Simple Random Sampling vs Thompson Algorithm

q3

# Question 3

# Import the libraries
import numpy as np
import pandas as pd

# Recreate the dataset function
def recreate_dataset(set_size, conversion_ratios):
    import random
    
    dataset = [[0]*len(conversion_ratios) for _ in range(set_size)]
    dataset_idx = list(range(set_size))
    for i in range(0, len(conversion_ratios)):
        conversion_ratio = conversion_ratios[i]
        
        random.shuffle(dataset_idx) # randomly shufle the dataset index
        # and select the required number of indeces from the begining
        random_idx = dataset_idx[0:round(set_size * conversion_ratio)] 
        
        # change the values of the dataset to 1 for the random index
        for idx in random_idx:
            dataset[idx][i] = 1
        
        # reduce the dataset index to exclude previously selected indeces
        dataset_idx = [e for e in dataset_idx if e not in random_idx]
    
    return dataset

# Simple random sampling function
def simple_random(dataset):
    N = len(dataset)
    d = len(dataset.columns)
    
    from random import randint
    
    random_selections = []
    random_matches = []
    for n in range(0, N):
        random_selection = randint(0,d-1)
        random_selections.append(random_selection)
        if dataset.loc[n, list(dataset)[random_selection]] == 1:
            random_matches.append(random_selection)
        else:
            random_matches.append(None)
    
    all_selections = []
    numbers_of_rewards_1 = []
    for n in range(0,len(conversion_ratios)):
        all_selections.append(len([selection for selection in random_selections if selection == n]))
        numbers_of_rewards_1.append(len([selection for selection in random_matches if selection == n]))
    
    
    return [numbers_of_rewards_1, all_selections]
    
# Thompson sampling function
def thompson(dataset):
    N = len(dataset)
    d = len(dataset.columns)
    
    import random
    
    thompson_selections = [0] * d
    numbers_of_rewards_1 = [0] * d
    numbers_of_rewards_0 = [0] * d
    
    total_reward = 0
    for n in range(0, N):
        variant = 0
        max_random = 0
        for i in range(0, d):
            random_beta = random.betavariate(numbers_of_rewards_1[i] + 1, numbers_of_rewards_0[i] + 1)
            if random_beta > max_random:
                max_random = random_beta
                variant = i
        
        thompson_selections.append(variant)
        reward = dataset.values[n, variant] 
        if reward == 1:
            numbers_of_rewards_1[variant] = numbers_of_rewards_1[variant] + 1
        else:
            numbers_of_rewards_0[variant] = numbers_of_rewards_0[variant] + 1
        total_reward = total_reward + reward
    
    all_selections = [sum(x) for x in zip(*[numbers_of_rewards_1,numbers_of_rewards_0])]
    return [numbers_of_rewards_1, all_selections]

# Set parameters
variant_names = ['baseline','variant1','variant2','variant3','variant4']    
views = [595, 599, 622, 606, 578]
quotes = [32, 30, 18, 51, 38]
conversion_ratios = [quotes[i] / views[i]  for i in range(0, len(views))]

# Recreate dataset
dataset = recreate_dataset(30000, # total 
                           conversion_ratios,
                           )
dataset = pd.DataFrame(dataset, columns = variant_names) # convert to Pandas dataframe and add headers
all_quotes = dataset.sum()


# Run Simple Random Sampling algorithm
random_selections = simple_random(dataset)

# Run Thompson Sampling algorithm
thompson_selections = thompson(dataset)