CRF Inference

Chain-structured Gaussian Conditional Random Fields (CRFs) for efficient discrete-time probabilistic inference with O(log T) complexity on parallel hardware.

When to Use

• Discrete-time state-space model inference
• Computing marginal distributions at each timestep
• Sampling from joint distributions over sequences
• Kalman filtering and smoothing
• Any chain-structured Gaussian graphical model

Key Concepts

CRF Structure

A chain CRF has the joint distribution:

p(x1, ..., xT) ∝ ∏ φt(xt) × ∏ ψt(xt, xt+1)