Statistical Learning Methods Reading Notes (11)-Conditional Random Field

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Conditional random field (CRF) is a conditional probability distribution model of a given set of input random variables and another set of output random variables. Its characteristic is to assume that the output random variables constitute a Markov random field. Whiteboard Derivation Series Notes (17)-Conditional Random Field

1. Probabilistic undirected graph model

The probabilistic undirected graphical model, also known as Markov random field, is a joint probability distribution that can be represented by an undirected graph.

• Pairwise Markov property
• Local Markov property
• Global Markov property

The joint probability distribution of the probabilistic undirected graph model is expressed as an operation in the form of the product of the function of the random variables on the largest clique, which is called the factorization of the probabilistic undirected graph model.

Group: Any two nodes are connected by edges.
Largest group: It is a group and cannot join any node to form a new group.

The joint probability distribution $P\left(Y\right)$ can be expressed as the following form:$$\begin{gathered} P(Y)=\frac{1}{WITH}\prod _C{\Psi }_C({And}_C) \\ WITH=\sum _{WITH}\prod _C{\Psi }_C\left({And}_C\right) \end{gathered}$$

2. Definition and form of conditional random field

The conditional random field is a given random variable XXUnder$X$ condition, random variable$Y$ 's Markov random field.

The linear chain conditional random field is also a log linear model.

Third, the probability calculation problem of conditional random field

• Forward-backward algorithm
• Probability calculation
• Expected value calculation

Fourth, the learning algorithm of conditional random field

• Improved iterative scaling algorithm
• Quasi-Newton Method

V. Prediction algorithm of conditional random field

• Viterbi Algorithm
  

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