Coding Challenge 187: Bayes Theorem

The Galaxy Book Probability Example

In a library where 1% of books are sci-fi (80% containing "galaxy") and 99% are non-sci-fi (5% containing "galaxy"), the probability that a random book with "galaxy" in the title is sci-fi is only 13.9%, not 80%.

Prior Probability Importance

The prior probability (base rate) of a category is essential to accurate calculations—ignoring that only 1% of books are sci-fi leads to massive overestimation of classification likelihood despite strong correlation with keywords.

The Mathematical Formula

Bayes Theorem calculates P(Sci-Fi|Galaxy) = P(Galaxy|Sci-Fi) × P(Sci-Fi) / P(Galaxy), where the posterior probability depends on both the likelihood of evidence and the prior probability of the hypothesis.

Bag of Words Approach

Text classification treats documents as unordered collections of words, calculating probabilities based solely on word frequencies while ignoring grammar, syntax, and word order.

The Naive Independence Assumption

The algorithm assumes all word probabilities are independent events (unlike reality), allowing the system to multiply individual word probabilities together to calculate the likelihood of an entire document belonging to a category.

Multi-Category Application

The classifier can evaluate multiple genres simultaneously (romance, thriller, sci-fi) by comparing calculated probabilities to determine the most likely category for new incoming text.

Browser-Based Architecture

The entire algorithm runs in a p5.js sketch without GPUs, cloud servers, or pre-trained models, demonstrating that effective text classification requires minimal computational resources.

Frequency Data Structures

The implementation uses JavaScript objects to track word frequencies, maintaining both global word counts across all documents and per-category counts to enable Bayesian probability calculations.

Text Processing Pipeline

The training function converts text to lowercase, splits words using regex (matching non-word characters), and increments counters for each word-category combination to build the probabilistic model.