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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Selecting the number of mixtures / hidden states / latent variables

My question applies to Gaussian Mixture models, Hidden Markov models (HMM) or any type of clustering or latent variable model, for which we can devise a likelihood function. Specifically, I train a ...
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How can we compare two probabilistic models(markov networks) such that its prediction(confidence) depends on amount of training data?

I have a task of comparing two CRF models where each node and edge probability is associated with reliability depending on amount of data it is trained .How can I have a confidence metric for ...
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Conditional distribution of current state of HMM given past observations and state

I want to compute the following conditional probabilities for an HMM, where I shall refer to the state at time $t$ as $X_t$ and the observation at time $t$ is $O_t$: $$\text{Pr}\left(X_t | O_1, ...
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Gesture Recognition with HMM and Matlab [migrated]

I'm trying to classify some gestures with Matlab, using k-means and Hidden Markov Model. As example, I trained 10 samples of 'circle' hand gesture, organized in three .csv files where each columns ...
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How to Format Data for Structured Learning Problem?

I'm working on a project classifying discussion forum posts into various pre-defined categories, and would like to use a sequential learning model such as CRF's. I code mostly in Python and have found ...
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Train HMM with multiple sequences in R

I have multiple sequences and I want to train one HMM model. Is there a way to do it in R? I looked into 'HMM' package and there is only a way to train for 1 sequence of observations Thanks!
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How long does it take two identical hidden Markov models run on same observations to forget their initial distributions (if ever)?

Let $H_1$ and $H_2$ be two instances of a finite Hidden Markov Model (HMM) $H$. That is, $H_1$ and $H_2$ have identical state spaces $Q$ as well as identical transition $A$ and emission probabilities ...
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Hidden Markov Model vs Markov Transition Model vs State-Space Model…?

For my master's thesis, I am working on developing a statistical model for the transitions between different states, defined by serological status. For now, I won't give too many details into this ...
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Is this a job for mixture of experts regression or semi-hidden markov models or something else?

Data I have several thousand timeseries each comprising around 365 data points. Browsing through a few of them, it looks like each timeseries consists of several regimes (different number f regimes ...
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32 views

make prediction with HMM

I want to use HMM to make some prediction. say $O$ is the observation, $S$ is the hidden states, and I know how to train the model with forward-backward algorithm. I just get confused with how to ...
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Finding occurrences of specific patterns in time series

I have to locate occurrences of Cyllinder, Bell and Funnel patterns in univariate time series $X$ of gamma-ray sensoring. This is a specific case of the general CBF synthetic problem found in a few ...
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Flow of influence in a v-structure for Probabilistic Graphical Models

I'm not very sure I understand why an observed v-structure have different flow of influence behaviour for a directed and an undirected graph. What is the intuition behind the actual definition for ...
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1answer
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Hidden Markov Model to fill missing elements in a sequence

In my project I have a set of sequences (elements are letters from English alphabet) and some of the sequences have missing elements. I need to fill them with the most probable elements. I've been ...
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1answer
60 views

Can Hidden Markov Models be used to predict next observation?

I am reading up on Hidden Markov Models (HMMs) for my research and would like to know if it is applicable to the problem I wish to tackle. My problem is to detect/estimate the next value of a ...
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1answer
43 views

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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14 views

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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18 views

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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33 views

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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18 views

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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40 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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116 views

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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109 views

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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316 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 ...