Ducati's blog

Proof of the Strong Law of Large Numbers (SLLN) using Kronecker's lemma, Kolmogorov's maximal inequality, and Khinchine-Kolmogorov convergence theorem.

We provide an easy-to-understand proof of the No Free Lunch Theorem, along with a discussion on why it doesn't contradict the success of machine learning in practice.

Proof of the Weak Law of Large Numbers (WLLN) and its generalization, which relaxes the finite expectation condition to a milder tail condition. The proof employs Chebyshev's inequality to establish convergence in probability.

A detailed explanation of the Stochastic Variance Reduced Gradient (SVRG) algorithm and its convergence analysis (linear convergence rate under strong convexity and smoothness assumptions).

A detailed proof of Tonelli's and Fubini's theorems for product measure spaces, including preliminaries (e.g., Carathéodory's extension theorem) and a step-by-step proof with the traditional bootstrapping approach.

The characteristic polynomials of AB and BA are related by a simple formula.

A note on normal, self-adjoint and unitary operators and matrices.

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An overview of generalized linear models(GLM) and their applications.