Implementation of Probabilistic Classifiers from Scratch

Built and validated three fundamental probabilistic classifiers from scratch to solve multi-class classification problems. This project showcases a deep understanding of Bayesian inference.

Derived binary and multiclass Gaussian classifiers (LDA/QDA variants) incorporating asymmetric loss matrices, achieving 3% error on 4-class data and 0-13.5% on binary, with quadratic boundary plots outperforming baselines by 72% on correlated features.

Multiclass Bayes classifier

(Final Results)

Computed ML parameter estimates and risk-minimizing decisions, analyzing covariance assumptions' impact via confusion matrices, for robust pattern recognition in low-data scenarios.

Binary Bayes classifier

**(**Final Results)

Bayesian Regression

Built Bayesian regression with Gaussian conjugates, visualizing prior/posterior contours for 8 hyperparameter sets (means 0/5, variances 1/10), showing variance shrinkage with sample increase (4 to 400).

Prior Distributions

Posterior Distributions

Unsupervised Learning: Clustering Algorithms

Implemented two clustering algorithms, DBSCAN and Spectral Clustering, from scratch to identify clusters in datasets with complex, non-linear structures where traditional algorithms like K-Means would fail.