Technical writing
Machine Learning Algorithms
Intuitive and mathematical guides to probabilistic inference, Monte Carlo methods, graphical models, filtering, and sequential estimation. The articles build from foundational ideas toward algorithms used to reason under uncertainty over time.
Foundations
Structure, dependence, and probabilistic reasoning
Graphical Models in ML and How Easy It Is to Break Conditional Independence
An introduction to graphical models, conditional independence, and how common modeling decisions can quietly invalidate the independence assumptions we rely on.
Monte Carlo methods
Sampling, weighting, and convergence
Importance Sampling vs. Self-Normalized Importance Sampling
Why Monte Carlo estimators use importance weights, when ordinary importance sampling is insufficient, and how self-normalization changes the estimator.
What Are Markov Chain Monte Carlo Methods?
A conceptual introduction to homogeneous Markov chains, convergence, detailed balance, and the relationship between MCMC and importance sampling.
MCMC: Metropolis–Hastings
How the Metropolis–Hastings algorithm constructs a Markov chain, satisfies detailed balance, and depends on the quality of its proposal distribution.
Annealing Importance Sampling
How annealing connects MCMC and importance sampling to estimate difficult marginal likelihoods through a sequence of intermediate distributions.
Sequential estimation
Estimating hidden state over time
Sequential Monte Carlo
A step-by-step account of importance weights, resampling, and how particle populations represent a changing posterior distribution.
Kalman Filter
An intuitive explanation of recursive state estimation for linear systems with Gaussian uncertainty, followed by the underlying update equations.
Particle Filters
How weighted particles approximate nonlinear or non-Gaussian state distributions when a single Gaussian estimate is not expressive enough.
Why these methods still matter
Modern machine learning still depends on the same questions: what is observed, what is hidden, how uncertainty is represented, and whether the available information can identify the quantity we want to estimate.
