Hidden Markov Model Matlab Download
Problem DefinitionIn this assignment, we are using Hidden Markov Models (HMM) for Language Processing. The goal of this assignment is to have a computer recognize and parse the sentences with our select vocabulary.We used Forward and Backward Procedure to recognize the pattern. We also implement Viterbi algorithm to determine the optimal state path for each observation. We then use Baum-Welch algorithm tooptimize the the HMM. This program is useful since the HMM can be used as a learning tool and optimization of real world situations like in a strategy such as chess moves. The program will learn fromits database and calculate the optimization move.Method and ImplementationWe create a file input as the which will read line by line from the its calibrating set.
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The first input will tell the number of states, number of observation symbols, and the length of theobservation sequence. The second line would read the basic English syntactic structures which is correlated to each of the states. The third line will contain its vocabulary. The lines after willstate the matrix a, matrix b, and vector pi which will utilize for Viterbi algorthim and the Baum-Welch algorithm. We will then run with some examples to observe the probability in reaching thatsentence using Viterbi algorithm. We split each line and store their values.
In the rocognize.java file, we have forward method which will calculate the alpha values. There's also a backward functionwhich will calculate the beta value. There are stage function which will read the word and go to the various stages.
In statepath.java, we use Viterbi algorithm to to determine the optimal state pathfor each observation set and report its probability. In optimize.java, the Baum method will calculate the new optimization which will print the before and after. Question 1: For the current application, why does this probability seem lower than we expect? What does this probability tell you? Does the current HMM alwaysgive a reasonable answer?
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For instance, what is the output probability for the below sentence? 'robots do kids play chess'chess eat play kids'You may want to use different observation data to justify your answer.Answer:'robots do kids play chess'Probability: 0.999999997'chess eat play kids'Probability: 0.0With the 8 given words,we can generate a lot of possible sentences with different length, different sequence, and the probability of each sentence only occupies a small rate of the total probability1. As long as the probability is bigger than 0, it shows that this sentence is valid according to this HMM. It does not always give a reasonable answer, for example:'robots do kids play chess'Probability: 0.999999997The HMM decides that 'robots do' is valid and 'do kids play chess' is valid, it doesn't know it's actually a combination of two valid sentences.To prove it,I combined other valid sentences andexperiment as follows:'kids can kids play chess'Probability: 0.999999998It's not a valid sentence but the probability is bigger than 0..
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Question 2: What can we tell from the reported optimal path for syntax analysis purpose? Can the HMM always correctly distinguish 'statement' from 'question'sentence? Why?Answer: We can tell the syntax estimation from the output result, which gives a meaningful explanation of the 'question sentence'.Below is the connection of syntax-words relationship from the b matrix. We can tell that the HMM may not always correctly distinguish 'statement' from 'question' because of the red probabilitybelow, which might cause confusion between OBJECT and SUBJECT.b:SUBJECT- 0.5 0.4 0.0 0.0 0.0 0.0 0.05 0.05kids robotsAUXILIARY-0.0 0.0 0.5 0.5 0.0 0.0 0.0 0.0do canPREDICATE-0.0 0.0 0.0 0.0 0.5 0.5 0.0 0.0playeatOBJECT - 0.1 0.2 0.0 0.0 0.0 0.0 0.3 0.4chess food.
Question 3: Why should you not try to optimize an HMM with zero observation probability?When it's zero, we can not calculate sai(i,j)t because observation probability is the divendence. This is one of the limitations of this method.in the Baum method, for newA and newB calculation part, I added the if condition which stated: when the dividend(observation probability) is zero(I wrote. Model EnhancementNow supposed you want this HMM to model new syntax structures, like 'PRESENT TENSE' or 'ADVERB,' so that the following sentences can be parsed:'robots can play chess well'kids do eat food fast'Question: What kinds of changes will you need to make in the above HMM? Please describe your solution with an example of the modifiedmatrices a, b and pi in the submitted web page.5 10 5SUBJECT AUXILIARY PREDICATE OBJECT ADVERBkids robots do can play eat chess food well fasta:0.0 0.4 0.6 0.0 0.00.7 0.0 0.3 0.0 0.00.0 0.0 0.0 0.5 0.50.0 0.0 0.0 0.5 0.50.0 0.0 0.0 0.0 0.0b:0.5 0.4 0.0 0.0 0.0 0.0 0.05 0.05 0.0 0.00.0 0.0 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.5 0.5 0.0 0.0 0.0 0.00.1 0.2 0.0 0.0 0.0 0.0 0.3 0.4 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.5pi:0.6 0.3 0.1 0.0 0.0.
DescriptionTRANS,EMIS = hmmestimate(seq,states) calculatesthe maximum likelihood estimate of the transition, TRANS,and emission, EMIS, probabilities of a hidden Markovmodel for sequence, seq, with known states, states.hmmestimate(.,'Symbols',SYMBOLS) specifies the symbols that areemitted. SYMBOLS can be a numeric array, a string array or a cell arrayof the names of the symbols. The default symbols are integers 1 through N, where N is thenumber of possible emissions.hmmestimate(.,'Statenames',STATENAMES) specifies the names of thestates. STATENAMES can be a numeric array, a string array, or a cellarray of the names of the states. The default state names are 1 throughM, where M is the number of states.hmmestimate(.,'Pseudoemissions',PSEUDOE) specifiespseudocount emission values in the matrix PSEUDOE.Use this argument to avoid zero probability estimates for emissionswith very low probability that might not be represented in the samplesequence. PSEUDOE should be a matrix of size m-by- n,where m is the number of states in the hidden Markovmodel and n is the number of possible emissions.If the i → k emission does not occur in seq,you can set PSEUDOE(i,k) to be a positive numberrepresenting an estimate of the expected number of such emissionsin the sequence seq.hmmestimate(.,'Pseudotransitions',PSEUDOTR) specifiespseudocount transition values.
You can use this argument to avoidzero probability estimates for transitions with very low probabilitythat might not be represented in the sample sequence. PSEUDOTR shouldbe a matrix of size m-by- m,where m is the number of states in the hidden Markovmodel. If the i → j transition doesnot occur in states, you can set PSEUDOTR(i,j) tobe a positive number representing an estimate of the expected numberof such transitions in the sequence states.