My name is Sam Vagny. I'm the author of Malignan Cercolava, Narcissism Revisited.  The first trait is the narcissist's sense of entitlement. The second is the narcissist's haughtiness, arrogance and innate conviction that he's superior. And the third trait is the narcissist's aversion to routine. The narcissist's sense of entitlement encourages his indolence. He firmly believes that he should be spoon-fed and that accomplishments and honors should be handed to him on a silver platter without any commensurate effort on his part. His mere existence justifies exceptional treatment. Many narcissists are under-qualified and they lack skills because they can't be bothered with minutiae of obtaining an academic degree of professional training or exams. They are above such mundane chores. The narcissist's arrogance and belief that he's superior to others whom he typically holds in contempt. In other words, the narcissist's grandiose fantasies. These hamper his ability to function in society. The cumulative outcomes of this social dysfunction gradually transform him into a reckless and an outcast. The narcissist is shunned by colleagues, employers, neighbors, erstwhile friends and finally even by long-suffering family members who tire of his tirades and rants. Unable to work in a team, to compromise, to give credit or due, and to strive towards long-term goals, the narcissist, skilled and gifted as he may be, finds himself unemployed and unemployable. His bad reputation preceding him. Even when offered a job or a business opportunity, the narcissist recoins. He bolts, he obstructs each and every stage of the negotiations over the transaction. He becomes passive-aggressive or, in professional terms, negativistic. But this passive-aggressive, negativistic and masochistic conduct has nothing to do with the narcissist's aforementioned indolence. The narcissist is not afraid of some forms of hard work. He invests in ordinary amounts of energy, forethought, planning, zest and sweat, in securing narcissistic supply, for instance. So it's not that he avoids work generally. He avoids certain types of labor and toil. The narcissist's sabotage of new employment or business prospects is owing to his abhorrence of routine. He hates routine. Narcissists feel trapped, shackled and enslaved by the quotidien, by the repetitive tasks that are inevitably involved in fulfilling one's assignments in a job. They hate the methodical, step-by-step, long-term approach. Possessed of magical thinking, they'd rather wait for miracles to happen than make them happen. Jobs, business deals and teamwork require perseverance and tolerance of boredom. And the narcissist likes both. Life forces most narcissists into the hard slog of a steady job, or successional jobs. Such unfortunate narcissists, coerced into a framework they resent, are likely to act out and erupt in a series of self-destructive and self-defeating acts. But they are other narcissists, the luckier ones. Those who can afford not to work. They laze about, indulge themselves in a variety of idle and trivial pursuits. Pursuits seek entertainment and trills wherever and whenever they can, live off others in parasitic form, and while their lives away. At once content and bitter. They are content with their lifestyle and the minimum demands it imposes on them. They are bitter because they haven't achieved more. They haven't reached the pinnacle of their profession. They haven't become as rich and famous or powerful as they believe themselves deserving. Yet, even though they realize that they are failures, the narcissist cannot draw a line between his current station in life, the defeats and failures that he has experienced, and the reasons, the causes, his own traits, his own misbehaviors, his own misconduct. The narcissist doesn't see the connection between these two. It does not realize that actions have consequences. He believes that he is immune to the cosmic justice. He believes that everything should transpire without effort, without toil, without labor, without perspiration. He believes in inspiration. He believes himself to be an artist of life. And the world is his compass.


Hello and welcome to lecture nine of our introduction to machine learning course We are going to Start talking about unsupervised learning in the remaining three lectures. We spent eight lectures talking about supervised learning problems Just remind you supervised learning means that we have some input data and we have some output data that we are trying to predict So these are always prediction problems Essentially in supervised learning we're learning the mapping between the input and the output and this can be Regression if we're predicting continuous variable or classification problems if we're predicting categorical outputs and so on and so forth in the unsupervised learning which is our topic from now on we just have Input data if you want we do not have output data. We don't have labels We don't have any values to predict we just have a data set and we want to do something with so we want to we Want to find some structure in it usually So unsupervised learning is often connected to data mining and Similar similar things so What can we what can we hope to find in the input data if we don't have labels to predict? So broadly at least in this course We're going to talk about two different two different aspects to different applications parts of unsupervised learning That's dimensionality reduction and clustering we're going to start with clustering. That's our topic for today. So what is a clustering problem? Here's some toy data very simple data set with two variables and And these are the points are the samples and in the clustering problem. We want to find if there are groups Clusters in this data right so here. It's quite obvious to the human eye that this is a cluster This is a cluster. This is one cluster. Perhaps two clusters And that's what we want the clustering algorithm To tell us especially if the data are higher dimensional than two dimensions and we cannot just plot it in 2d and look at it so easily So it turns out that the clustering problem is actually a very very difficult a very complicated problem And it starts the the problems start with even formalizing it. So what does it mean? to To cluster the data what does what does what is the definition of the of the cluster? Very very hard to say what captures our human intuition about what the cluster is I can give difference and and we will later In this in this video in this lecture, we will see some examples Even people might disagree even human observers might disagree about whether this for example is one class or two clusters, right? And so this is hard to formalize Many questions arise like how many clusters are in the data is it is it is a three or four in this case Or perhaps perhaps it's only one cluster. They have the data are not clustered at all. So you just have one one blob and If you if you put it in some clustering algorithm, it will maybe give you several clusters But perhaps perhaps the problem is ill-posed and the data this particular data said is just not clustered Or if you have two clustering algorithms and they give you some clustering results, how can you compare them? How can you choose the better one in the prediction setting? You take a test set and you apply two models on a test set and you see what performs better, right? It's very it's very easy to in principle at least to say which prediction is better here You have two clusterings. So how do you decide which one is better? So there's a lot and a lot of these conceptual problems people sometimes say that in clustering is is not a science But an art And there's some truth to it We definitely don't have time to cover all of that or even discuss all of that in this lecture today But we will we will talk about two clustering algorithms This is just should serve as a caveat for you to know that these this is If you apply this in practice, there are problems like that that you have to to think about but in this lecture, we're going to discuss two particular clustering algorithms One is k-means and another is Gaussian mixture models. So we'll start with k-means In a k-means clustering. So this this loss function that I'm going to define now that serves to formalize this notion of clustering, right? So we want now to To put it into math. What does it mean to cluster and that's just one particular way of doing that? Okay, so we have some input data x i we want to split it into k clusters and that's something important from the beginning So in k-means clustering, we're choosing k from the beginning So we're clustering a data set a given data set into four clusters or into ten clusters, right? This is the question of how to choose the number of clusters That's a question that we're actually not going to to be discussing today Let's say, you know that you want to split it into four clusters. How do you do it? So we are going to in the k-means clustering We're going to represent each cluster by its average by the mean by some vector That I call mu here that will that will in some sense represent the cluster and the loss function of k-means It's just it's very simple. It's just a squared error in some in some sense. So it's the sum over all overall clusters from one to to capital K and then the second sum is Overall examples overall samples that belong to this cluster and what I'm summing is the squared distance from my sample to this representative vector mu Okay, so this is what we want to minimize so we want what do what are the parameters here? The moves are the parameters the splitting into clusters. So this s K sets, right? These are just the sets of indices the set of in the set of samples that goes to cluster one the set of samples that goes to cluster two And so on so these s and moves is is something that we can adjust in order to minimize This loss. Okay, there's another way to to write the same loss where we just some the second sum is over the entire is the entire data set and I'm introducing here this are I K variables that will be equal to one if the sample I belongs to cluster K and zero Otherwise, so it's the same thing just written slightly differently Okay Yes illustration So here is here is how it may look for a simple two-dimensional again data set with three clusters So these points here are my my sample points this in the middle is Is the mu so this is mu two mu one and three and these are the lengths lengths, right? That enter the the loss function So I'm taking the sum over all these edges of the squared length Of each edge and then I'm summing everything that belongs to this cluster and everything that belongs to this cluster and to this cluster Okay, and it's it is rather intuitive that if you like assign this point for example to this cluster and Then your loss function will increase right you will perform worse because you will replace this short distance with this long distance Or if you move this this mean Point mu somewhere to the different location all these lengths will increase Okay, so the loss function makes sense. Good. How do we minimize it? So here's the same loss again so the First piece of bad news is that it is not analytically solvable. There's there's no way for the arbitrary data set to to have a formula for what the moves and the Rs or s variables are Okay Second piece of bad news is that it is not convex. That's something That is not so easy to see from this formula directly, but you will see this later on It's non convex and it's badly non convex. It has a lot of local minima. It can have bad local minima And we have we have to deal with it The third piece of bad news is that gradient descent can be used to minimize that But it actually is a little messy to write down the derivative especially derivatives It's it's not You have to deal with some constraints here if you operate on these are variables here with this s It's not even clear how to take a derivative of that. So it's it can be a little messy The good news is that there is an alternative approach that actually is very simple very intuitive and works well and It's 4k means it's called Lloyd's algorithm. So let me explain what the Lloyd's algorithm does here It's iteratively optimizes over our and over moves. So this means that we first Optimize over me. So we find optimal moves having the R's so this means having the the split into clusters fixed we optimize the position of the new Vectors and then we hold the new vectors fixed and we optimize the the splitting of points into clusters and we keep Repeating these two steps until it converges. So let's discuss both steps separately And it turns out as you will see now that each of the steps is very very easy actually So the first step is for example, we're holding the moves now fixed. So what does that mean? We want to find in which cluster should each point go if you think about that each Sample will contribute to the loss function the square distance to the cluster Representative vector right so if the representative vectors the moves are all fixed and you have your sample Where should it go? Well, it should go to the closest new that will this will minimize its contribution to the loss So you just assign each point to the nearest cluster center. That's all it's very simple So here is how you can write that? Mathematically that for each point you assign it so each sample I goes into cluster K Where the K is the is the value that minimizes this so that's just the closest new to X I okay The second step would be now we having the We having these sets fixed so we're saying all these points belong to cluster one and all those points belong to cluster two How can we choose the new vectors to minimize the loss and that is also very simple and directly given here So if you look at this look at this sum if these are fixed then basically the sum decomposes into some for each cluster That you can optimize separately and then you take the sum that is that relates to cluster one For example, and you want to choose the new that minimizes that but this is just Minimizing the the squared error loss. It's basically Like the estimation of a Gaussian the the best the maximum likely estimate is just to take the mean The the average of the samples as as the new vector So that's a very simple regression problem or Gaussian Estimation problem you can directly see from here that if you want to minimize This one sum for one cluster then you just take the average also. I think is very intuitive if you remember the Let's catch on the previous slide, okay So we have these two steps that each of them is super simple here. We assign each point to the nearest cluster here we We choose the mean Of each cluster as the average of all points that are currently assigned to it and then we alternate So it's actually so simple that it may even be Surprising the first time you encounter it that this works at all like this seems that seems even Like this seems so simple. It's almost dumb. So let's see how it works because it does work. I Find this remarkable. So here's the illustration in a very simple case where you have a two-dimensional data So this is taken from from this textbook You have two-dimensional data and We will just we will just go over the iterations and see what happens We have to start somewhere. So this is actually one One aspect that I didn't mention you have to start somewhere and in this case I think we just start randomly. So we choose to to move so we choose the New one and the tool and they're just randomly chosen within the Within the range of the data Okay, so now first step we assign all points To the closest cross right so these become red points these become blue points now We do the second step we put the cross the crosses will move them to the average of The all points of the same color right so the red cross moves here and the blue cross moves here Okay, great now We reassign all the points so that each point gets to the closest cross and now we move the crosses again and now with the reassign the points again then we move them again and Again and you see that it almost doesn't move anymore and actually after this point I can stop because this converged now So if I now keep keep iterating nothing will change anymore now every point is already Assigned to the closest cross and the cross is in the middle Is in the average position of all the blue points so you can keep iterating if you want but nothing changes So you can stop the Lloyd's algorithm when it converges and it's actually pretty easy to see that it will always it will always converge To some minimum to a local minimum in this case and that is because there is just a finite number of Of the ways how you can split these points into two classes And it's easy to see that each step of the Lloyd's algorithm decreases or leaves unchanged the loss function So the loss will never go up During the iteration so it has to go down or stay constant and there are a finite number of ways you can reassign points So at some point you will just you will just hit You will converge you can however converge to a bad local minimum So you converge to a local minimum, but it doesn't have to be the best possible solution And this is something I want to illustrate here This Strongly depends on the number of clusters So if you do this in 2d and you have two clusters like on the previous slide it will I think it will more or less always converge to the to the good solution But if you have something like that So in this case you have a lot of clusters right and notice that the clusters are actually very simple here So there's not really there's not really this conceptual question of what is a cluster doesn't really arise here because these data are Sampled from a bunch of identical spherical Gaussians Just located in different places here Right the I think the number of points per Gaussian is the same here So it should be like the easiest possible data set for for clustering in a way, right? You have a bunch of identical spherical Gaussians the same number of points per cluster and then you start came in and this will be an example Solution that it will converge to depending on the initialization and you see clearly that it is not it is not very good and What happens in particular is that you have areas like that where one cluster? Well one actual Gaussian is one underlying cluster is gets split into several three Here in this case or two in this case and there are other examples like this one Where two Gaussians are actually assigned to one cluster and this is a minimum So if you if you iterate Lloyd's algorithm nothing changes because there's no No like local simple change There's no point that you can reassign to the neighboring cluster so that the loss decreases You can decrease the loss, but you need to do a drastic change You need to say I split this cluster in two and I merge these two classes together at the same time and then And then the loss will decrease but This the Lloyd's algorithm will not achieve that right so you have to think of a of the loss function of this Of this problem having having a lot of a lot of local minima So if you are in this local minimum you can do gradient descent or you can do Lloyd's algorithm And you are already you are already in the optimum. You need to change it a lot to move it to another local minimum That actually contains a better solution. So there's what can we do? there's several Essentially heuristical ways of how you can how you can do better so you can there are smart ways to Initialize the K-means clustering Something called K-means plus plus for example chooses the these initial points somehow in a smarter way this can help another thing that can help is that Okay, very a very simple thing that can help is that you just run it a number of times for example starting with different random Initializations you ran it ten times and then choose the solution with the lowest With the lowest loss this can help a little bit too a Smarter thing that can help is that after after in converged or or even during the iterations You check whether you can decrease the loss if you split if you split some cluster into or merge to class to neighboring clusters together So this is the there are several of approaches like that split and merge Heuristics, so you iterate the Lloyd's algorithm and then you're checking Perhaps if you if you if you merge this and split that then your loss may go down and then you do that and then you continue with the Lloyd's iterations All right, so this is the the K-means clustering so apart from these difficulties of conversion that can be to large extent Addressed with this with the smarter heuristics that I'm not going to explain in detail There are some more more fundamental Drawbacks of K-means or even the global minimum of the K-means loss function may not be the best clustering that you're after So this is something I want to discuss here. So here is an obvious An obvious example where the data are just very far from from from being Like a Gaussian blobs in space, right? For example, you have one blob and then this ring around so you would maybe say these are two clusters Just one of them has a funny shape K-means will will never be able to find that right because Because assigning all these points to one cluster actually is is This will have a high loss In that in that loss function the distances Of all these points to the mean of this ring cluster will be large and K-means will think it's a bad solution There are though situations that may seem Less extreme, but K-means will still give you something that you don't expect so one example is that where the guy where the Classes even maybe perfect Gaussian, but are stretched, right? So they are not like a spherical blobs, but they they are very elongated blobs So if they're elongated enough for example on this on this sketch K-means may decide to split them in Like that, so this will become one cluster and this will become the second cluster Because this will this will just minimize the the squared error if you assign all these points to one cluster Then some of the distances will be really really large and this will be sub Optimal as as as far as the K-means is concerned here is another example here the The blobs are spherical But one is really small and one is large just the radius The the variance of this Gaussian if you want In this case what can happen is or what actually will happen is that they will split like that And that's because even if the means are exactly correct So here's the mean of my cluster one and here is the mean of my cluster two So where does this point go it goes to its closest mean which in this case may be this one, right? So the part of this cluster will be a part of the Gaussian will be chopped off and assigned to the wrong one And that's not the convergence problem. That's just what K-means will do in this case And here is the fourth example in this case. They are These two clusters have the same size Like geometrically they have the same size, but the not but the sample size is different So there are few points here, and there are many points here And what can happen here is that again came in will choose to chop off a part here Because even though these distances are all pretty large. That's the price It's paying but then actually these distances here will be mean will be a little smaller To its mean and since there's so many points here Then it's it can be The loss can be smaller if you if you assign some of these points to that other cluster So you will get problems with came or you may get Problems with K means if you have very different sample sizes in in your clusters if the or if the covariances I've like either just the the variance is is very different or the covariance is very far from spherical and all of that can be addressed if we're using if we if we were to use a model of the cluster that is more complicated than what came in Implicitly assumes and this brings us to the Gaussian mixture models, right? So all three examples on the previous slide Were examples where the data within each cluster were a Gaussian and If that is if you happy to assume Gaussian data Then the it's it's much it's often better to use a Gaussian mixture model That just explicitly assumes that your points your samples come from a mixture Distribution a mixture of several Gauss and so you have a Gaussian here And you have a Gaussian here the third Gaussian here and the the distribution that is a mixture of them Which has this this density is just a sum Well a weighted Sum of several Gaussians So these are the weights and these are the means of the Gaussians covariance matrices The weights sum to one so that the entire thing sums to one as the probability density Function should right so and that is something that we want to fit to our given data set That's the problem of the Gaussian mixture model fitting. So If you think about that, it's actually it's it's a little similar to what we did before with the with the K-means and with the Lloyd's algorithm, so intuitively one could try to use here and Iterative approach similar to Lloyd's Algorithms right, so I'm not deriving in here. I'm just saying well one could try something like that. What would it be? We assign each point to the closest Gaussian not to not to the closest in K-means the closest just meant the closest move vector right the move with the smallest Euclidean distance here it will be a bit more Complicated because the Gaussians have some shape the covariance matrix, and they also have these weights Pies so we can but we can still assign each point to the nearest Cluster like to the best fitting class in the sense that this posterior Expression is the is the is the largest so we just check for every point to which of the Gaussians it is Most likely have come and put put it there And then so that's one step and on the next step we update the parameters of each Gaussian based on the points there So one could try something like that and it will probably work, but let's see what happens if we actually try to derive Derive the the how to optimize the likelihood of this model because this is now a nice probabilistic model, right? This is the probability If we have a sample then we have the the complete probability under our depending on these parameters Of our Of our data set to observe the data set given the parameters, right? So we can we can use the maximum likelihood principle that we want to find the the parameters that That that give us the data set with the highest likelihood So let's see what happens if we actually if we actually go through this math here I will directly write the log likelihood and not the likelihood itself, right? So this is the sum and the log this is the sum of all the all the Samples this is the logarithm because this is the log likelihood And within is just this the same thing here, right? Which is another sum over? components over Over this mixture components, okay, and just to remind you the that the Gaussian Multivariate Gaussian has this exponent in it in the density function. So just to see what happens Let's try to set the derivative with respect to one of the one of the moves to zero Because we want to find the the maximum of that, right? So we just take the derivatives and set them to zero and see what happens So let's let's do this We're taking the derivative of this thing So we have the sum it stays a sum then we have the log of of of this sum So this goes the in the so it's a chain rule what I'm doing here So the sum goes in the denominator because I'm that's the derivative of the logarithm Then I have the sum but only one one Term in the sum depends on new k So only this one term survives the derivative and it goes here in the norming numerator and then I have to take the derivative of this thing inside the exponent Right, and I have the sigma k in the inverse of sigma k goes here and This x minus mu Is over here and then we're done and this would be equal to zero if we are at the At the maximum and notice that this thing here Is just constant in the sense that it does not it's the same When you sum over I this thing is always the same so I can take it out of the sum and And cancel out and I'm left with Let's rewrite it here and I'm left with this Red term and x minus mu and that should be equal to zero So let's call this thing zik and let's let's look at that for a second and try to understand the meaning of this zik term It's and it should remind you of the Bayes formula and it good it is good if it does if you have If you take one sample I so if you if you fix one sample I here then This expression the zik Let's say you fix the I and the k then the zik will tell you what is the posterior probability of your sample I to belong to cluster k right because this in the numerator Is the probability that it that it and that it comes from from cluster k and this in the bottom is the sum overall Overall possible clusters So if you divide one by another you get this zik that will actually if you sum over k will sum to one as it should with posterior probability and Yeah, as I said for each I for each k it just tells you what's the probability that the sample I came from from the cluster k Remember what we're doing here. We're trying to solve for mu right so this is now very simple expression that we can immediately solve and this is just the The weighted mean of all points So you you have the sum of the entire data set But the points that have high probability of having come from of coming from cluster k will contribute More than the points that have very low probability of coming from cluster k so you take the average Of the entire data set but with weights That are That are given by the probability that these points belong to this cluster k Okay, so this this makes a lot of sense if you think about that you you have some points Assigned to this cluster some with high probability some with very low probability Those are far away and then you just take the average of essentially the points that have high probability And this gives you the optimal mu However, this brushes a very important thing under the carpet sort of if I write it like that because this might seem as I solved it Here's my solution But of course I didn't solve anything because I have this z z z terms in here and the z depends on this On this and this depends on mu And on sigma and on everything else right so this is This should be true If I am at the maximum But these guys over here depend on mu two so this is not a formula that I can use to just write down Write down analytical solution unfortunately I can follow very similar steps Taking the derivative with respect to sigma is just a bit more cumbersome Or difficult to derive but if one does that then one gets that the sigma should be the weighted covariance matrix And the if you do the same with respect to pies then you get this formula for pies that this is just the Basically weighted fraction of points that belong to each to each cluster So I think these formulas for mu sigma and pi make a lot of sense But as I said, they are not really giving you analytical solutions So what can one what can one do we have the mu the optimal mu defined through The the z's that are given through the mu again But at this point we can finally do something very similar to what we did in the in the Lloyds algorithm We can optimize them iteratively and in this case, it's called expectation maximization algorithm On one step, which is called the e-step. So the expectation step We compute this probability zik for each point to be in each Gaussian component And given the parameters mu sigma pi fixed. So this expectation step just means You're computing these red terms that I had on the previous slide. Okay That's the entire step. So simple Okay, and then in the m step, you now update all parameters of each Gaussian To using the formulas that we derived these weighted averages and the weighted covariance and so on And then after you updated them, you go back to reassign the points By computing this new posterior probabilities depending depending on the new parameter values And then you update the the parameters again And this should remind you very very strongly of the Lloyds algorithm that also assigns points Then updates the moves assigns point reassigns points and then updates the moves Here we have more parameters to update because we have to keep track of the covariance and this In the weights of each Gaussian component And another so one difference is that we have more parameters in the second difference is that we don't just hard assign each point to one of the clusters, but we're computing this Probability that for each point that it belongs to each of the clusters It can be probability can be very high for one of the clusters and very very low for others But it will not be exactly zero for any of them So it turns out that expectation maximization is a very generic algorithm that can be used for many different and is used In machine learning and in statistics for many problems where you're optimizing likelihood Of a probabilistic model that has some latent variables So in this case the latent variables are the True class membership. So each point actually belongs to one of the Or we can think that each point in our data set Belongs to one of the like really came from one of the components of the mixture But we don't know which component it really came from. So this is latent variables that we cannot observe But we can use this this approach where we estimate the probability over latent variables and then we update the parameters of the model having the latent variables fixed And then we estimate the posterior gain and then we update the parameters again and one can in a very general setting Um derive and prove that if you do this in a latent variable model, then your likelihood will never go Down it will always increase And again you can run there there can be local minima But at least you will you will always you're guaranteed to reach to converge Towards one of the one of the maxima Of the likelihood We will I will mention another example of the of the latent variable model in the next lecture That that can also be optimized using em. So it's it's a very powerful It's a very powerful approach Okay illustration I'm taking the same data from the same textbook And now instead of clustering k means I'm clustering a Gaussian mixture models again We need to initialize with something. So and here This shows two Gaussians. So this is the me one and this is the me two and the sigmas are initialized Spherically and the pies are probably initialized half As 0.5 weight here and 0.5 weight here and now we assign all points To these components and here you immediately see one of the Like the second different thing from from from the k means is that the points don't just have two colors, right? They are They have they have some posterior probability to belong to cluster to this or to that cluster So for some points here in the middle, it may be close to 50 50 and they will be of intermediate color So you get this spectrum of colors here. Okay, so once you did that you can compute the weighted mean Which is essentially the mean of the red point the more red the redder Points here, right, but you compute the weighted mean and you compute the weighted covariance And you get these two Gaussians After the after the first step So now you hold the parameters of these Gaussians fixed and reassign the Reassigned the points not much changed here to step two If you skip scabral steps, then actually one Gaussian will start to cover this region And another Gaussian will start to cover this region, but this is already step five. So actually This usually happens slower than than than in k means we need more iterations, but if you keep iterating then after 20 iterations, for example, you have the split That that that makes sense, right you recovered the two The two components here and notice that the final Gaussians Have different not only the means but also the covariance is different. So this is like a bit more vertically oriented This is a little bit more horizontally oriented This will So the Lloyd's algorithm will just converge in the sense that it will stop You will you will reach an iteration After Which nothing will change anymore. So this is not the case here. You can all this this will converge In a sense that it will become stable and the differences like the updates from iteration to iteration will become very small But it not necessarily or usually it will not like entirely converge, right? It's like creating descent. You will just approach the minimum Close and close. Okay There's one There's one tricky point that I also brushed under the carpet until until now when discussing the GMMs the gaussian mixture models And that is so let's consider the the gaussian mixture equation again And let's consider a very simple case where we actually just have one dimensional data Right. So these are these these points are my data points here. That's one dimension And here on on the y-axis I have the actually the density function so and and let's say I want to cluster it in two components and It so happens on on one of the steps that all these points are assigned to to one of the components Or basically one component looks like that And another component looks like like this very high gaussian so that this point is very likely to come From that component and all these points are more likely to come From the other one and then you keep iterating and what will happen Is that this gaussian will shrink more and more and more and more around this one point and basically Become completely localized and diverge Essentially to the delta function on this and why does this happen? This happens because then the likelihood of this one point Will become super high right the likelihood of this point will diverge to infinity if the likelihood is just this this value So if this becomes narrow and narrow and narrow and high and high and higher then The likelihood will diverge to infinity and when you compute the The the sum log likelihood or the entire likelihood of the data set it will also diverge So it turns out that there is actually a way to make the likelihood go to infinity And we're trying to maximize the likelihood so that should be like the best um solution as far as the um as the likelihood function is Um concerned and but that is of course not the solution we want. It's trivial. It can always happen if you make one of the components Variances go to zero Okay, so this may become a problem if you actually implementing gaussian mixture model algorithm and you're doing the iterations And one of the gaussons basically becomes Localized around one point and then you get in this regime that it just shrinks and shrinks and shrinks and your likelihood explodes So one has to in practice It can happen that one of the gausson collapses So to say and one has to to do something about this to prevent this degenerate solution to happen So for example, if you see that one gausson The standard deviation of one of the gaussons becomes super small. You basically kill these gaussons and randomly reassign it in some other part of the Part of the dataset and and then keep it a rating. It's um, it's like an edge case That a good implementation should take care of And also shows but more like philosophically it shows that there is some problem with using this um With using loss function this loss function in the first place So in practice we can prevent this from happening and get away with it from it But I think conceptually it means there's something Something About this this loss that's that's not great because it allows these degenerate solutions This can be prevented if you if you have some prior Like a hyper prior on the parameters and say the the sigma Cannot is not allowed to to become very small Like in a fully Bayesian setting you can put priors on sigma and a mu And this may may may address that but in In this setting as I explained it actually this model can diverge Okay Some comments on the expectation maximization versus the gradient descent. So we did Um here for the for the Gaussian mixture in principle. It's possible. I said it's cumbersome for k-means, but one can do one can do Gradient descent for k-means or Gaussian mixture model They are both iterative algorithms, right? They can both converge So they they both converge to a local minimum in the sense that they Guaranteed to bring you to a local minimum the likelihood will not increase but the minimum can be local and You you are not guaranteed to to reach the global minimum actually With the gradient descent you are not guaranteed that your likelihood will that your loss will not That it will not increase right? It's possible that you make a too large step and your loss goes up Or the likelihood goes down in e m. This will never happen So e m current comes with a guarantee that after each expectation maximization iteration your likelihood increases or stays the same So that's actually an advantage it's good and in fact, it doesn't need a learning rate There's no learning rate in the e m algorithm So you don't need to think about how to choose the learning rate or how to change the learning rate If you get stuck and and and so on and so forth. So that's also that's a good thing another good thing about e m is that You don't need to impose constraints on the parameters. So for example, all the pies should sum to one So if you do gradient descent You somehow need to ensure that all pies Always sum to one and the all coverances should be positive Definite matrices So you do a gradient descent step and maybe one of the covariance matrix becomes non positive definite, right? So what do you do? You need to somehow fix that or the pies don't sum to one. You need to make them sum to one It's possible to to to do all of that, but you need to take care of that In expectation maximization these problems don't arise on each step You get meaningful covariance matrices because your covariance is just the Is the weighted covariance matrix Of of your points, right? It will by construction. It will always be positive definite your pies will by construction sum to one and All yeah, so all parameters and also the z i k everything will be meaningful on each step of the e m So this can be actually This is a nice property one thing That I still wanted to say on the previous slide is that G m m So the Gaussian mixture model can also converge to a bad local minimum If you start the Gaussian mixture model on that example that I had before with A lot of different Gaussians in 2d It can converge to to a suboptimal solution similarly to chemins So all these heuristics that I briefly mentioned Split and merge Of of clusters or smart initialization smarter than just random this all applies also um to Gaussian mixture models and in fact G m m typically converges slower than chemins. So what is often done is that you run chemins first You get the chemins solution and then you initialize Gaussian mixture model with the um with the chemins solution This can help in practice too So let's revisit again. What is what is the difference between chemins and Gaussian mixture models? similar To what we discussed in the lecture on discriminant analysis one can constrain the covariances in the Gaussian mixture model In different ways So you can constrain them such that the covariance of each cluster has to be the same That's what linear discriminant analysis does right remember in the Classification setting here. We have unsupervised setting. We don't have labels, but still we can we can say our covariance matrix In let's say I'm fitting two clusters and I am fitting this I don't fit two covariance matrix one here And and and one here and then they can be like that. No, I'm saying they have to be the same So they have to also turn the same you can it's relatively easy to update the formula for this weighted covariance matrix such that you Only have one covariance matrix covering all clusters This is not always a good idea, but it can be a good idea in some cases or you can constrain it differently You can constrain it to be diagonal You say maybe you have a lot of variables a lot of features. So if you have a lot of features, then you have quadratic Quadratically large number of parameters in the covariance matrix, right? It's a lot of things to fit So maybe one can say we'll forget about the off diagonal terms the correlations I will just fit the diagonal covariance. We can even constrain it to be spherical So they say all the same choices and all the same considerations that Applied for LDA apply here apart from in LDA We can at least hope to cross validate or to have a test set and then choose the the best working model here You have to go with intuition or with some heuristics of what is a good clustering result To choose between these things but in practice if you have Many features and your sample size is not is not big enough Then it's it's often helpful to choose a simpler parametrization than than the full covariance matrix Um, okay, so a special case would be if we take spherical Covariance matrix. So just sigma some sigma squared times identity matrix, which is shared across all clusters, right? So we say all clusters have the same covariance and this covariance is spherical And this actually then becomes very very similar to the k-means The main difference Is that the k-means perform something that I earlier called hard cluster assignment on the east step of the Lloyd's algorithm each point gets to the To the cluster That's closest that the point is the closest to and and that's it. So it just gets here and And belongs is said to belong to this cluster. So that's the hard assignment in the mixture model update in the east step. We compute these posteriors and if the point is very close It will get a high posterior probability to belong to this cluster But all other probabilities for all other clusters will still be non-zero. So this can be called soft cluster assignment but the if if the covariance is spherical and shared then This notion of what Gaussian is the closest that's the same as the I'm just looking at the distance to the To the to the to the mean right because if you think about the the Gaussian multivariate Gaussian function if you plug this In there then the covariant There's no covariance anymore and everything just depends on your Euclidean distance From your point To the respect of mu that this becomes very close to the K means with this one difference hard clustering Hard cluster assignment on the east step versus soft cluster assignment in the east step. So in some sense Lloyd's algorithm and you can you can if you now put sigma to zero Then so if you don't fit sigma, but say sigma is really really small that actually the soft assignment will converge to the hard assignment so you can You can see Lloyd's algorithm as the limiting case of expectation maximization for gaussian mixture model if You impose the constraint that the covariance is spherical and shared and the variances go to zero Yes, I already mentioned that it may be convenient to initialize gaussian mixture model where they came in solution and just to get back On this last slide to to this picture from before so these these three examples were the cases where k means would not give you the The clustering that you expect maybe if you If you look at this picture and these three examples are the cases where gaussian mixture model Will actually work will be more appropriate and will work correctly in the sense that it will get you um These two components here and these two components correctly here and also these two components here Of course, if you use in this case if you use the non non spherical full covariance matrices, right So you can think that these cases are solved by the by going to the gaussian mixture model These cases don't won't be right. So this is clearly a non gaussian shape Um So if you have if you have complicated non gaussian shapes that you still want to Call one cluster just one cluster with a funny shape Um, then the gaussian mixture model will not help you and then there is actually a huge literature Um on how on the alternative and completely different partially non probabilistic density based and so on ways of clustering Uh data where the gaussian mixture model assumptions do not apply, but this has to remain for another course Thank you


Hello everybody thank you for joining us just to make sure you're in the right place this should be that you signed up to because you never know. An LBQ webinar where we're talking about staff shortage we're going to kick off formally in about 10 or 20 seconds or so. So just bear with us and I'm sure you're all zoom pros at the chat box, the your comments your questions come to me only so that just allows everybody to focus on the discussion. There's no slides, we're going to have a little bit of a talking heads, sharing ideas, those types of things so if you're familiar with the zoom I'll just put hello in the chat box, there you go so you can see where that is so the messages come to me. And this recording will be shared so it will be circulated through the event bracket ticket page, and we'll stick it on our YouTube channels to. So it's just come past four o'clock, I'm going to kick off formally. So welcome, my name's Ross McGill and I'm on teacher toolkit, former school leader, a bit of a blogger and I got a little small audience online where I like to kind of share lots of ideas and when I'm not struggling with my doctoral degree, I am physically and more increasingly digitally in the school supporting teacher training and trying to find out great ideas that make a difference to our teachers and to our young people in schools all over the country and I'm lucky enough to be joined by two experts still on the front lines when I introduced them in a moment now if I just give you a heads up I want you to introduce yourself your role and tell us something interesting about yourself that's not related to school.  The title this session dealing with COVID staff shortage issues now in my former life as a school leader managing cover for a secondary school in Westminster London 250 staff 2000 pupils was a headache day to day at the best of times throughout COVID I suspect it is a bit of a nightmare and there are two years of perhaps dealing with this. There are certain things that we can do to optimize and reduce margins, etc make things a little bit easier. But how do you make sure that learning still happening when there are fewer teachers to do the teaching looking at a few government announcements earlier today. The average is about 10% of staff at this is at the moment. So, be interested to hear what Sam unless you have to say in terms of their attendance patterns for staff. The skills across the country. Well here from Samsung beads, Roman Catholic primary school has been hit with staff shortages as well. And their attendance issues because of the pandemic. And this has led to a variety of issues in and out of the classroom whether it's widening learning gaps. And we know people are focusing on curriculum changes and supporting pupils with their mental health so we'll have I'm going to ask Sam to introduce himself first and then we'll also hear from Alicia sure who works at the shine class. So, at least if you can tell us a little bit more about the trust and how you're also dealing with the shortages and then we'll get into the formality of going through a lot of questions I want to post and just to unpick. And some of the issues and some of the solutions that have been dealing with and then for people watching and people watching live pose your questions in the chat box they come to me only and I'll ask them on your behalf and we'll also talk about the LGBTQ software which we're fortunate enough they're hosting this event and brought us all together and I'll talk about my experiences of using that software as well as hearing from Sam. And Alicia so that's enough from me and Sam can I ask you first, you your role and something interesting and outside of education what what keeps you excited and motivated and looking after your mental health in particular. Hello everyone I'm just going to move because the light sensors just said that I've gone to sleep so I'm just. Well, there you go. I'm Sam. Deputy Head, yes it's teacher and Senko at Catholic Primary School in Newcastle, Central Newcastle just at the outskirts. Love my job. What's interesting to me about me outside of education I'm a new dad for a six month old daughter who slept in her own room this weekend so fantastic bags are slightly smaller. And I'm also a Newcastle natives fan and that certainly. I don't know if excitement is the right word. Keep your emotions busy but um, yeah congratulations on becoming a parent I suspect now you realize what real tiredness is compared to teaching right thank you Sam Alicia. Hey, so I'm Alicia short I work at shine and we are a charity based in Leeds, and our aim is to reduce the attainment gap between kids from low income families and then more people and peers, and we particularly focus on the north of England. We are a grant giving charity so we give grants to schools and teachers who have got innovative ideas about how they can reduce that gap so if you've got any innovative ideas. Have a look at our website or feel free to get in touch with one of us and we give grants of various different sizes just to projects lasting up to three years. We don't work directly with schools. So we haven't sort of had the the impact of staff absences that I'm sure Sam has, although members of our team have been off since Christmas because of covered. But we do hear a lot from schools that we work with about the challenges that they're having and the delays that happening to the projects that they're trying to run because of the challenges of staffing and attendance kids attendance as well and parents coming into school because of and something interesting about me. I guess that something that I do that I find really helps with my mental health is getting outside a lot going for walks and sort of getting into nature. And that's it I thought you're going to forget that I wasn't going to lay off the hook so thank you Alicia for sharing that I guess from me and having lived and worked in London for 30 years. I'm one of those that left the big smoke in the pandemic so I'm now in Halifax, Yorkshire. And I absolutely love the outdoors up here so you know further away you move from the southeast the more space. And so my favorite word at the moment is diaphanous and I think it's because I've been learning more about nature and planting lots of trees and all sorts of things and really enjoying the outdoors. Right, let's get into some formalities and so Sam will start with you. What's the situation at St B to tell us a little bit about the school your demographics etc and how it reflects the kind of national struggle that all schools have been through particularly last 18 months. Yeah, so we are the West End in Newcastle, which is a real. I described as like a melting pot really we've got all sorts of different children from all sorts of different backgrounds were about 25% people premium 25% English is additional language and got a higher than average amount of children on the SCN register. A growing number of people with autism that's a bit of context for us and we're right in the middle of a countless days we've got no green space whatsoever which provides other challenges. And in terms of the picture of the last couple of years it's been really tough, our families have really struggled, our schools really struggled. And as much as maybe as we're okay budget wise to taking a real hit over the last sort of particular the last few terms with absences of staff and we're a close knit family. And then one of us goes down we don't just suffer in terms of worrying about that member of staff being off we're also suffering because that means cover it's pulled you know your support staff is no longer support staff they're doing someone else's job. I think myself in the head over the last two years of being cooks with being cleaners with being caretakers with being in men with being, you know, you name it we've done it. All hours of the day and I'm sure I'm speaking to many people are in a similar situation.  We've had times where, you know, we're waiting for PCR results but we're feeling healthy but we can't be in school we've had all of these things that everyone's gone through. And it's been a real, you know, real tough place to be it's made everyone question whether what they're doing is the right thing to do. It's made everyone look, you know, look for answers. You know, I'm fortunate enough I'm quite active online and I'm looking around on Twitter to see what else is going on out there but I know lots of schools in our area on as connected as maybe as we are. And it can be a really lonely place it can be nice, you know, an isolated profession at the minute where you know you're reading the press and teachers are getting a bit of a pattern and then you go into work and you're really stuck against it anyway.  Yeah, we've just, we've recently joined a bigger multi-academy trust as part of the Catholic schools up here and the Newcastle sort of local authority kind of disbanded a few years ago and so there's lots of the support that lots of local authorities might give we don't really get you have to look privately for that and when you look for private support you can face different kinds of challenges and different kind of hurdles. So, yeah, I mean, just my starting to see the benefits of that now, and I say we're only six months in. Right, so I mean, I guess the earlier part of the pandemic you could have, you know, you could have quite rightly felt quite isolated as a staff body. So, in terms of the reminders of the kind of demographics, how many form entry are you in? One form entry, we haven't got in history but 210 kids from reception to six. Okay, lovely. So I'll come back to you, Sam, thanks for that, that's an interesting context. Alicia, you know, your insights, you know, supporting lots of different schools across the country. What's the national picture? You know, we've heard lots of stories about disadvantaged kids being left behind. What insights have you unpicked from Shine based in Leeds? Well, as you both said, the picture on the media and on social media gives you a pretty good but bleak idea of what's happening. So, as Ross said before, the survey seemed to be suggesting between 10 and 20% of staff are absent. And that's pretty reflective of the sort of conversations that we're having with schools. So, for example, I spoke to a teacher in a secondary school in Leeds the other day, who spoke about the fact that they've got 10 teachers and seven teaching students due to COVID at the moment, really struggling to get any supply cover and so that's obviously really affecting the learning of the children at their school as it is having an effect on sort of thousands of children across the North. It's just an ongoing challenge, isn't it, with the lack of staff and the challenges with supply, with binding supply staff. And we all know that it's resulting in children potentially having to be sent home for online learning or having to, schools having to combine classes and year groups so that they can, they can teach the schools, teach the children, sorry. And for the children who are being sent home, it affects all children but it seems to affect disadvantaged children more profoundly than children from more affluent homes. National analysis of data nationally shows that the attainment gap has been exacerbated by the pandemic. There are loads of different reasons for that. It's been a really challenging pandemic for everybody but I think we can see the challenges if you are living in a low income, in a low income household with less resources, potentially with less time and the online learning has been really challenging for a lot of kids from low income families because of lack of resources, lack of access to the internet has really sort of deepened that attainment gap. I don't know if anybody saw some data that was presented by the FFT education data lab last week about the differences in absences between children from low income families and those from more affluent families that the kids who in the FSM six group had much higher levels of absence and were much more likely to have had really, really long periods of absence than their more affluent peers and so it's all just adding to this picture where we already had a gap, an attainment gap that was not acceptable before the pandemic, but lots of different reasons and the pandemic has just exacerbated it. Lisa what kind of things have schools been getting in contact with you about in terms of what are their kind of urgent needs that you were you would normally the kind of support that you would offer as a trust. So we, we tend to offer support, as I said around innovative ideas to reduce the education gap. We tend to focus on the transition into primary school and the transition from primary secondary school because we know that those are really fundamental areas where the gap can grow. It's really important to make sure that kids from low income families are keeping up. We've been hearing from schools that, especially the sort of the nursery settings and reception sessions that we talked to the staff are really concerned that that gap is is bigger than they've ever seen before. That everybody's coming in, so the average level of language and communication and social skills that kids are coming up in with is sort of lower on average, but that particularly for the kids from disadvantaged families. So an early as teacher from Blackpool recently who are saying that she's really noticed that children from low income families are coming in with much lower levels of communication language that they did in the past. And it's always a good reminder that you know if you think of a year three student they've not they've had two years of, you know, no steady schooling at all impact on all the different new groups. I'll see. Sam, if I come back to you thank you Alicia. How have you cope with staff shortages so you know, I don't know if you can give us some statistics you know staff attendance and things like that over the last couple of years or this term, and come to some of the strategies that you're you're doing to deal with these problems. Um, I haven't necessarily got numbers off the top of my head but I've got sort of anecdotes that staff shortages have come in different ways so we've had some people who have been ill themselves who are often you know and understandably ill, and maybe it's longer than the two weeks of the old isolation period, and we've had some staff who are off intermittently whether they're going for PCR test or they've been close contact or whatever. But it feels like when we talk about this pandemic it's like various different eras isn't it and some of them feel like a lifetime ago. So juggling that short term absences whether it's a day or an afternoon or you know a couple of days while waiting for a result, or whether it's prolonged it's been a real Valentine act, and we're lucky that we've got a couple of members of staff who are HLTAs so can soap in and do some cover. And we're kind of felt a bit of a responsibility at the same time to not reach out to supply teaching as much. I guess in the early stages we were like don't necessarily want new staff coming into the school we don't want to put them at risk we don't want to put our community at risk. So it was like a real, it was like a moral decision isn't it to decide whether we're going to try and bring somebody else in to help piece staff shortages in school or whether we're going to close the doors and keep outsiders out you know what I mean. So we've tried to use as much cover as possible we've used goodwill of staff a lot of the time where you're losing that extra member of staff in your class. And as Alicia has just said, you know that's also impacting on our children from those, you know, the income families, or SCN children and things like that who've got this designated support. It's been really hard. And there's never been a case where I felt that we've done everything right, had to make sacrifices. You know I had a teaching assistant full time, and then for a number of months because of various cover one after the other, after the other. I lost my support so I was teaching solo, and as a deputy head and Senko, you know that's going to have an impact on me so I'm working more, more into the, you know into the afternoons in the evenings because I've got so much stuff to do because I've missed my, my leadership time. So we've been looking really for whatever we can to try and pull back some of that control and make sure that the learning still take place and make the staff are feeling valued. We've tried our best to scrap direct time for an extended period of time so staff have got a little bit more freedom to leave a bit earlier after school is a bit of a wellbeing boost. We've pulled in things and I know we'll go on to talk about more, pulling things like learning by questions that is a bit of a time to it's a massive time saver in terms of planning and assessment and ensuring that that learning is still taking place. We've really had a box clever and it's not, it's not been easy and it's still not easy, but you know that the whole time there's a few things at play. The kids have missed out on a lot. You said that some of the, you know, my year sixes didn't have a full year of school since year three. They've missed out a lot of learning. We've got a real catch up agenda recovery curriculum, whatever you want to call it. We need to make sure that's happening. We've got staff who are already on their knees because they've worked so hard and we've got, you know, we've got to look after them too if they've been through it. And then we've got the families who are really relying on us to understand the situation. Some of them are scared still. Some of them, you know, are worried about their children being passed even now two years on. Yeah, it's been in place really. I am so I know LBQ really well but maybe one or two people watching are not familiar with this as a potential solution to help with staff shortages keep learning going online as well as in school. Can you give us a little synopsis of what it is and what can it do. It's, it's basically, it's basically a complete teaching tool. So it's a bank of question sets which cover all different, you know, shapes and sizes lessons, particularly English maths and science and I can set a question set online to my kids. Click of a button. It'll distribute a code onto my screen. The children log on and whatever device they've got. We're lucky enough to be part of the shine project where we've got some tablets in our class that are specific for our learning by questions. The kids log on, take the code. They access this, you know, this question set. They work through at their own pace. They're given prompts are given little reminders itself. Tess has marked it moves them on at their own pace. And it gives me instant feedback through through my teacher screen so I can see who's doing well who's struggling who needs support and pause the lesson bring up on screen, use it as a teaching point. It is all encompassing. So I've got questions set already that are of a great standard of all different sort of levels and abilities. I've got access to the kids on a one to one level. And then it's got that instant feedback. So I know lbq and it's a fabulous bit of software. I think the best thing is one, it saves you marking to really holds kids to account and helps with their learning journey. And that immediate assessment that you get as a teacher on your dashboards just fabulous. And I know there's lbq kind of stuff in this session watching maybe they can correct me but last time I I believe 60 to 80,000 questions on their database I think at least maybe might be one or two off but it's a fun phenomenal resource so if you're not familiar with it do check it out. Sam what's pupil attendance been like for you at St beads. And although you've used lbq to support that and many other things and what's been your attendance like throughout the pandemic. And there was a massive day last Friday where I had full class for the first time this year. Which just sort of illustrates it and it's, it's kind of the theme throughout school. And I know the figures that Alicia was talking about earlier on would definitely, would definitely different dip and beneath that. That national figure. And I would say at its worst classes have had up to 16 children off at its best will probably only had one or two up in each class. So I've never, I had my past full for the first time last week in the schools never had all children in even on the first day. And opening in the 80s percentage wise, which is really, which is really sad. It reflects that national picture, I suppose. I'm going to come back to you Sam on lbq and preparing for sats and your thoughts on exams and stuff and I jumped back to Alicia. I guess schools struggle financially. We know budgets are not enough and we know a lot of schools have been picking up the flak for, you know, cover budgets, etc. I guess the question is when it comes to tablets and resources and what can shine do to support our schools could you tell people watching a little bit more about the kind of things that you can offer. Definitely. So, a few years ago shine awarded a grant to learning by questions for schools specifically in the Northeast, so that they can access learning by questions, and they've got sort of the funding to do that. So the grant allows schools in disadvantage areas to access the resources they need to take part in the project and to try using lbq. We've spoken about what lbq is it's an online tool which gives children question sets and then immediate feedback on how they've done. So obviously to be able to use that you need to have some kind of tablet or laptop or computer desktop computer the children can use. So our funding allows provides teachers with the, the, I think they're all tablets aren't they sorry. They're all tablets and the pupils can use and they provide some of the funding towards the lbq subscription as well. So there's some slots still available for schools in the Northeast to have this funding so that they can trial lbq, they get all the technology that they need. And so, yeah, again touch with school you don't think right I can get some money and when's the deadline. What do I need to do where I don't need to go any links anything like that you can share. You need to get in touch with not some keys but some way right who is currently hasn't got his screen on but you can get in touch with Sam. And Sam will be able to talk to you about whether or not you meet our criteria and yeah how you can move forward with that. Okay so we'll share the links in the ticket list if you've signed up to this to watch this live and people watch the link in the, the kind of details sorry Alicia. You know just the sooner those seven slots filled up the better from our point of view because we want kids to be accessing this, this great intervention as soon as they can. But we're certainly hoping that all of them will be filled up by the summer. So there you go so get some funding and some devices fantastic thank you Alicia. Thank you. No cost for schools managing your budget, you know, me my life as a kind of school leader and then evolving into a blog and seeing all these resources come my way and all these end tech solutions for years and then all through through the pandemic has been an explosion of them all. And we've all got a good understanding of how much the cost and what value they have and obviously we want to use things that we know will make a difference etc. I guess lots of questions how does lbq compared to other things that you use you know the kids the things that kids are logging into daily and you know is it good value for money. Yeah, and I'll start by saying just quickly that shine project, it was a revelation for us and it was so easy to go through the loop that we needed to go through to get on board with that so definitely if you're in the northeast. No, not at all and we haven't got time you know what it's like. Our email boxes inboxes are full of, as you said all of these solutions that are going to be the game changers that are going to save our time our money all of this stuff. And ultimately, if it doesn't stick, it's not going to work is it. And if it costs too much, we can't afford it. I'm learning my questions and again I don't work for them I'm just an advocate I started like many people do with with learning my questions I saw Mr booth on Twitter years ago telling me that it was brilliant. I did a little trial and before the sats one year. The kids loved it so automatically there was buying from them. It was saving me loads of time. It was getting me away from that for a couple years so I decided to sign up and just as it happened as I was going to sign up the time project had a space so we went through it. I'm going to try all of these different products, but, like I said, claim to be the next big thing. This is the cheapest of the products that we've signed up for and it's had the most impact, and they put it in simple terms. And like I said, the kids love it so it does become a daily thing. Like I've said before, it's saving me time it's saving the school money and it's it's really led to some great games with kids. Have you found yourself, you know, where you've had to you know collapsing classes and team teaching or in the whole you know that the usual scenarios. Yeah there's been different setups like that there was one scenario where I was waiting for PCR results. I was absolutely fit and well fine, but I couldn't be in school. But I knew that I needed to teach it was it was a fractions lesson and you did something before I came back to school the next day or the day after whenever these results came. And I knew that I could have learning by questions on I could set questions set from home. I emailed the code to my teaching assistant who's in the class to run the lesson. And I had the data so I knew that the next day that my lesson was fine.  And then it was like so I'm teaching this lesson on Monday. I don't know how they've put on until Thursday, but I've got to teach Tuesday and Wednesday in between. You just have to you have to change the way you do things and learn about questions let us do that because I had that instant feedback and I could plan, you know, plan accordingly. Are you are you now in a position where all your kids have access to a device at least in school. We're not the whole school where we're in a looking position where we've got lots of devices, but because of the learning by questions devices that we've got as part of the shame project. My class have got them, you know, all through the day every day. If you know sometimes you plan to use learning by questions and that's going to be the main party lesson sometimes it's like, oh my days they've flown through that task. They need to give them more learning by questions is then the tablets being there's been great. Sometimes you have some children that maybe need something slightly different and learning by questions and cut that in half. See as we haven't got the photo copy for another task. You know, one example was when I did start the fractions topic. I was doing this lesson on equivalent fractions and I sort of did my introduction as I've done for however many years I've been in Essex and had a couple of well I had many blank faces looking at me and I was like, I'm going to check what's going on here. And one of the children says, what are those numbers with the line in between? And I said, do you mean a fraction? I said, yeah. And I said, and I stopped from when I thought, right, the last full year in school was year three. Well, it will have had fractions introduced in a basic level. Yeah, therefore, they left halfway through fractions hadn't been taught the five teachers cloud so much effort into the basic skills that fractions probably being scraped on this stuff. Some of these year six kids haven't seen what a fraction was. And I had this worksheet that was the Essex level equivalent fractions. I thought, well, I can't give them back. Yeah, well, my son's in year six now and I know that, you know, you know, one example of millions of kids but he was he loved maths but he's a bit maths averse now to be fair because of that routine being destroyed in some respects. So that's the only question of preparing for sats and things like that, Sam. And how are you six, you know, let's ignore the thoughts about sats and all that. You know what what you're doing day in there to just get kids in a better place and you know that's that preparation, etc. What does all that look like. That's a massive advocate of not making schools factories and not plowing papers into them every five minutes. You know, yes they need to see what they look like and be comfortable with that before it gets to me but I'm all about giving them that experience in a nicer way. So the fact that the kids love learning by questions and love being on those devices and love having to go. It means that I can sort of feed practice without it being, you know, that formal sitting down answering the test paper type thing. And we've got sats boosters that we're having a breakfast club three days a week where it's volunteering the kids come in, we use learning by question to that really nice friendly environment where the kids enjoy being there. Yeah, we'll try to give them as diverse an experience as possible without, you know, plowing past papers in front of their face. And give me a sense of kind of your general staff, you know, I suspect staff are exhausted but I know teachers as ever are always up for the challenge and go above and beyond. What's the mood on the ground in your school. I'm really lucky to have staff that we have in school. Everyone's chipping in everyone's helping out interventions are happening, you know, all over the place. We're not doing it for that we're doing it for the kids we're doing it for the kids to be ready for the next step on their journey which is high school really. We've got a real understanding that lots of the kids in our area, possibly suffered more than more than others in that, you know, we have got lots of low income families who didn't access much through the first lockdown, needed devices sent to them that maybe took a little bit longer than they should have done. You know, that's by the by. But yeah, there's a real atmosphere in this school that we're a community that, you know, the kids come first and we need to do all we can for them. Often, you know, you know what teachers are like, we often put others before ourselves, don't we, the expense of our wellbeing and we'd never make that a directive to staff but it's definitely what they're trying to do. I'm going to bring a listen but Sam I'm going to come back to you and ask you just for just general well being things that you've done to support your staff but Alicia, you're aware of what St Beads is doing with the funding for LBQ devices. You know, maybe not saying any names particular schools but could just give us a general picture of what you see from your side in terms of how other people have used your funding how they've deployed resources how they're dealing with the same challenges. And do you mean specifically with LBQ or general things that you do with shine but you know maybe you've got one or two LBQ examples also but I'm not not in particular but if you have them even better. Hello. So actually, before I took the job at shine, I worked for a charity called the Institute for Effective Education. And we also had a link with LBQ and ransom ransom projects where people evaluated using LBQ in different ways. A lot of them were disrupted by the pandemic they started sort of in 2019 and so they didn't necessarily finish, but people used it in, in lots of different sorts of ways so some people used it specifically to target the transition to make sure that things were consistent between schools and some people used it as sort of making sure that once kids got to year seven that they knew where all the kids were and where the gaps were and the kids from different primary schools could then be sort of caught up if they haven't done a bit or made sure that everyone was engaged so it was used for sometimes for transition. In some cases it was used to focus on a really specific skills so one school really sort of was thinking about how best to help kids have really good recall of times tables, and they were trialling various different options and LBQ was one of them. So yeah there's loads of different ways that schools that I've been engaged with, both at Shine and previously at the IEE have a view Shine, sorry LBQ. And before I come back to Sam, have you seen any great kind of wellbeing or reducing you know support and staff with the attendance or absence, you know those types in your kind of view in Shine Trust anything. Presumably more broadly than LBQ. Yes, just general good practice or things that I think oh that's a great idea. So for, I'm putting it on the spot so don't worry.  Now I'm just trying to think of all of our different projects because they all do fantastic things. I think that the schools that we work with generally are really thinking about how they support their staff and how they support wellbeing. And people have done, yeah various different things I suppose that it depends on your staff and how you, what people need and what people want at the time. So, Sam, you know, what kind of things have you done so I was at my son's school yesterday as a parent governor and we were, I was actually in the school this morning, talking to them about their or they were talking to me more about their wellbeing solutions their staff policies that how they've adapted the marking policy online assessment tools their email culture, the whole kind of shebang I suppose. So what kind of things have you done throughout the pandemic to support your staff support and teaching staff mental health. Yeah, lots of the things you say in there.  We thought really carefully about staff meetings and how, how, how we could sort of change the focus of some of those make some of them more online. If there's a webinar type format or a prerecorded format just, you know, aware of people's time. We introduced PBA from home. If I wanted to do that, I had that time and space to get away. We were looked in particular classes that have been really hard hit, and we employed extra support staff. As much to support the kids but also possibly, you know, share the workload a little bit actually employed an extra teacher so that we could cover some more PBA and give some more leadership time to, you know, to dedicate the intervention and catch up as well. Yeah, we've just tried, like I say, we were in a position where our budget was quite strong so we could do that and also supply staff just like most of us. Yeah, it has been a struggle. And again, I said to you before we're tackling that issue of whether we thought that was the right thing for us and our kids. So what we did was we ended up removed some of the teaching assistants and dedicated them just to intervention, and so that the classes were slightly smaller, increased roles and contracts of some of our staff already so they have the ability to cover classes. We just tried to use our staff as best we could. We did end up needing to apply in the end and that was a struggle and finding the right staff as well was a struggle. So I guess we kind of thought our staff knew our kids best, their best place to support them so that's where we're going to start. Yeah, it's been the fault for many. So people watching live, here's an opportunity to either pose a question in the chat box it will come to me only or if you're confident, unmute yourself and fire a question to Alicia or to Sam so I'll give you an opportunity to do that now. Thank you, makers. And Alicia, can I just pop back to you. Oh, here we go. Yes, Dave, please question. Oh, come on. Oh, yeah, there I am. It's about music. Actually, I'm the director of North East Music Foundation. So we supply Perris into schools. I just wanted to know how schools are coping with the music provision of the found we found out there's a sort of reluctance for schools to put music back on. I don't know if that's because there's a lack of teachers teaching specialists out there. Let's hear what Sam, how's your music curriculum been throughout the pandemic. I think I think you're right, Dave. I think it has definitely suffered lots of the arts have suffered the hardest things I guess to teach remotely. And we've got we have gone down the line of we're actually we've increased the amount of music we're teaching now because we're aware that you know there's been a real deficit of that same with PA and we've increased the amount of sport to get the children as active as possible. But I know from what I've heard, especially schools in our local area, there has been a shortage of shortage of teachers. And I guess, as I said before, about some of that reluctance of letting other people come into school, I know they're perfectly sometimes that's been a bit of a battle too. But yeah, we're going along the lines now with we've got a job to sort of pay back what what we've missed out on. And but I know not all schools are in that same position. Any any insights from your side. Our projects really focus on reducing the attainment gap between English math and in English math and science so music isn't a major focus for us, although quite a few of our earliest projects do use, use creative subjects to improve school readiness. So we certainly used to, even if we don't anymore, have a project that used music to music workshops with parents to improve speech language and communication and school readiness in lots of different areas. David, as you're probably aware, you know, the, I guess the earlier COVID guidance with bubbles and people being restricted to use practical spaces such as music technology classrooms. Yeah, of course. Obviously, would have hindered your resources and your your interventions that you normally give back to school. So I would say if the, you know, the guidance is slightly different and the vaccines are all out and things like that we might be in a better place where you're starting to see a little bit more traffic your way but maybe gives a picture of, you know, the stuff that you do and support and you know your your general sense of the world at this stage. Yeah. We're just bringing around schools and trying to get music back in to sort of help schools with the music provision really if we can. And like we're just finding that it was a lot quite reluctant to get the back in, you know, with the restrictions. Here's your chance. Give yourself a plug. What website or company are we looking at here? It's North East Music Foundation. North East Music Foundation. So there you go. And website address. www.northnemf.co.uk.  Yeah, if you could. And the other thing I'd like to just mention that we've also been developing a music resource for the last three years or something. We'll just get a little bit of fun from the Arts Council recently just to help with this. We'll find it really hard to sort of get into schools to get this out there. But the schools that are using it, they find it absolutely fantastic in terms of accelerated learning stuff. Follows around the Rosenstein principles that you talk about a lot. You know, revisit them, the learning and small chunks and everything. Yes. We'll be able to do it quite late. It's like a video resource. We would like schools to sort of trial it out at least. Yeah. And also we'd like you open. Sorry. I'd like you to have a look at Ross and see what you're looking at. All right. Let's talk offline, but I want to kind of keep on top of that. That's okay. Yeah, no problem. I think that would certainly help schools in terms of like whole class ensemble teaching. We've got like a resource that really helps with that. So we'll give you a shout out. If you put the link Dave in the chat box, I'll read it out just at the end. But yeah, the kind of synopsis of all the state of the nation has been, you know, practical subjects, particularly creatives and your scientists, I suppose, had all of a bit of a knock on the head in the earlier stages of the pandemic. Hopefully things are opening up a little bit now. I have a question in the chat box. Thank you, Dave, for Alicia and Sam. What is the criteria for assessing the shine fund in Alicia? And is it related to pupil premium numbers? Generally speaking, yes. So our remit as a charity is to improve outcomes for children from low income families. So the projects that we fund are nearly always working in schools, which have higher than average pupil premium numbers. If you are a school that's got quite low pupil premium numbers, but you've got an amazing idea would be really happy to work with you. But we would need to talk to you about how you could deliver that or scale that to schools which are in more disadvantaged areas. Okay, so great. Thank you. And I might have lost track of my questions, Alicia. But did I ask you for the seven slots? So is there a particular deadline for those slots? Or is it just seven funding slots to fill? There's seven funding slots to fill once they're gone. So the deadline is open until the last slot's gone. Yeah, we're hoping to get them filled by the summer though.  So there's your last chance. I'm going to start to wrap things up. So Dave, just a reminder, if you can put your web link in the chat box, I'll give you a shout out. And in the chat box earlier, I put a link to LBQ. You can log in. I know and have a free trial and play with some of their quizzes and questions and look at their tools. There's obviously the paid full side. And there's all the kind of sets preparation that you can look at there in terms of resources. So I'll put that link in the chat box again for everyone you've heard from Sam. I think that my takeaway message from you Sam was, you know, a low cost high impact. Yeah, absolutely. And especially schools and staffing in the Northeast. If you want to see it in action and more than we're going to show you, you know, as restrictions sort of lesson, you're more than welcome to come and see it in action in our school. But there you go. So there's a, there's an invite to and I'm up in Durham soon it's probably a little bit away from Newcastle. But yeah, once I get back up in the Northeast, I'll come in and pop in Sam on my travels and say hello but I'm going to start to bring things to a formal conclusion. And people watching live if you've got any other questions that you're burning to ask. This is your last opportunity. Okay, last chance last chance.  And so we've been talking about staff shortages, managing absences, digital devices, ed tech solutions that make a difference. Plug in LBQ again, as a solution obviously got the shine trust funding for schools schools are always looking for a bit of funding Alyssa can you reassure me that the paperwork is not too laborious for school leaders. So we really try to make things easy that shine. As some said, the application process is as smooth as we can make it for the LBQ grants, but also for our grants more generally we, we know how busy teachers are. So we try to make things and if I can give you some analytics from my website 70 seconds is the average reading time from 16 million teachers so there you go so 70 seconds is about 450 words. The application forms are short and punchy or your one page policy Sam, 450 words, then you're on to a winner. And there's that link from Dave so thank you Dave so www.add, add, add notes, a DD. That that's actually the reason what's got the resources code where you can get the website covers both companies if you like. Okay, I'll share that and circulate it through the ticket and put it online. So wrap things up there everybody and thank you for your precious time thank you to Alicia for your insights from shine and from free funding what's not to like there and to Sam. On the front line working tirelessly and a new dad to and I hope you've mastered the nappies. I hope you're enjoying fatherhood and Alicia as well and me and in Yorkshire now enjoying the, the, the wonderful outdoors. And so I'm going to leave it there on behalf of lbq. My name is Ross bill been your host, and I've been joined by the delightful Sam keys and Alicia sure. And thanks for watching keep well keep safe and see you again in the future bye for now.