Conditional Random Fields

A CRF assigns a conditional probability to a structured output given an input. For sequence labeling, the input may be a sentence or signal and the output a sequence of labels such as part-of-speech tags or named entities. Lafferty, McCallum, and Pereira introduced CRFs as probabilistic models for segmenting and labeling sequence data. Their formulation can use multiple, overlapping features of the observations and their relationships to label sequences without modeling the full distribution of the input itself. A common example is named-entity recognition. The model considers words, capitalization, neighboring tokens, and candidate label transitions when choosing tags. A linear-chain CRF scores a complete label sequence and normalizes across possible sequences, allowing the decoding stage to account for label-to-label compatibility. This differs from a hidden Markov model, which models a joint distribution over observations and states, and from a maximum-entropy Markov model, which locally normalizes each transition. The original CRF paper discusses label bias as a limitation of locally normalized directed models that CRFs avoid in the described setting. CRFs do not automatically understand language or guarantee a valid interpretation. They require representative labeled data, a suitable structure, and careful training; annotation errors and distribution shifts can reduce performance. They are useful when output labels have dependencies and a task needs structured prediction, but transformer models or simpler classifiers may be better for other tasks. Compare with relevant baselines and evaluate sequence-level precision, recall, and error patterns. A CRF is a model family, not a synonym for any language model or tagging pipeline.