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HMM and MEMM are a directed graph, while CRF is an undirected graph. HMM directly models the transition probability and the phenotype probability, and calculates the probability of co-occurrence.

CRF-RNN is a formulation of a CRF as a Recurrent Neural Network. Specifically it formulates mean-field approximate inference for the Conditional Random Fields with Gaussian pairwise potentials as Recurrent Neural Networks.

The goal of a named entity recognition (NER) system is to identify all textual mentions of the named entities. This can be broken down into two sub-tasks: identifying the boundaries of the NE, and identifying its type.

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account.

Edit. Conditional Random Fields or CRFs are a type of probabilistic graph model that take neighboring sample context into account for tasks like classification. Prediction is modeled as a graphical model, which implements dependencies between the predictions.

Conditional Random Field (CRF) The purpose of CRF is to refine the coarse output based on the label at each location itself, and the neighboring positions' labels and locations. Fully connected pairwise CRF is considered. Fully connected means all locations are connected as shown in the middle of the figure above.

Conditional Random Fields (CRF) CRF is a discriminant model for sequences data similar to MEMM. It models the dependency between each state and the entire input sequences. Unlike MEMM, CRF overcomes the label bias issue by using global normalizer.