Math

An image is blurred out via a convolution, and then recovered via Wiener deconvolution. Notice the horizontal artifacts in the recovery, likely due to mismatching assumptions.

Understanding Wiener Deconvolution

Direct derivation, interpretation of assumptions, characterization of error bounds and code with examples

DEC 28, 2021
categories: PROOFS
tags: ALGEBRA, CALCULUS, COMPUTER VISION, CONVEX OPTIMIZATION, INTERPRETABILITY, PROOF, SIGNAL PROCESSING, SPARSITY

Comparison between 3-element matching pursuit and the analogous 3-element OMP.

The Orthogonal Matching Pursuit Update Step

Auxiliary derivation and explanation

SEP 10, 2021
categories: PROOFS
tags: ALGEBRA, COMPRESSED SENSING, MATCHING PURSUIT, PROOF, SIGNAL PROCESSING, SPARSITY

Mathematical derivation of the variational evidence lower bound.

Deriving the Variational ELBO from Bayes’ Theorem

Succint, direct and comprehensive derivation with interpretation

AUG 10, 2021
categories: PROOFS
tags: INTERPRETABILITY, MACHINE LEARNING, PROBABILITY, PROOF, VAE

A circular 2D cloud of points becomes linearly separable when lifted to 3D.

Feature Map of the Gaussian RBF Kernel

Explicit expression with direct proof

JUL 23, 2020
categories: PROOFS
tags: ALGEBRA, KERNEL TRICK, MACHINE LEARNING, PROOF

Main theorem: factorization of the normal distribution into 2 normals.

Factorization of a Multivariate Normal Distribution

A mathematical proof and brief explanation

DEC 10, 2019
categories: PROOFS
tags: ALGEBRA, PROBABILITY, PROOF