CRF / HMM

Best for: Sequence labeling, older NLP

How it works

Hidden Markov Models treat tagging as a Markov chain over latent labels with parameters $\lambda=(A,B,\pi)$ — transition matrix $A$, emission $B$, and initial distribution $\pi$. The Viterbi algorithm returns the most likely tag sequence $\arg\max_y P(y,x\mid\lambda)$, while the forward algorithm computes $P(x\mid\lambda)$ for scoring. Conditional Random Fields replace this joint model with a discriminative one, $p(y\mid x)\propto\exp\sum_t w^\top f(y_{t-1},y_t,x,t)$, relaxing the HMM’s independence assumptions and allowing arbitrary overlapping input features.

Common fields

Named entity recognition · POS tagging