Why does a first-order Hidden Markov Model fall short for financial markets, and how do higher-order HMMs get around it? Part 2 covers the intuition behind higher-order models, the trick that makes them trainable, and a live example of an HMM discovering hidden regimes on its own.

Hidden Markov Models power everything from speech recognition to stock market prediction — but most explanations skip straight to the math. This post builds HMMs up from scratch: Markov chains, hidden states, and the three classic problems every implementation needs to solve.

A single neural network often struggles to price options accurately across every regime. Why ask a LEAPS expert to price a 0DTE call? k-Sparse Gating solves this by acting as an intelligent ‘triage’ system. By activating only the Top-k specialists from a committee of 9 regime-trained experts, we eliminate ‘model noise’ and slash GPU latency. This tutorial moves beyond standard averaging to build a faster, specialized intelligence for complex market regimes.