Optimization
Bayesian Optimization: Learning Where to Evaluate Next
Gaussian-process conditioning, expected improvement, and a finite-domain GP-UCB regret bound, with reproducible Python examples.
Blog
Optimization
Convex Optimization III: A Reference to Convex Functions
Convexity properties and derivatives of common losses, norms, and penalty functions.
Optimization
Convex Optimization II: Duality and KKT Conditions
Lagrangian duality, KKT conditions, and worked examples of constrained convex optimization.
Optimization
Convex Optimization I: Convexity and Examples
First- and second-order criteria for convexity, with worked examples.
Statistical Models
Support Vector Machine
Maximum-margin classification, hinge loss, kernels, and primal-dual formulations.
Statistical Properties and Proof Tools
Conditional Expectation under Squared-Error Loss
Conditional expectation as the minimum mean squared-error predictor, with proof and applications.
Statistical Models
Multinomial Logistic Regression
Softmax probabilities, likelihood derivations, and estimation for multiclass outcomes.
Statistical Models
Binary Logistic Regression
Modeling binary outcome probabilities through likelihood estimation and Bayesian inference.
Statistical Models
Bayesian Linear Regression
Posterior inference and prediction in linear regression with Gaussian and Laplace priors.
Statistical Models
Linear Regression
Least squares, likelihood estimation, and ridge, lasso, and elastic-net regularization.
Linear Algebra & Matrix Calculus
Vector and Matrix Derivatives
Gradients, Jacobians, and matrix derivatives, with dimension conventions and worked formulas.
Linear Algebra & Matrix Calculus
Linear Algebra Essentials
Matrix identities for inverses, determinants, and traces, with common matrix decompositions.