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Gaussian Processes & Bayesian Optimization
# Description
Gaussian Processes (GP) for regression and Bayesian Optimization (BO) for efficient optimum search, implemented in Python with scikit-learn. Part 1: GP Regression with calibrated uncertainty (+-1sigma, +-2sigma), RBF kernel optimized via maximize log-marginal-likelihood, 8 training points producing a full predictive distribution with confidence bands. Part 2: Comparison of 4 kernels -- RBF (isotropic, smooth, single length-scale), Matern nu=2.5 (semi-flexible, 2x differentiable), Matern nu=1.5 (rougher, 1x differentiable) and RationalQuadratic (mixture of length-scales). Part 3: Bayesian Optimization with Expected Improvement (EI) acquisition function, BO loop of 25 iterations (model, acquire, evaluate, update) converging to the global minimum. Part 4: BO vs Random Search vs Grid Search comparison over 30 evaluations -- BO converges faster to the minimum. Part 5: Real-world application tuning RandomForest hyperparameters (Wine dataset) -- n_estimators x max_depth x min_samples_split space, 20 BO iterations achieve Accuracy 0.9607 vs 0.9606 (default RF). 5 visualizations.
# Key features
$ Gaussian Process Regression with calibrated uncertainty (+-1sigma, +-2sigma) and RBF kernel optimized via maximize log-marginal-likelihood
$ Comparison of 4 kernels: RBF, Matern (nu=2.5 and nu=1.5) and RationalQuadratic -- each with distinct smoothness properties
$ Bayesian Optimization with Expected Improvement (EI): 25-iteration loop converging to the global minimum in black-box function
$ BO vs Random vs Grid Search: BO converges faster to the minimum with only 30 evaluations
$ Real-world application: BO to tune RandomForest hyperparameters (n_estimators, max_depth, min_samples_split) -- Accuracy 0.9607 on Wine dataset
$ 5 visualizations: GP with uncertainty, kernel comparison, acquisition and BO progress, convergence comparison, and parameter space
# Gallery
# Technologies used
