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keywords= annotation, Baum-Welch, classification, classifier, decoding, EM algorithm, expectation maximization, hidden Markov model, HiddenMarkovProcess, hidden Markov process, HMM, machine learning, Markov chain, Markov process, profile HMM, regime switching model, supervised learning, supervised training, tagging, unsupervised learning, unsupervised training, Viterbi, Viterbi training;
description=HiddenMarkovProcess[i0, m, em] represents a discrete-time, finite-state hidden Markov process with transition matrix m, emission matrix em, and initial hidden state i0. HiddenMarkovProcess[..., m, dist1, ... ] represents a hidden Markov process with emission distributions disti. HiddenMarkovProcess[p0, m, ...] represents a hidden Markov process with initial hidden state probability vector p0.;

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Text of the page (random words):
m language code data temporaldata automatic 0 026793454724470367 0 35850818519254457 0 20299955749743726 0 15309292139988245 0 20794459094145828 0 16142235868874535 0 28313028545065905 0 20603684513399712 0 27201827188085237 0 1470958372294 42583037 0 03313734850968875 0 22865919859041547 0 12342603192198957 0 16548359389522804 0 28756847141700326 0 15 1 3 continuous 3 discrete 1 1 valuedimensions 1 metainformation false 10 wolfram language code class hiddenmarkovprocess 2 gaussian baumwelch is the default estimator that iteratively maximizes the likelihood of given emissions wolfram language code 𝒫1 estimatedprocess data class processestimator baumwelch absolutetiming viterbitraining is an iterative estimator that maximizes the joint likelihood of given emissions and their unknown underlying states wolfram language code 𝒫2 estimatedprocess data class processestimator viterbitraining absolutetiming stateclustering is commonly used to make a fast heuristic non iterative estimate wolfram language code 𝒫3 estimatedprocess data class processestimator stateclustering absolutetiming compare log likelihoods of estimated processes wolfram language code table loglikelihood pr data pr 𝒫1 𝒫2 𝒫3 supervisedtraining is an estimator that maximizes the joint likelihood of given emissions and given states wolfram language code proc hiddenmarkovprocess 0 3 0 7 0 95 0 05 0 1 0 9 0 9 0 1 0 5 0 5 wolfram language code ems 1 1 1 1 2 2 2 1 2 2 2 2 2 1 1 1 2 1 1 1 1 2 1 2 2 2 1 2 1 2 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 2 1 2 1 2 2 2 2 1 1 2 1 2 1 2 1 1 1 1 1 1 1 2 2 2 wolfram language code states 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 use the template form to specify the class of process to estimate wolfram language code class hiddenmarkovprocess 2 2 use the statedata suboption to specify data about underlying states for given emissions wolfram language code ps estimatedprocess ems class processestimator supervisedtraining statedata states estimate a three state model with two emissions and a silent state wolfram language code data temporaldata automatic 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 2 2 2 2 1 1 1 2 2 2 2 1 1 2 2 1 2 1 1 2 1 2 2 2 2 2 1 2 1 1 2 2 2 1 2 1 1 2 2 2 2 2 2 2 1 2 1 2 1 1 2 2 2 1 2 2 1 2 1 1 2 2 1 2 2 2 1 1 2 1 2 2 1 2 1 0 12 1 250 discrete 250 discrete 1 1 valuedimensions 1 metainformation false 10 wolfram language code min data max data estimate the model using a starting value process wolfram language code sv𝒫 hiddenmarkovprocess 0 5 0 3 0 2 1 4 0 3 4 0 1 3 2 3 1 4 1 3 5 12 3 4 1 4 0 0 1 3 2 3 wolfram language code e𝒫1 estimatedprocess data hiddenmarkovprocess 3 2 sv𝒫 if no initial process is given specify which states are silent in the template wolfram language code e𝒫2 estimatedprocess data hiddenmarkovprocess 3 2 2 compare log likelihoods of resulting processes wolfram language code loglikelihood data e𝒫1 e𝒫2 process slice properties 4 find the pdf of the emission distribution at a fixed time wolfram language code 𝒫 hiddenmarkovprocess 1 0 1 2 1 2 1 2 0 1 2 1 2 1 2 0 bernoullidistribution 1 4 bernoullidistribution 2 3 bernoullidistribution 1 2 wolfram language code pdf 𝒫 2 e compute the mean and the covariance for symbolic times for multivariate emissions wolfram language code 𝒫 hiddenmarkovprocess 2 5 3 5 1 2 1 2 2 5 3 5 binormaldistribution 1 3 binormaldistribution 2 3 wolfram language code mean 𝒫 t wolfram language code covariance 𝒫 t fullsimplify sample emissions of the hidden markov process at specified times wolfram language code hmm hiddenmarkovprocess 0 5 0 5 0 9 0 1 0 1 0 9 0 5 0 5 0 8 0 2 wolfram language code ems16 randomvariate hmm 1 6 10 4 visualize frequencies and compare to theoretical results wolfram language code histogram3d ems16 automatic probability wolfram language code table e1 e6 probability x 1 e1 x 6 e6 x hmm e1 1 2 e6 1 2 find stationary distribution of emissions following a hidden markov process wolfram language code hmm hiddenmarkovprocess 0 5 0 5 0 7 0 3 0 25 0 75 0 2 0 6 0 2 0 4 0 2 0 4 wolfram language code probability e infinity k e hmm generalizations extensions 1 specify that randomfunction should include the hidden state path wolfram language code 𝒫 hiddenmarkovprocess 0 3 0 7 0 95 0 05 0 1 0 9 exponentialdistribution 2 erlangdistribution 2 3 wolfram language code data randomfunction 𝒫 0 50 method automatic includehiddenstates true the hidden states are stored as metadata in the produced temporaldata object wolfram language code data hiddenstates visualize the state path wolfram language code listplot data hiddenstates ticks automatic 1 2 filling axis applications 11 games 3 an occasionally dishonest casino offers a coin betting game and uses an unfair practice of using a biased coin for which the head is three times more likely than the tail the casino dealer is known to secretly switch between the fair and biased coins with probability 10 wolfram language code fair biased 1 2 tm sparsearray fair fair 9 10 fair biased 1 10 biased fair 1 10 biased biased 9 10 the probabilities of getting heads or tails wolfram language code faircoin 1 2 1 2 biasedcoin 3 4 1 4 the resulting hidden markov process assuming equal probabilities of starting with either coin wolfram language code unfaircasinohmm hiddenmarkovprocess 1 2 1 2 tm faircoin biasedcoin faircasinohmm hiddenmarkovprocess 1 1 faircoin the probability of getting a head given that the previous roll was a head wolfram language code nprobability x 1 1 x 0 1 x unfaircasinohmm wolfram language code nprobability x 1 1 x 0 1 x faircasinohmm if you intend to play six games compute the probability that at least three tails will be tossed wolfram language code atleastk k_ v_ booleancountingfunction k length v length v v wolfram language code nprobability atleastk 3 table o t 2 t 0 5 o unfaircasinohmm the probability if the casino is fair at all times wolfram language code nprobability atleastk 3 table o t 2 t 0 5 o faircasinohmm given a sequence of tosses guess on which occasions the dealer used the biased coin wolfram language code tosses randomfunction unfaircasinohmm 0 100 wolfram language code probablecointypes findhiddenmarkovstates tosses unfaircasinohmm wolfram language code listplot probablecointypes ticks automatic 1 fair 2 biased axesorigin 0 0 there are three urns each containing a large number of balls colored red blue and green wolfram language code urn1 urn2 urn3 1 2 3 red blue green 1 2 3 each time a person randomly selects an urn selects a ball announces the color and returns the ball to one of the urns the process is repeated four times the probabilities of moving to the next urn are as follows wolfram language code tm sparsearray urn3 urn3 1 urn2 urn2 urn2 urn3 0 8 0 2 urn1 urn1 urn1 urn2 urn1 urn3 0 5 0 3 0 2 the probabilities of picking a certain color from each urn correspond to the fraction of different balls for each urn wolfram language code em 0 3 0 5 0 2 0 4 0 4 0 2 0 6 0 3 0 1 construct the hidden markov process for the given probabilities of choosing the first urn wolfram language code hmm hiddenmarkovprocess 0 9 0 1 0 tm em the probability of getting the color sequence red blue green green wolfram language code likelihood hmm red blue green green given the color sequence find the most likely sequence of urns that were picked wolfram language code findhiddenmarkovstates red blue green green hmm in a first person shooter game an agent is hiding inside a level and waiting to jump out at the player the agent cannot see the player but can hear what they are doing and can then match that against its knowledge of the layout to estimate the player s position consider a layout with 27 regions of four types grass metal grates water and door portals wolfram language code grass alternatives 1 2 4 5 11 12 13 14 15 16 17 18 19 20 metal alternatives 3 6 21 22 24 25 water alternatives 7 8 9 10 door alternatives 23 26 27 assign colors to the different types of regions wolfram language code colors transpose grass green metal gray water blue door brown walking on the different terrain types produces different kinds of noises wolfram language code none footsteps splashing creaking unclear range 5 probabilities of giving out noises depends on the terrain type wolfram language code em sparsearray grass none grass unclear 0 9 0 1 metal none metal footsteps 0 1 0 9 water splashing water unclear 0 9 0 1 door creaking door unclear 0 9 0 1 27 5 visualize the layout of the level wolfram language code edges 27 1 1 2 2 3 3 4 3 7 4 5 5 25 25 24 24 22 22 21 21 23 21 20 20 19 19 18 18 17 17 7 17 8 18 9 19 10 10 9 9 8 8 7 10 26 10 14 9 14 8 13 8 12 14 15 15 16 14 13 13 12 13 11 12 11 11 6 6 1 wolfram language code regions range 27 mapthread vert 1 style vert 2 colors wolfram language code gr graph regions edges vertexsize large vertexlabels placed name above vertexshapefunction square assume the player enters through one of the doors with equal probability wolfram language code p0 sparsearray door 1 length door 27 the player remains in their current region with probability 10 and otherwise is equally likely to move to any of the neighboring regions giving the following transition probability matrix wolfram language code adjm adjacencymatrix gr tm 0 9adjm total adjm 2 0 1 identitymatrix 27 wolfram language code hmm hiddenmarkovprocess p0 tm em the agent hears the following sequence of noises wolfram language code obs creaking none footsteps none none splashing splashing footsteps splashing this shows that most likely the player entered through the door marked 27 and is currently in region 7 wolfram language code findhiddenmarkovstates obs hmm mapthread v 1 framed v framestyle 2 colors genetics 3 a dna sequence consists of letters a c g and t subsequences called nucleotide sequences are characterized by the frequency with which different letters occur one important task is to split the sequences into their different nucleotide subsequences suppose you are given a sequence that begins in an exon contains a 5 splice site and ends in an intron if the exons have a uniform base composition the introns are deficient in c and g and the splice site consensus nucleotide is a g with probability 0 95 the nucleotide frequency distributions are the following wolfram language code exon 0 25 0 25 0 25 0 25 intron 0 4 0 1 0 1 0 4 splice 0 05 0 0 95 0 wolfram language code dnaseq characters cttcatgtgaaagcagacgtaagtca a 1 c 2 g 3 t 4 the state machine has states for exon 1 splice 2 intron 3 and end 4 with the following transition probabilities between states wolfram language code tm 0 9 0 1 0 0 0 0 1 0 0 0 0 9 0 1 0 0 0 1 the emissions are nucleotides a 1 c 2 g 3 t 4 or end 5 wolfram language code em padright exon splice intron unitvector 5 5 wolfram language code hmm hiddenmarkovprocess 1 tm em find the most probable current nucleotide sequence exon splice intron or end wolfram language code sites findhiddenmarkovstates append dnaseq 5 hmm the joint probability of the above nucleotide sequence and the dna sequence wolfram language code fold times likelihood discretemarkovprocess hmm sites mapthread part em 1 2 sites append dnaseq 5 model breast cancer risk transmitted via a damaged allele b of the brca1 gene with each parent contributing one of their alleles with probability 1 2 for each allele wolfram language code states bb bb bb if the mother has a functional allele pair bb the probabilities of their son having each allele combination are wolfram language code sm 0 1 0 0 1 2 1 2 0 0 1 the emission probabilities for the son are the same as for the father since they are both male the emission is 1 for cancer and 2 for no cancer wolfram language code em 0 2 0 8 0 2 0 8 0 1 suppose you know the priors for the father wolfram language code p0 0 3 0 3 0 4 wolfram language code hmm hiddenmarkovprocess p0 sm em find the probability of both the father and the son developing breast cancer wolfram language code cancer 1 probability health 0 cancer health 1 cancer health hmm two genes of a diploid plant are being investigated having the following alleles wolfram language code alleles a a b b there are nine distinct genotypes wolfram language code genotypes gene tuples select tuples orderedq alleles the plant is self pollinating i e the genotype of its offspring depends on the genotype of the parent only wolfram language code offspring g_ tuples map sort tuples g wolfram language code frequencies data_ block fr tally data fr all 2 total fr all 2 fr graph of genotype transitions between generations that encodes transition probabilities wolfram language code gr graph genotypes annotation 1 probability 2 join table frequencies directededge gi offspring gi gi genotypes vertexlabels placed name tooltip model generational genotype changes using discretemarkovprocess wolfram language code gene𝒫 discretemarkovprocess normalize table 1 vertexcount gr total weightedadjacencymatrix gr edgeweight probability alleles control the plant s phenotypes i e visible features assuming complete dominance of capital letter alleles over respective lowercase letter alleles wolfram language code totrait ___ a ___ purple totrait a a white totrait ___ b ___ tall totrait b b short wolfram language code totrait gene p1_ p2_ traits totrait p1 totrait p2 the genotypes control four distinct phenotypes wolfram language code ind union phenotypes totrait genotypes ind thread ind range length ind the plant s phenotypes indexed by an integer are modeled by a hidden markov process wolfram language code hmm hiddenmarkovprocess gene𝒫 sparsearray table vertexindex gr gi totrait gi ind 1 gi genotypes simulate mendel s observations which he collected for 2734 plants over four generations wolfram language code data randomfunction hmm 0 3 2734 estimate genotype transition probabilities from these observations wolfram language code class hiddenmarkovprocess length genotypes length ind wolfram language code estpr estimatedprocess data class hmm wolfram language code loglikelihood estpr data linguistics 1 classify the characters from sample text into vowels and consonants using a two state hmm wolfram language code text exampledata text declarationofindependence wolfram language code chars append characterrange a z wolfram language code data cases tolowercase flatten characters text alternatives chars thread chars range 27 find the best parameter estimate wolfram language code proc estimatedprocess data hiddenmarkovprocess 2 27 precisiongoal machineprecision accuracygoal machineprecision for each character pick the state with highest probability from the emission matrix wolfram language code arrayplot em last proc wolfram language code res chars cases transpose em pv_ pc_ if pv pc vowel consonant transpose wolfram language code groupby res extract 2 extract 1 weather 2 tree ring sizes are well correlated with average annual temperatures using two temperature states hot and cold and three tree ring sizes...