that's not an inspirational comment. We're looking for inspirational comments. Sharing stories. Okay, wobbly captain said, I too have been doing YouTube for about one year now and the freedom videos with their advice over the year have helped me a lot. I sometimes can lose motivation when you get the haters and trolls, but I guess that's all part of YouTube. And as I replied to wobbly captain, never feed the trolls if they provoke you. Just ignore them. Don't reply to their comments. I find if you starve the troll with no attention, he goes away. Does this help? Yes, very true. I think I took that advice on board in maybe a past video and you did. And it's very good advice for anyone starting a YouTube channel or a present YouTuber. I think you should maybe do another video on the subject. Okay, it's a good suggestion, wobbly captain. Thank you. Interactive gardening said, Hey George, I've been partnered with Freedom for almost a year now. That's great. And I'm really, really happy that I joined. I've grown my channel from 13 subscribers and 100 or so views to a channel with almost 125 subscribers and close to 10,000 views. And as I replied, wow, that is 10 times growth. Well done, interactive gardening. And thank you for sharing your journey. I hope we can continue to walk it together. And you never know when a spotlight may come from the freedom family. So let's spotlight your channel since you asked so nicely. So interactive gardening, here we go, has 123 subscribers. They clearly do videos about gardening. So let's take a look at the latest video, dragon fruit from tissue culture. Here's the story of how the small plant has grown from a couple cells in a jar. Okay, waiting for the next punchline. Could be a little sooner. Oh, that was the intro. Ah, okay, that was a little misleading. I thought we were gonna get to the next next piece of that comment. Okay, so you get the idea, guys. This is a channel talking about talking about plants and how they're growing. And if you're interested in gardening and seeing these kinds of helpful tip, not tip, but educational videos, then please visit interactive gardening and subscribe to their channel. And in terms of feedback, I like your thumbnails, they're very clear. If I am looking for pomegranates, I can see that right away from the text. Oh, and guys, this is another feature of Heartbeat. You'll notice that it shows all the thumbnails in a series, so you can get a sense for the video just by hovering over each thumbnail to help you decide whether you wanna watch it or not. Okay, and I think it would help if you added your own commentary to these videos. Commentary will help you grow your audience because people will subscribe for your personality, not just for the content. Otherwise, it's a good channel. You also upload regularly. I see at least one or two uploads a week, which is good. It would be better if you upload even more regularly. If you can do three or four regular uploads a week, that would be even better. I hope this helps. Okay, so let's move on to Jonathan MX. Oh, wow, sorry, I can't read that, Jonathan MX. But hopefully in the future, Google, YouTube will have a translate this button here. I don't see one, so I don't know what he's written. So Fawz Rashand said, I have two goals in my life. Make my viewers happy and make a living out of YouTube. And be forever with freedom. I suppose that's the third goal. Those are great goals, I said, and I hope we can help make all of them come true, especially the forever with freedom part. I like that phrase, forever with freedom. We have been using freedom be free, but forever with freedom is a bit catchier, don't you think? I like it. So hide the body gaming, said hi, George, your freedom family. I'm having my doubts if I should keep going or not. I started the channel with a couple of other guys in the hopes of growing a good channel, but they left as things were not moving as fast enough for them, oh oh, they gave up.  So I replied to hide the body gaming, saying, of course you should never give up if this is your passion. I checked out your channel and I have some suggestions. Start each video with the most exciting 10 seconds, not your intro. People get tired of seeing the same intro and automatically skip ahead to a random part of the video, which is probably not exciting. If you put the most exciting 10 seconds at the beginning, you can hook your viewer right away. And do not just do play by play commentary. Talk about the game. I misspelled that, let me edit my comment. You know you can edit comments, guys. Just click those little three lines and click edit. Where is it? Do not just talk about the game. Save, there we go. But talk about the game. Why do you like it? Why the viewer should play it? Be educational as well as entertaining to help your audience grow even faster. Hope these tips help. Oh and hide the body already replied. Great advice George and thanks for taking the time to check out my channel. That's just what I needed. This means a lot to me. I will do as you suggest and keep going. Thank you very much. Thank you so much. Never give up. Oop, what happened? I clicked never give up. It took me to a search for never give up. That's not what I wanted to do. So, all right guys. Let me just stop the video here. I hope these comments help inspire you. I encourage you to read all of the comments in that video. Reply to the ones that you feel deserve a reply and let's help each other grow together by replying to everybody's comments so that we all feel like a family because that is the spirit of freedom. We help each other grow together so we can all be successful in the future as a family. And who am I? I am George, CEO and founder of Freedom and I have the right shirt on today. Yesterday I didn't. And you've been watching and we will grow together as a family because this is the freedom family. You are part of it. We are all part of it. And we're all growing together. So grow with us and partner with freedom. That play now button right there on the video bar is all you need to click to get started.


QuickBooks Online. Receive payment forms. Get ready to start moving on up with QuickBooks Online. We're going to be using the free QuickBooks Online test drive searching in our search engine for QuickBooks Online test drive selecting the item that has the Intuit.com in the URL. Support accounting instruction by clicking the link below giving you a free month membership to all of the content on our website broken out by category further broken out by course. Each course then organized in a logical reasonable fashion making it much more easy to find what you need than can be done on a YouTube page. We also include added resources such as Excel practice problems PDF files and more like QuickBooks backup files when applicable so once again click the link below for a free month membership to our website and all the content on it. Intuit being the owner of QuickBooks will be using the United States version and verifying that we're not a robot. Go ahead call me a robot again see what happens QuickBooks I'm sick anyways I'm gonna hold down control scroll up on the scroll wheel we're currently at 125% on the zoom and also note that if you hit the cog drop down we're in the account view as opposed to the business view we'll try to toggle back and forth between the two views we're gonna be opening up a few tabs duplicating those tabs that is in order to put reports in we're gonna right click on the tab up top to do so and duplicate it tab to the right right click on it and duplicate it and then we'll go back to the middle tab and we're gonna go to the reports on the left hand side opening up the balance sheet report and then we're gonna go back up to the top reports on the left hand side this time the income statement profit loss P&L scrolling up change in the range I'm just gonna do a manual change highlighting it from 010122 that's January 1st 2022 tab to 1231 22 December 31st 22 tab run it to refresh it close the hamburger tab to the left close the hamburger scroll up and then we're gonna choose the 010122 tab 1231 22 tab run it there's our setup process we do every time back to the first tab where we're actually doing the action and hitting the plus button we've been focusing in on the customer cycle noting that the customer cycle we expect at the end of the cycle to be getting money generally to be increasing our checking account the way that will happen the flow that takes place will differ depending on the type of industry we are in the easiest kind of business would be like gig work you're getting paid by like YouTube or something and you're just going to get the money and then record it possibly with a bank feed like it as a deposit the second easiest system would be a cash-based system but maybe one where you have a cash register where you'd be recording the sales receipts at the point in time you make the sales and then making the deposit and then we've been focusing in now on the full accrual system which means that you would be creating an invoice and then you're gonna be receiving payment on that invoice and then you're going to be making the deposit into the bank or that's the typical flow that you would be expecting to happen now you would only be invoicing people if you had an accrual system that's typically driven by the type of industry you're in if you have to bill people such as such as a bookkeeper an accounting firm a law firm landscaping and so on those are the type of businesses that are going to have to enter the invoice and then track the invoice and then try to collect on them receiving the payment and then make the deposit last time we talked about the invoice this time we're going to talk about the receive payment but we're going to create a custom invoice to start out so that we can follow that invoice along so I read we closed up the file and opened it back up again so the work that we did last time is not included in this file we're just going to redo it from the same point every time so everybody has the same information I'm going to create another invoice I'm going to call it a a a tab that'll put the customer at the top of the customer field going to save it with just the name we would need an email if we were going to send it by email the terms will be 30 days meaning it's going to be due in 30 days the date of the invoice will be 1222 it's going to be due 30 days later 121 in this case and then I'm just going to create and make up a service item I'm not going to be dealing with inventory because I'm really focused just on the collection side of things at this time which isn't really focused on the inventory side of things so let's just add an item and let's say that it's going to be a service item I'm just going to call it service one I'm going to copy that and then tab tab tab tab I'm going to put that in the description right there and then we'll say that it's good old $110 let's say and it's going to go to a service income I'm going to say it's not taxable because it's a service item and that'll make it a little bit easier so we'll say non-taxable and save it and we'll just say that we got let's say three of those so that brings it up to 330 there's no tax involved what's this going to do when we record it it's going to increase because it's an invoice accounts receivable it's going to increase the sales driven by the item which went to service revenue and the sub ledger which is what we're going to track will increase by customer the AAA which is a sub ledger of accounts receivable giving more detail on that line item of accounts receivable let's save it and close it save and close we're going to go to the tab to the right scrolling up run the report again hold control down and scroll up a bit I'm zooming in in other words and I'm going to go into that accounts receivable so once in there I'm going to zoom back down a bit so I could see that better and then scroll down so there is the 330 clicking on it takes us to the actual document and so there we have it and we've got the 330 increasing closing that back out scrolling up to the top back to the balance sheet the other side is on the income statement tab to the right holding control down I'm scrolling in again and then zooming and we got the service item so there's the service item the services and there's the income on this side notice the income was recorded even though we didn't get the money that's what happened on an accrual system that's how the accrual system works because we earned the revenue the point of earning revenue is when we do the work and the invoice is the closest form to when we did the work it's still not perfect on an accrual system because we might have done the work and then didn't invoice them till like the next month but and we'll talk more about that in the adjusting entries area but that just note we're recording the revenue that's how it works with an invoice typically we've recorded even though we didn't get the money yet so then if I go back to the first tab note now we've got the AR so now we've got a track that the next thing I expect to happen is to get paid now as we're tracking the AR that the next step is going to be the plus button and I'm going to hold control and scroll down a bit the receive payment right there but we're gonna have to track it in order to receive the payment so if I go to the tab to the right I'm gonna right click on this tab and duplicate it just to look at the subsidiary report for accounts receivable which we can find in the reports on the left hand side closing the hamburger scrolling down to who owes you money let's go to the customer balance detail report and we'll keep it as of that date that's fine so there's our AA they owe us money the point here is that we're breaking the same information out not by date of transaction but rather by customer and if we add up all the customers that owe us money there's the five thousand six eleven fifty two that ties out to what's on the balance sheet so now normally in practice when we're working in the accounting department we're gonna be tracking this internally go into the tab to the left by searching and what I would call the customer center which under the accounting view is in the sales area business view it would be under the get paid and paid area and we can sort them multiple different ways so you might like going into the sales item here and this has all your sales transactions this is under the bookkeeping view under the business view bookkeeping tab I think and then you can track this has basically all of your sales kind of forms in it all of these forms not just the invoices but you can clearly sort for the open invoices and the overdue invoices by going to the open invoices here and there's our AAA you can use your sorting options this way as well and then your sub-sorting down here open overdue and so on down below and then you can find the ones that are open and take any action that you need at that time the action hopefully will be receiving a payment but you can also hit the drop-down and you might have to duplicate it if you wanted to make another invoice that's similar if you have these long detailed invoices then maybe it's easy to copy one and then make the new one you can send it so if you need to send it out you can send a reminder on it and so on as well you can also possibly select all the ones periodically that you need to get information from and try to possibly send them a reminder as well in a group kind of format so and then we can also go to the invoices area where we have basically similar information in here but focus directly on the invoices so if I scroll down to the bottom of this one well let's just sort it by customer here I just sort it by customer there's our AAA item here so it gives us some more detail this is another area that you might like to go to to kind of sort your open invoices or you might prefer going to the customer field which gives you your customer information and then you can go into the customer but even here you could sort basically your open invoices which is quite nice and then you can you know receive payment on those invoices and you can sort all these items and batch batch them and create statements as well which could could be a useful tool if you're going into there periodically to try to collect on them so then you can go into the actual invoice so there's the actual invoice which once again I can select that actual invoice and receive payment so to record the receive payment then I could go here and then hit the receive payment and there's our receive payment form or I can close this out and I can go into the receive payment form multiple areas but oftentimes the main one would be the drop down up top we did the invoice the next one would be the receive payment and when I type in AAA as the customer so we're imagining we got paid by AAA and now we want to tie it to link it to the invoice then we see the invoice down below here so if I had multiple invoices out for AAA then I can select the applicable invoice but the point is I'm going to tie it out to an invoice there it is on 222 the payment method this is more of an internal kind of document if it was something like an electronic transfer you can hit the plus button and add something different if you wanted to a reference number if applicable and then whether it's going to be deposited into the checking account directly or into something like a clearing account like the undeposited funds now notice what this is going to be doing this it's a receive payment so the receive payment form is always going to be reducing the accounts receivable and then the other side is going to go to some kind of cash account it could either go directly into the checking account or we might want to put it into a clearing account so that we can then put it into the checking account in the same grouping that we expected to appear on the bank statement also it's going to be closing out typically tying out to an invoice so it's nice with the forms that you have these nice linkages so we're not just thinking debits and credits here we're not just thinking you know the accounts receivable is going to go down we want to think about that but we also want to think from a bookkeeping standpoint when I go into the invoice the invoice should be linked to the payment I can see that it has been paid I can talk to someone on the phone and be able to say yeah we we had an invoice and here's the payment that's linked to that invoice so these are the connections happening between the forms often not fully appreciated by people that learn accounting just in terms of debits and credits but don't work as like a bookkeeper doing the actual accounting internal accounting processes okay so then there's this issue of putting the money into undeposited funds or the checking account now if you got paid by an electronic transfer or you got paid by by a check then you might be able to put this directly into the checking account here because that's going to be the same format meaning you expect the bank to be hit with the 330 the same amount which will allow you to tie out the checking account to the to this this amount here for the receive payment however it's still a little messy to do that because now when you look at the checking account you're gonna have the increases to the checking account which are usually just deposits and sometimes transfers but now you're gonna have these receive payment forms that will be increasing the checking account so when you sort your data you're gonna have to be aware of that so I still kind of like going to the undeposited fund and then using a deposit form to put it into the checking account but it could be easy to do that the other reason you might want to use the undeposited funds which is this one which is a clearing account is because you might get multiple payments of like cash or you might be going through a credit card for example and a credit card or cash like if you had cash then you might get multiple payments from different customers that you're then going to go to the bank and deposit in one lump some so if that's the case I don't want to be putting the 330 directly into the checking account on my side if when I deposit it into the bank it's gonna be grouped with other deposits and be like $500 deposit total but what I want to do instead is going go into undeposited funds and then group them together deposit them into the checking account in the same format they'll appear on the bank statement or through the bank feeds so that we could reconcile so I typically still use the undeposited funds by default so we will typically we will do that we're gonna say save it and close it let's check it out and if I go to the balance sheet second tab let's go ahead and run that report again and so now we've got this undeposited funds now the other thing that it's a little bit annoying on the undeposited funds is that you would think they would be up here in the cash account so there's some differences in reporting from like a bookkeeping standpoint to external reporting for like a company reporting to their shareholders or something like that on and so you would think up here you wouldn't call this this bank accounts normally for external reporting you would call it you would call it cash and then all of your cash type of accounts cash and cash equivalents would be up here but from a bookkeeping standpoint we have to keep the checking accounts different than other accounts because the checking accounts have those special characteristics of being able to connect to the bank so in other words you would think that the undeposited funds would be up here in the cash area instead of down here in other current assets but from a functionality standpoint the undeposited funds is not a checking account so it's it actually functions more like an other current asset so it's down here but it's just a clearing account it should just go up and then back down to zero after you make the deposit so you got to you kind of got to be okay with that you know if you're gonna you just if you're tying out to cash unlike your like on your statement of cash flows you got to include the undeposited funds as part of cash even though it's down here okay so I'm gonna go into the undeposited funds hold down control and so there's the payment so if I go into that that'll drill down onto the actual form so that looks good closing that out scrolling up back to our account undeposited and the other side went to the accounts receivable so if I go into the AR and I hold control and scroll down we're gonna say there's the received payment so notice what happens in here we're gonna have the invoices increasing and the payments decreasing that's what happens with accounts receivable that's the only types of forms that you expect to basically see in here so let's go back on over so that is that and if I go back to the first tab and open up my my reports I can go into the sales area and I can go to my sales transactions and I can sort my invoices my my invoices let's go for the open invoices it's no longer an open invoice right so you got the open invoices are no longer there and recently paid so you've got the recently paid they're the recently paid items I can also find that so it's under this item here and if I go into that it gives me a summary so it says we've been paid but not yet deposited if I want to edit the item I can go into the item here and there's the actual item notice it says paid up top and it's got this nice link to the actual payment again those links are quite nice from a bookkeeping perspective because that's usually what you're concerned with whether or not you've got paid on it or not but we also want to keep in mind from the bookkeeping perspective that these all this information here is really like a sub ledger so if I go the tab to the right and I look at it from the sub ledger report breaking out the receivables by who owes us the money we could see a AA is gone because we got paid by them the total down here for this report five two eight one fifty two still ties out to the balance sheet over here five two eight one fifty two from an internal perspective we're usually dealing directly with the clients and just trying to get paid by them so we're tracking this information internally I'm gonna hit the plus or the button up top and let's go now to the sales area and then let's go into the invoices so we can track in a similar fashion here the invoices so here's that amount and it has been paid and we've got similar kind of filtering options up top so we're currently in up top a not deposited area so if you could so that's another way you could sort through those items and then of course we can go to the customers and we can sort by our customers and I'm gonna go up top and say clear the filters and there's a AA up top and you've got your open invoices it's no longer open that's why it wasn't there before and then paid the last 30 days so it's in that category or you can clear all the filters and then if I go into AA and I and they had a question that I can say okay yeah there's your invoice and then the payment there's the payment that has been linked to the invoice these are kind of the connected items okay so the next step in the process would then be to make the deposit because now I've got this money in undeposited funds that should go up and go back down so you can imagine I've got cash on hand from multiple payments or I'm going through some kind of payment processor like a credit card and I'm trying to group my money in undeposited funds before I actually deposit it into the checking account so that I can deposit it into the checking account in my system in the same grouping that will happen on the bank statement because that helps me to do the bank reconciliation which is a huge internal control which we really want to do if you don't do that and you get like amounts coming coming through a credit card feed or you're making deposits with cash that are different than what's gonna show up on the bank statement meaning you're recording into the checking account for example for each sale that you make each $5 sale and then the credit card is going to group like $25 sales together or whatever then when you bring in the fees for the bank fees you're not going to be able to match them out very easily you can have to do all this ticking and tying kind of trying to tie things out at that point you don't want to do that you want to come up with a system that you can make the deposit on your side that matches what goes on to the bank side and that's what we'll do next time so then the next thing if we hit the plus button up top is going to be making the actual bank deposit over here and as we make the bank deposit this first section shows those things that are in basically the undeposited funds so you can see here this ties out to the undeposited funds so now you can pick the ones that you deposited together to try to come up to the same grouping of the lump sum deposit you put into the system so we'll talk more about that in a future presentation let's just go back here to the cog drop down and let's look at the business view just to locate these same areas we've been talking about under the business view so if we were going to the business view the home is the get things done page we opened up the reports in the business overview and then the reports and then we've been working mainly in the the get paid and pay center which I would call the sales center or the revenue center but they've got the revenue and vendor centers together we've been looking at the customers that sorts our information by customer we looked at the invoices here which is another way we can sort our items and then we had in an external area another area under the bookkeeping tab that's where they have this transactions up top and you would want to go to the sales transactions when we're talking about those sales items and this is the one that has all of the all of the transactions in essence that you can kind of filter through here which oftentimes you would be filtering for invoices or possibly if you're using estimates for customers those would be the common two areas you'd be looking at through in this area


On the one-year anniversary of the air assault mission that killed 9-11 mastermind Osama Bin Laden, flight crews from board operating base Fenty, where the raid team launched from, reflected on the historic feat of their peers. I was kind of amazed by the pilot's skill.  Just knowing about the type of environment this is out here, the challenges of flying that distance, finding a place in the dark, and then coming back essentially with no injuries for the U.S. forces. It's an amazing feat. Chinook pilot William Haynes and his crew routinely fly night missions. Basically one of the main things you want to do is maintain secrecy and opsec. Lots of stuff is leaking out these days on social media and stuff like that. So basically keep yourself safe by keeping that information tight. While operating under the cover of darkness keeps Chinook crews safer, they still have to contend with flying over the same mountainous terrain as daytime pilots. Really for us, flying at night is a trade-off. Less likely to be shot at by the enemy due to them not being able to see us, but the challenge becomes more environmental. And the mountains that we fly into, the Hindu Kush mountains, can be anywhere from 7,000 up to as much as 20 plus thousand feet. Despite these obstacles, Haynes says his crew is able to accomplish their mission every night. From Nangahar, I'm Army Sergeant Tanangachi Mislini.


So in today's tutorial we're going to talk about the humble histogram. So in my first cell here in my Jupyter notebook I'm just importing my cascading style sheet as per usual just to get away from this bland looking black to just something a bit more interesting. There we go. If I run the cell we see these nice little colors and different fonts for the markdown that is used. So let's set up the library. I'm going to import from plotly.offline my iplot so that I can plot directly in this Jupyter notebook and to the init notebook mode just to initialize the notebook. We did that with the previous tutorial on the bar chart. We're going to do exactly the same here and again we're going to make use of one of the high level charts so we're going to do plotly.graph objects as go will do that import as well. Now for this case I just want to generate some random values so I'm going to import the random module the python random module so that's for easy import random and I also want to import the numerical python library numpies and I'm going to use this namespace abbreviation so I'm going to say import numpy as np. Now I'm going to just seed this cdorandom number generator so that we get the same results every time we generate these random values and I'm just going to seed it with a value 1234 and there we go so let's create a few random values my first variable here is called age and I'm going to just use a uniform distribution I'm so I'm going to say an np for numpy.random so I'm doing the random module in this numpy library and from there I want the uniform distribution my lowest value must be 21 my highest value was 75 and the last argument size meaning I want 100 values from that distribution the next one I'm just going to use the computer variable salary again that's numpy.random and this time from a normal distribution I want the mean which has the argument loc to be 3000 I want the standard deviation which is the scale argument here to be a thousand and again the size the number of samples I want drawn being 100 now I'm just going to use a choice between just purely for the sake of simplicity use a gender binary gender here just for purely for the sake of simplicity we use and I'm going to create the the computer variable binary gender and I'm going to use from the random module I'm going to use random.choices and what you can do with the this choices function is just to pass a list of all these various text the string elements that you want to choose from so I've got female then male and I'm going to say draw at random 100 of those and it is it is drawing that at random with replacement so the first one might be female it puts female back in the box draws another one blindly out of the box that might be female again throw it back so a hundred of those choices now I want to place these inside of a pandas data frame it's a beautiful thing to use I urge you to have a look at pandas I'm going to import pandas and use the abbreviation PD and I'm doing that because I want to create a data frame I'm going to call my data frame DF and I'm going to call the data frame function here PD dot data frame and I'm going to create this data frame out of using a dictionary so I'm going to have this age column and underneath that age column think of a spreadsheet so the header in the first row I have my header values my variables and I'm going to call this first one age and down that column all the rows are going to be populated by these hundred age values the salary is going to be the next column header in my spreadsheet basically which was what a data frame can be seen as in a simplistic way pass all the 100 salary values and then gender this binary gender values of mine so let's run that and I've created a data frame and I'm going to split my data frame in two one for female and one for male and the one that we're going to do how the way we're going to do that create these two computer variables female and male the first one says take this data frame and then we're going to use this square bracket notation because it wants to run down row by row so I'm just indexing this DF dot gender column so it's going to look down the gender column and only select those so this is a Boolean double equal sign only the females and then male will only be contained contain the male so I have two data frames now female and male so let's create our first bare bones histogram now that we have some data again per usual just by convention I'm going to use this trace computer variable and it's go go because this was a graph object one of the high level graph objects and it's a histogram I'm going to pass at the x value because let's just stop there for a moment what you know just to discuss what a histogram is where's a bar chart looked at categorical variables on the x axis the histogram is going to look at numerical variables so age is definitely a numerical variable a ratio type numerical variable because there's a true zero and we have we're going to split that up into little bins and if we just pass the age here plotly we'll decide how large those bins are so what are bins well as soon as I show you the histogram I can show you what bins are again the computer variable data and pass the list of all these histogram elements I want to put on my figure and then instead of using go dot figure I'm just going to use this dictionary notation so I plot and then data please and we see here look at the bottom this is new these are numerical variables it's not categorical and what it's done is it seems to be having plot from 20 to 25 25 to 30 30 to 35 35 to 40 and that's what I mean by these little bins so all it's going to do it takes those hundred values and it and it decides how many are between 20 and 25 and it'll count them and it note that there was eight and between 25 and 30 there was 30 between 30 and 35 there was five so between 25 and 30 there was eight etc and so it goes on so that is why a histogram is not a bar chart and what you can see here also there is really no spaces between these just to indicate that we're talking about a continuous a continuity here where's a bar chart by definition has these gaps and just to create this visual impression that we are dealing with categorical variables that this is not a continuum and here we do have a continuous random variable at the bottom called age now let's just change that to a frequency distribution otherwise known as a normalized histogram because what you can see on the top one here is we count we count how many were between 20 and 25 but if we normalize that it gives us a frequency distribution and the way that we do that is just by in this histogram element that we create at the top we pass a new argument his norm and we pass to it this equals probability I'm going to introduce a layout here by format by dictionary format so if title and its frequency distribution of the age gen age variable and my x axis I'm going to bring in a title also dictionary with a key value pair the value pair being a dictionary itself consisting of a key and a value and why I plot via a dictionary as well and now we can see frequency distribution of age I have age in five year increments here at the bottom but most notably you'll know now you'll see now this this is normalized so the area under this curve which is the area of this rectangle and this rectangle and this rectangle and this rectangle is going to sum up to be one it's mutually these these bins are mutually exclusive but collectively exhaustive so they are all here and the area under this stepwise curve is going to be one so it's a frequency distribution so I'll have to if I want to get how many there are this increment is five times 0.08 to get to to get to the value that we have there that we have well let's have a look so that was eight so remember these are now units of one so 0.08 times times a hundred is going to say it's going to give you that eight so let's create two in an overlay fashion so to do that I'm going to create two traces by convention calling them trace zero and trace one so go dot histogram and I have x equals female dot age and this time I'm going to give it a name so that we can have this little sidebar that indicates what is what and the second one that I plotting it's going to layer them from the back to the front so the back one is going to be female the one in front is going to be male so I just want to lower the opacity of the front one so we can still see the bottom the bottom histogram the bottom trace through that so I'm going to set opacity equals 0.8 everything else being the same I'm bringing in my little layout there and now we can see I've got two plots here it's going to give me this little legend on the side and I've created a bit of opacity here in the orange which is the male just so that this female at the back shines through and but if we hover over them beautiful beautiful it's beautiful what plotly does and you can see that it's still going to give you the values let's stack them so I don't have to do the opacity there and it is just going to stack them but it's still going to give me these values to say in male there was four and in the female there was 12 and look at one thing a difference that it made it is now making these blocks of unit length of 10 years so I've put in that as 10 years that didn't that didn't influence that this was done I drew this first and saw by you know automatically it chose 10 and I put the 10 in there after the fact so let's do that let's control the bin size and the way that we do that is by introducing inside of our traces here we introduce the X bins argument and I'm going to pass a dictionary for that in this format not the curly braces format so start is 20 in that 80 so just the left hand side of the x-axis the right hand side of the x-axis and I want a bin size of five units I'm going to do the same for male and I'm changing my title here to five because now I'm in control of it and if we run this we'll see that now we are back with this increments of five we're back with this increments of five let's just do that again this time we're just going to stack them and just for argument's sake this time I'm looking at female dot salary and male dot salary and we have introduced a bin size of 200 years starting at 500 ending in 5500 and because we do that from a normal distribution you can see this tending towards this normal distribution the last thing I want to show you just in this little tutorial is the cumulative histogram and when you do statistics you start looking at cumulative cumulative distribution functions etc this is important but we're not dealing with that at the moment this is the histogram and the way that I do that inside of this histogram object that I've created I'm going to use the argument cumulative and pass to that a dictionary with a key value pair of enable being true and I use the dict function instead of the curly braces notation here and if we just execute that we see this beautiful step wise and we can see the largest steps here meaning we are dealing with a normal distribution you can see that from this cumulative distribution function so that is that for the humble histogram remember that is for numerical variables and we're just going to start counting them or putting them in a frequency distribution by creating these artificial little bins and we can control the bin size as I've shown you so that's the histogram I'll see you in the next lecture where we continue our look at this wonderful world of plotly and this wonderful library plotting library that plotly is please please please remember to subscribe and hit the notification button because that's going to allow you to know when new videos or new tutorials do come out I'll see you again