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🎯 Probability Theory in Hyperparameter Optimization

A live Gaussian-process surrogate model over a 2D hyperparameter landscape, showing how Bayesian optimization uses probability and uncertainty to choose the next hyperparameter trial.

AI & Machine Learning3DAdvanced60 FPS

A Gaussian-process surrogate model builds a live probability distribution over an unknown validation-accuracy landscape, then an acquisition function decides — using both predicted performance and uncertainty — exactly which hyperparameters to try next.

🔬 What It Demonstrates

Each trial (learning rate, regularization pair) updates a Bayesian posterior mean and variance over the whole 2D hyperparameter grid. Colour encodes uncertainty; the Upper Confidence Bound acquisition function trades off exploiting known peaks against exploring uncertain regions.

🎮 How to Use

Adjust the kernel length-scale, exploration weight κ, and observation noise, then click "Sample suggested point" to run a Bayesian-optimization trial, or "Random trial" to compare against blind search. Toggle the true landscape and acquisition surface to see how the surrogate compares.

💡 Did You Know?

Because a Gaussian process gives a full predictive distribution — not just a point estimate — Bayesian optimizers like the ones in Optuna and Ax can find near-optimal hyperparameters in a fraction of the trials that grid or random search would need.

⚙ Under the hood

A live Gaussian-process surrogate model over a 2D hyperparameter landscape, showing how Bayesian optimization uses probability and uncertainty to choose the next hyperparameter trial.

bayesian optimizationhyperparameter tuningprobabilitygaussian processsurrogate modelmachine learningThree.js

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install