Visualizing Naive Bayes

In this lab, we will cover an essential part of data analysis that has not been included in the lecture videos. As we stated in the previous module, data visualization gives insight into the expected performance of any model.

In the following exercise, you are going to make a visual inspection of the tweets dataset using the Naïve Bayes features. We will see how we can understand the log-likelihood ratio explained in the videos as a pair of numerical features that can be fed in a machine learning algorithm.

At the end of this lab, we will introduce the concept of confidence ellipse as a tool for representing the Naïve Bayes model visually.

import numpy as np # Library for linear algebra and math utils
import pandas as pd # Dataframe library

import matplotlib.pyplot as plt # Library for plots
from utils import confidence_ellipse # Function to add confidence ellipses to charts

Calculate the likelihoods for each tweet

For each tweet, we have calculated the likelihood of the tweet to be positive and the likelihood to be negative. We have calculated in different columns the numerator and denominator of the likelihood ratio introduced previously.

$log \frac{P(tweet|pos)}{P(tweet|neg)} = log(P(tweet|pos)) - log(P(tweet|neg))$
$positive = log(P(tweet|pos)) = \sum_{i=0}^{n}{log P(W_i|pos)}$
$negative = log(P(tweet|neg)) = \sum_{i=0}^{n}{log P(W_i|neg)}$

We did not include the code because this is part of this week's assignment. The 'bayes_features.csv' file contains the final result of this process.

The cell below loads the table in a dataframe. Dataframes are data structures that simplify the manipulation of data, allowing filtering, slicing, joining, and summarization.

data = pd.read_csv('bayes_features.csv'); # Load the data from the csv file

data.head(5) # Print the first 5 tweets features. Each row represents a tweet

# Plot the samples using columns 1 and 2 of the matrix

fig, ax = plt.subplots(figsize = (8, 8)) #Create a new figure with a custom size

colors = ['red', 'green'] # Define a color palete

# Color base on sentiment
ax.scatter(data.positive, data.negative, 
    c=[colors[int(k)] for k in data.sentiment], s = 0.1, marker='*')  # Plot a dot for each tweet

# Custom limits for this chart
plt.xlim(-250,0)
plt.ylim(-250,0)

plt.xlabel("Positive") # x-axis label
plt.ylabel("Negative") # y-axis label

Text(0, 0.5, 'Negative')