"NLP" revealing Markov Model mystery series article (v)

solving the problem of Hidden Markov model machine learning with forward-backward algorithm

Bai Ningsu

July 12, 2016 14:28:10

absrtact: The definition of the earliest contact Markov model stems from Mr. Wu's book "The Beauty of Mathematics", which at first felt esoteric and useless. Until we learn the natural language processing, we really use the hidden Markov model, and realize the magic of this model. Markov model is a powerful function in the process of sequence classification, such as: Speech tagging, voice recognition, sentence segmentation, Word suyin, local parsing, block analysis, named entity recognition, information extraction , etc. Also widely used in natural science, engineering technology, biotechnology, utilities, channel coding and many other fields. This article is written in the following ways: The first introduction of Markov profiles and Markov chains; the second chapter introduces three problems (likelihood degree, coding, parameter learning) of Markov chain (explicit Markov model) and hidden Markov model and hidden Markov model. The third to fifth one introduces three major problem-related algorithms: ( Forward algorithm, Viterbi algorithm, forward-backward algorithm); Finally, thanks to Mr. Feng Zhiwei's Natural language processing tutorial, Feng Lao Studies natural Language for more than 10, in this field do not have achievements. ( Original, reprint annotated source : forward-backward algorithm to solve the hidden Markov model machine learning Problem )

Directory

"Natural language Processing: Markov model (i)": initial knowledge of Markov and Markov chains

"Natural language Processing: Markov model (ii)": Markov model and hidden Markov model

"Natural language Processing: Markov model (three)": A forward algorithm to solve the likelihood problem of hidden Markov model

"Natural language Processing: Markov model (four)": The Viterbi algorithm solves the problem of decoding hidden Markov models (Chinese syntax notation)

"Natural language Processing: Markov model (v)": A forward-backward algorithm to solve the problem of hidden Markov model machine learning

Markov personal Profile

Andre Markov, Russian, PhD in physics-Mathematics, academician of St. Petersburg Academy of Sciences, representative of the School of Mathematics, is known for his work on number theory and probability theory, and his main works are "probabilistic calculus". 1878, won the gold medal, 1905 was awarded the title of Merit Professor. Markov is the representative figure of the School of Mathematics in Petersburg. Known for its work in number theory and probability theory. His main works are "probability calculus" and so on. In number theory, he has studied the continuous fraction and the two-time indefinite theory, which solves many problems. In probability theory, he developed the Matrix method and extended the application scope of the law of large numbers and the central limit theorem. The most important work of Markov is the Markov chain, a general scheme which can be used to study the natural process by means of mathematical analysis in 1906-1912 years. At the same time, the study of a random process-Markov process with no effect is initiated. It is found that the state of the nth conversion in a system is often determined by the results of the previous (n-1) test, as observed by several experiments. After the study of Markov, it is pointed out that, for a system, the transfer probability exists in the conversion process from one state to another, and the transfer probability can be deduced from the former state, which is independent of the original state of the system and the Markov process before the transfer. Markov chain theory and methods have been widely used in natural science, engineering technology and public utilities in modern times.

1 Overview of the forward and backward algorithms

Forward-Backward algorithm solved: PROBLEM 3 (Learning problem): Given an observation sequence O and a state set in a Hmm, automatically learns the parameters A and B of Hmm.

This algorithm involves machine learning, more complex, the author does not intend to explain in-depth, interested students can refer to Feng Zhiwei "natural Language Processing Concise tutorial" p594-602, this article is just to understand the aspects of the explanation.

Baum - The Welch algorithm (Baum-welch algorithm): The standard algorithm for training hmm is the forward-backward algorithm, which is the desired maximization algorithm or the Baum-Welch algorithm, which helps us train hmm's transfer probability B and launch probability A.

Baum - Welch algorithm ideas:

(1) The Count of repeated estimates, starting with an estimate of the transfer probability and the observed probability, uses these estimated probabilities repeatedly to introduce more and more good probabilities.

(2) For an observation, calculate its forward probability, thus obtaining the probability of our estimation. The estimated probability amount is then apportioned on all the different paths that contribute to the forward probability.

backward probability : The backward probability remembers that β is the observed probability for a given automaton λ, at state I and moment T observing the next moment t+1 to the end, expressed in the formula as follows:

Calculate the backward probability by calculating the forward probability similar to the inductive method:

2 steps for backward induction 3 Calculating the backward probabilities at the moment T and State J: More formulas, using notes as follows 4 algorithm Derivation process: More formulas, notes as follows 5 iterative forward-backward algorithm core:

6 References

"1" The basic christopher.manning of natural language processing, such as the Law of Wan Chun

"2" A concise tutorial on natural language processing Feng Zhiwei

"3" The beauty of mathematics Wu

"4" Viterbi algorithm analysis article Wang Yachang

Statement : Regarding this article each chapter, I take the comb main, the smooth bright writing technique. A reference to the relevant information two according to their own understanding to comb. Avoid miscellaneous unclear, each article reader can clear core knowledge, and then find relevant literature system reading. Also, learn to extrapolate and not stare at the definition or an example. For example: This article examples of ice cream Quantity (observations) and weather (hidden values), the reader begs to ask what is the use of this? We change the amount of ice cream into Chinese text or voice (observation sequence), changing the hot and cold weather into English text or phonetic text (hidden sequence). To solve this problem is not to solve the text translation, speech recognition, natural language understanding and so on. Solve the natural language recognition and understanding, and then apply to the present robot or other equipment, not to achieve practical and contact the purpose of real life? This article original, reproduced annotated source : forward-backward algorithm to solve the hidden Markov model machine learning problem

"NLP" revealing Markov Model mystery series article (v)