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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
Step4:  ```
In this toy example, 
we want to see what are the baselines of prediction accuracy based on extremes scenarios of input signals.
We study two distinct cases
Step5:  a) Example with All probabilities 50 - 50  (input signal = noise)
Step6:  b) Example with some clear input singnal
Step7:  Example with some clear input singnal half noise
Step8:  We assume that there are 3 differnt values for dependent variable
Step9:  We have 4 categories for dependent var
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Python Code:
import pandas as pd
import numpy as np
def get_features_values_combinations(list_a, list_b):
     Returns a list of combinations of the values of 
    e.g. from the lists 
    list_a = ['L', 'M', 'W']
    list_b = ['F', 'I', 'S']
    we get the combinations:
    [('L', 'F'), ('L', 'I'), ('L', 'S'), ('M', 'F'), ('M', 'I') ...
    
    import itertools
    return list(itertools.product(list_a, list_b))
def generate_dataset_with_probabilities(n_datapoints,
                                        x_values,
                                        y_values,
                                        y_probabilites=None):
     Return a dataset of given possible values with given possible probabilities
    :n_datapoints: The number of datapoints we want to generate
    :x_values: 1-D array e.g. ['Man', 'Woman']
    :y_values: 1-D array e.g. ['meat', 'fish', 'vegetables']
    :y_probabilites: 1-D array-like e.g. [0.5, 0.25, 0.25]
        The probabilities associated with each entry in entries_values.
        If not given the sample assumes a uniform distribution over all entries_values
    
    import numpy as np
    datapoints = []
    for i in range(n_datapoints):
        datapoint = []
        datapoint = (x_values,) + (np.random.choice(y_values, p=y_probabilites),)
        datapoints.append(datapoint)
        
    return datapoints
def generate_datapoints(n_datapoints, var_x, var_y, case_probabilites):
    
    
    # Generate the datapoints according to the desired destribution
    datapoints = []
    all_cases = get_features_values_combinations(var_x, var_y)
    n_cases = len(all_cases)
    n_datapoints_per_case = int(1. * n_datapoints / n_cases)
    for case in all_cases:
        sex = case[:-1][0]
        case_probabilites = cases_probabilites[sex]
        datapoints.extend(
        generate_dataset_with_probabilities(n_datapoints_per_case,
                                            sex, 
                                            var_y,
                                            y_probabilites=case_probabilites))
    N_datapoints = len(datapoints)
    print "All the combinations we can have are: ", all_cases
    print "N total datapoints: ", N_datapoints
    return np.array(datapoints)
def get_transformed_dataframe(df):
     Transform the DataFrame accordinlgy (dummy vars / encoding)
    
    # And transform the categorical variables
    from sklearn import preprocessing
    df_transformed_X = pd.get_dummies(df[var_x_name])
    encoder = preprocessing.LabelEncoder()
    encoder.fit(df[var_y_name].values)       
    df_transformed_y = pd.DataFrame(data = encoder.transform(df[var_y_name].values), columns=[var_y_name])
    df_transformed = pd.concat([df_transformed_X, df_transformed_y], axis=1)
    df_transformed.head(2)
    return df_transformed
# Independent Variable
var_x_name = 'sex'
var_x = ['Man', 'Woman']
# Dependent Variable
var_y_name = 'status'
var_y = ['Died', 'Alive']
Explanation: ```
In this toy example, 
we want to see what are the baselines of prediction accuracy based on extremes scenarios of input signals.
We study two distinct cases:
a) The input is just noise
b) The input hides a clear signan (smoking affects men and die while not affects women)
We want to see how the model reacts on such conditions
```
End of explanation
# We assume that we do not have any strong signal in our input
# e.g. for men smoking or not 50% diy
# the same for women
cases_probabilites = {
    'Man' : [0.5, 0.5],
    'Woman' : [0.5, 0.5]}
datapoints = generate_datapoints(1000, var_x, var_y, case_probabilites)
# Cross check that the datapoints we generated follow the frequency we thought
all_cases = get_features_values_combinations(var_x, var_y)
for case in all_cases:
    print "Frequency of ", case, ": ", 1. * len([x for x in datapoints if tuple(x.tolist()) == case]) / len(datapoints)
    
df = pd.DataFrame(data = datapoints, columns=[var_x_name, var_y_name])
df_transformed = get_transformed_dataframe(df)
# Split our sample to train / set
from sklearn.model_selection import train_test_split
X = df_transformed[['Man', 'Woman']].values
y = df_transformed['status'].values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
# Apply model
from sklearn import  linear_model
logistic = linear_model.LogisticRegression()
print('LogisticRegression score: %f'
      % logistic.fit(X_train, y_train).score(X_test, y_test))
Explanation: a) Example with All probabilities 50 - 50  (input signal = noise)
End of explanation
# Here we assume that Men are affected a lot from smoking 90% die while women not, only 10% die
cases_probabilites = {
    'Man' : [0.9, 0.1],
    'Woman' : [0.1, 0.9]}
datapoints = generate_datapoints(1000, var_x, var_y, case_probabilites)
# Cross check that the datapoints we generated follow the frequency we thought
all_cases = get_features_values_combinations(var_x, var_y)
for case in all_cases:
    print "Frequency of ", case, ": ", 1. * len([x for x in datapoints if tuple(x.tolist()) == case]) / len(datapoints)
    
df = pd.DataFrame(data = datapoints, columns=[var_x_name, var_y_name])
df_transformed = get_transformed_dataframe(df)
# Split our sample to train / set
from sklearn.model_selection import train_test_split
X = df_transformed[['Man', 'Woman']].values
y = df_transformed['status'].values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
# Apply model
from sklearn import  linear_model
logistic = linear_model.LogisticRegression()
print('LogisticRegression score: %f'
      % logistic.fit(X_train, y_train).score(X_test, y_test))
Explanation: b) Example with some clear input singnal
End of explanation
# We assume that we do not have any strong signal in our input
# e.g. for men smoking or not 50% diy
# the same for women
cases_probabilites = {
    'Man' : [0.5, 0.5],
    'Woman' : [0.5, 0.5]}
datapoints = generate_datapoints(1000, var_x, var_y, case_probabilites)
# Cross check that the datapoints we generated follow the frequency we thought
all_cases = get_features_values_combinations(var_x, var_y)
for case in all_cases:
    print "Frequency of ", case, ": ", 1. * len([x for x in datapoints if tuple(x.tolist()) == case]) / len(datapoints)
    
df = pd.DataFrame(data = datapoints, columns=[var_x_name, var_y_name])
df_transformed = get_transformed_dataframe(df)
# Split our sample to train / set
from sklearn.model_selection import train_test_split
X = df_transformed[['Man', 'Woman']].values
y = df_transformed['status'].values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
# Apply model
from sklearn import  linear_model
logistic = linear_model.LogisticRegression()
print('LogisticRegression score: %f'
      % logistic.fit(X_train, y_train).score(X_test, y_test))
Explanation: Example with some clear input singnal half noise
End of explanation
var_y = ['Died', 'Alive', 'Almost_dead']
cases_probabilites = {
    'Man' : [0.333, 0.333, 1-0.333-.333],
    'Woman' : [0.333, 0.333, 1-.333-.333]}
datapoints = generate_datapoints(10000, var_x, var_y, case_probabilites)
# Cross check that the datapoints we generated follow the frequency we thought
all_cases = get_features_values_combinations(var_x, var_y)
for case in all_cases:
    print "Frequency of ", case, ": ", 1. * len([x for x in datapoints if tuple(x.tolist()) == case]) / len(datapoints)
    
df = pd.DataFrame(data = datapoints, columns=[var_x_name, var_y_name])
df_transformed = get_transformed_dataframe(df)
# Split our sample to train / set
from sklearn.model_selection import train_test_split
X = df_transformed[['Man', 'Woman']].values
y = df_transformed['status'].values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
# Apply model
from sklearn import  linear_model
logistic = linear_model.LogisticRegression()
print('LogisticRegression score: %f'
      % logistic.fit(X_train, y_train).score(X_test, y_test))
Explanation: We assume that there are 3 differnt values for dependent variable
End of explanation
var_y = ['Died', 'Alive', 'Almost_dead', 'Almost_alive']
cases_probabilites = {
    'Man' : [0.25, 0.25, 0.25, 0.25],
    'Woman' : [0.25, 0.25, 0.25, 0.25]
}
datapoints = generate_datapoints(10000, var_x, var_y, case_probabilites)
# Cross check that the datapoints we generated follow the frequency we thought
all_cases = get_features_values_combinations(var_x, var_y)
for case in all_cases:
    print "Frequency of ", case, ": ", 1. * len([x for x in datapoints if tuple(x.tolist()) == case]) / len(datapoints)
    
df = pd.DataFrame(data = datapoints, columns=[var_x_name, var_y_name])
df_transformed = get_transformed_dataframe(df)
# Split our sample to train / set
from sklearn.model_selection import train_test_split
X = df_transformed[['Man', 'Woman']].values
y = df_transformed['status'].values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
# Apply model
from sklearn import  linear_model
logistic = linear_model.LogisticRegression()
print('LogisticRegression score: %f'
      % logistic.fit(X_train, y_train).score(X_test, y_test))
Explanation: We have 4 categories for dependent var
End of explanation
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