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Thoughts, tutorials, and insights about web development, technology, and more.

9/14/2025
5 min read

EM-Vectorization

The EM algorithm for the two-coin problem estimates the biases of two coins when outcomes are mixed and unlabeled. Vectorization replaces nested loops with matrix operations, letting PyTorch handle $[B, N]$ computations in parallel. The E-step assigns soft probabilities (responsibilities) of each outcome belonging to coin A or B. The M-step updates the coin biases, and the best initialization is chosen via log-likelihood maximization.

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9/7/2025
7 min read

Uncovering Hidden Clusters: A Hands-On Guide to the EM Algorithm for Gaussian Mixture Models

Unsupervised clustering is a fundamental problem in machine learning: how can we find meaningful groups in data without any pre-existing labels? A powerful answer to this is the Gaussian Mixture Model (GMM), which assumes that the data is generated from a mix of several Gaussian (or normal) distributions. The challenge, however, is to find the parameters of these hidden distributions.

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9/5/2025
5 min read

A Basic Approach to the Expectation-Maximization Algorithm

In machine learning, the EM algorithm is a fundamental tool for unsupervised learning. It is the core mechanism behind clustering algorithms like Gaussian Mixture Models (GMMs) and is used in various fields, from natural language processing to computer vision, for problems involving missing data.

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