Hidden Markov Models are used for modelling systems that are assumed to be Markov processes with hidden (i.e. unobserved) states.

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HMCM vs Viterbi algorithm for calculating most likely path of an HMM [duplicate]

My expertise in machine learning and statistics is probably at a sophomore level. But anyway, my question is this: Given a Hidden Markov Model returned over a sequence of events with some states, how ...
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Use of Hidden Markov Models for Clustering

I would like to ask whether Hidden Markov Models can be used for clustering and if so, in what cases. I have found somewhere, references like this but practically I haven't found a way to do this. Is ...
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Calculate probability distribution $p\left(\left.X_{1:T}\right|Z_{1:T},y_{1:T}\right)$ in linear- non-Gaussian state space model

I have a linear, non-Gaussian state space model. Observation equation: $y_{t}=a+bX_{t}+cZ_{t}+\epsilon_{t}$ $\,\,\,\,$ $\epsilon_{t}\sim\mathcal{N}\left(0,\omega^{2}\right)$ Transition equations: ...
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loglikelihood for HMM with continuous emissions

I have a HMM and that has continuous valued emissions. I model the emissions using Weibull distributions. After I run the HMM I get the states, transition probabilities, priors and shape,scale ...
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How do you find mathematical expressions for the posterior marginals i.e. $P(x_n|y_0, … , y_n)$ in an HMM?

My goal is to find closed form equations for posterior marginals $P(x_n|y_0, ... , y_n)$ in a general HMM. I was told that we can calculate it exactly via BP (belief propagation, thought not sure how ...
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What are the states and observation in HMM speech recognition?

For example: Given a two state HMM a and b If I define a -> b = # a -> a = # b -> b = # b -> a = # Pr(A|a) = # Pr(A|b) = # Pr(B|a) = # Pr(B|b) = # ...
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HMM walk through for backward algorithm with given example

This pdf file is a resource that walk through a simple HMM algorithm of two states http://www.indiana.edu/~iulg/moss/hmmcalculations.pdf, I have question in step 4.1 of the algorithm Specifically ...
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Step training Baum-welch HMM

Referred to Baum–Welch algorithm, http://cs.au.dk/~cstorm/courses/MLiB_f14/slides/hidden-markov-models-4.pdf Is this formular correct ? I spend a couple days to figure out which part is wrong. I'm ...
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EM convergence when using em.hmm from PLIS

I use em.hmm function from PLIS package. I tried it on dimensions in range from 2 to 6. In every case of provided data (z-values) EM algorithm does not converge for dimensions 2, 5, 6. So, I wonder ...
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In Hidden Markov Model (HMM), is the transition matrix known, inferred, or assumed?

I'm reading Kevin Murphy's Probabilistic Machine Learning, which explains the forward algorithm to do filtering in HMM as follows (pp 610): The very first line says that the transition matrices ...
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Softmax factorization for a hidden markov model

I'm trying to formulate a hidden markov model where the transition and emission probabilities are governed by a softmax distribution. I'm not sure if this is a good idea, but I thought it could be ...
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HMMFit underlying algorithms

After reading article "Hidden Markov Models for Controlling False Discovery Rate in Genome-Wide Association Analysis" by Zhi Wei I am trying to use it in my project. I am using R and I have found out ...
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Embedding Markov Matrix

A stochastic matrix with states $S_1$, $S_2$, $S_3$, $S_4$ is given, now we would like to build up another stochastic matrix with finer states, meaning that the states $S_1$ will be considered as ...
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a joint probability distribution that passes through all markov network graph without being filtered

from filter view of the Markov Network where only those distributions can pass that satisfy all conditional independence statements given by the graph. • Can we think of distribution that can pass ...
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Using log of dependent variable as regressor

I am running a regime switching (hidden) Markov model, and I found out that if I construct the following model, it gives very interesting and useful state switches: $ y = \alpha_{S_t} + \beta_{S_t}\ ...
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Baum Welch and a 1 state Markov model?

I'm using the Baum-Welch algorithm to determine the parameters of a 2 state Hidden Markov Model. It determines fairly well. When I increase the sample size, the estimations get more concentrated, and ...
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What happens if you replace the sampling procedure in MCMC with maximization when fitting a HMM?

When using Markov chain monte carlo to fit hidden Markov models, after you use the forward algorithm to obtain the posterior distribution, you sample the hidden states for the current observation. ...
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Computational complexity gaussian continuos hidden markov model

As I know, the continuos Hidden Markov model does not use the emission probability matrix $B$ but obtains the probabilities of being of a given state by a gaussian (univariate or multivariate) pdf ...
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Hidden Markov Models with long sequence

I have a DNA sequence has 1682 observations, I got the initial HMM parameters and other parameters by EM algorithm (Baum-Welch). When I tried to evaluate the model by Log-odds scoring, I calculated ...
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30 views

How do I apply MDS analysis on my data set?

Consider the following dataset (it is the emission probability matrix of a Hidden Markov Model): ...
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HMM: class residience time from time series

I'm a newbie of the statistica subject. I've seen that HMM could be used in order to model state and state transitions for time series and, since I only know that in Markov Models I could state the ...
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Hand Coordinates Clustering for vector quantization

I've a sequence of pitch, yaw, roll of the hand, plus pitch and yaw of the fingers. So i got a 13-dimensional vector. Which is the best way to understand how to cluster these data in order to perform ...
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What is the number of “observed data” in a multivariate HMM

I am trying to calculate BIC scores for a couple of models with different states. (See general question 1 and a more specific q2 - no answers in either). I've done my own research a little bit and ...
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Choosing initial transition and emission probabilities while training HMM

A Hidden Markov Model (HMM) is defined by the following parameters: $HMM =(prior, transmat, obsmat)$ Using K Murphy's HMM toolbox [1], I ran a small experiment where I define a set of true ...
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what are parameters in a model and how do I get them?

I recently asked a way to calculate BIC score for a given HMM (transition, emission, initial distribution). After doing some more research (basically the wiki page and this CV thread) I realized its a ...
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How do I calculate BIC score for HMM?

2 line background: Applied/Pure Math (ODE, PDE, Functional, measure theory and a little of probability theory) doing research in bioinformatics. So my stats knowledge is limited. That being said, for ...
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Getting the log-likelihood per fold in LOO Cross Validation for HMM in Matlab

I am running Leave-one-out Cross validations for deciding the optimal number of hidden states in an HMM. At each iteration I am getting one model and with forward algorithm I estimate the probability ...
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Goodness of fit index in HMM

I am working on a dataset which I am training using the Baum Welch algorithm in order to produce an HMM. Because of the fact that my dataset is rather small I am using Leave-one-out cross validation ...
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HMM - Forward Algorithm - Initial State Distribution

In my case, I have a dataset of observations which have not been produced by an HMM meaning that I do not know what kind and how many hidden states should exist there. So, the only known factor are ...
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Hidden Markov Models with multiple emissions per state

I want to use Hidden Markov Models for an unsupervised sequence tagging problem. Due to the peculiarities of my application domain (recognition of dialogue acts in conversations), I would like to use ...
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Estimation of TRANS_GUESS and EMIS_GUESS matrices in Baum-Welch algorithm

I would like to ask how do we estimate the probabilities in TRANS_GUESS and EMIS_GUESS matrices (see here http://www.mathworks.com/help/stats/hidden-markov-models-hmm.html#f8288 ) as an input for the ...
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Hidden Markov Models relationship

I have a question regarding a small investigation that I have been conducting into the relationship between the length of observation sequence, T, on which two decoders (BCJR and classic Viterbi) ...
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Hidden Markov Model with conditional observations

I am looking for a research paper that basically describes a hidden markov model that has multiple observations, and some observations that have conditional dependencies. For example, please consider ...
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Probabilities in a Markov Model

I am reading a paper on Markov Models and I am trying to figure out how to compute the probabilities for the $\alpha$-pass. I am given an $N\times N$ matrix $A$, that has the probabilities of ...
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306 views

Predicting the Weather

Given a tree trunk with concentric circles, can we predict the weather for each year? Each concentric circle accounts for a year that the tree has been on the Earth. The innermost circle is the oldest ...
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HMM-forward backward algorithm

Let $x_t, \, t=1, \dots ,T$ be a time series and suppose that $x_t | \xi_t \sim N(\mu_{\xi_t},\sigma^2_{\xi_t})$, where $\xi_t \in [1, \dots,K]$ is a group indicator (or regime or state), the ...
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Predict observation using Hidden Markov Models

I have a sequence of observations e.g. ["Click","Scroll","Hover","Zoom","Select"]. I need to predict the next value of this observation sequence but not the next hidden state. I know that there are ...
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Stack of HMMs. Does this have a name?

Consider a sequence of tokens. One could fit a Markov model to this sequence by computing the empirical stochastic transition matrix. A refinement to this model would be to build a HMM on top of it, ...
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Expected required sample length to train a hidden Markov model

Say one wishes to train a hidden Markov model with $n$ hidden states, and (accidentally) the problem itself can be described with a hidden Markov model with $n$ (or less states). What is the expected ...
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Proper scoring rules for observations with different supports

Suppose to have a bivariate variable $z_t=(x_t, y_t)$ indexed by $t=1,2, ..., T$. Suppose now that the two components have different support, i.e. in my specific problem $x_t \in \mathcal{S}$, where ...
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What is the most appropriate method to recover words transcription from the phoneme sequence with errors?

I conduct some experiments on continuous speech recognition. After the initial application of the recognizer I have the phoneme sequence that includes some errors (three types of errors: substitution, ...
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Viterbi-like algorithm with a single observation

Consider a Metropolis-Hastings walk over an exponentially large, known state space S. The proposal/transition matrix P is known, as is the target stationary distribution. In fact, assume there is an ...
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determing states in HMM with BIC

I'm fitting a HMM to time series, for each data set I use BIC results to select the optimum number of states. In that, the BIC number is lowest and thereby indicating this model with that number of ...
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162 views

Way to train Hidden Markov Model in R with multiple sequences

i have multiple sequences for each of two states. I'd like to train a HMM with these to predict the state for unkown sequences. Here is an example for this problem: ...
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Posterior Marginal in Forward Backward

In computing Forward Backward Algorithm[http://en.wikipedia.org/wiki/Forward%E2%80%93backward_algorithm], it seems they are calculating posterior. I knew Forward Backward is an algorithm of ...
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Practical Implementation of Speech Recognition HMM

I'm trying to implement a GMM/HMM for phoneme recognition where I have for each phoneme a 3-state left to right HMM model with start and end states with no emission. The emission probabilities are ...
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How do I detect state change in multivariate time series?

I have a multivariate time series . For each row in the data we have the values of inputs and a label for stability (0 or 1 ) . What are the algorithms that can detect the stability for an unlabelled ...
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Speech recognition, words out of dictionary

I'm performing word recognition by using a tradional procedure. I'm extracting MFCC features. Then I'm creating a code book in order to do vector quantization. After that, I train discrete HMM for two ...
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HMM library, different length sequences training

I'm using the Kevin Murphy's HMM library in MATLAB(http://www.cs.ubc.ca/~murphyk/Software/HMM/hmm.html) There is a section called 'How to use the toolbox'. There is this example for GMM ouputs: ...
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Data requirements for building an HMM

I'm trying to describe the requirements that should be placed on data when building a Hidden Markov Model. Should the data fit the requirements for a Markov chain? That is, must it have discrete, ...