Organized from:
https://blog.csdn.net/woaidapaopao/article/details/77806273?locationnum=9&fps=1
- HMM
- CRF
- Comparison of HMM and CRF
1.HMM algorithm
Hidden Markov Models are generative models for labeling problems. There are several parameters ( π π, A, B): initial state probability vector π π, state transition matrix A, observation probability matrix B. There are three elements called the Markov model.
Three basic problems of Markov:
- Probability calculation problem: Given a model and observation sequence, calculate the probability of the output of the observation sequence under the model. – "Forward-backward algorithm
- Learning problem: Know the observation sequence, estimate the model parameters, that is, use the maximum likelihood estimation to estimate the parameters. – "Baum-Welch (that is, EM algorithm) and maximum likelihood estimation.
- Prediction problem: Know the model and observation sequence, and solve the corresponding state sequence. – "Approximation algorithm (greedy algorithm) and Vibit algorithm (dynamic programming to find the optimal path)
2. Conditional random field CRF
The density of the conditional probability distribution of a set of output random variables given a set of input random variables. The conditional random field assumes that the output variable constitutes a Markov random field, and what we usually see is a linear chain random field, that is, a discriminant model that predicts the output from the input. The solution method is maximum likelihood estimation or regularized maximum likelihood estimation.
The reason why HMM and CRF are always compared is mainly because both CRF and HMM use the knowledge of graphs, but CRF uses Markov random fields (undirected graphs), while HMM is based on Bayesian networks (with to the diagram). And CRF also has: probability calculation problems, learning problems and prediction problems. The approximate calculation method is similar to HMM, except that the EM algorithm is not required for the learning problem.
3. Comparison of HMM and CRF
The fundamental reason is that the basic concepts are different, one is a generative model, the other is a discriminative model, which also leads to different solutions.