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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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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38 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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11 views

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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15 views

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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44 views

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, ...
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Transition matrix in left-right hidden semi-Markov model

i'm developing a hidden semi-Markov model left-right . In a left-right model a sequence of $M$ states starts in state 1 and ends in state M, with no repetition of states. Since the model is ...
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How can you use HMMs and ANNs for on-line handwriting recognition?

I've asked this question on cs.stackexchange before. It has a 20-hours remaining bounty there. On-line handwriting recognition is the task of converting a series of $(x(t),y(t))$ coordinates to ...
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1answer
28 views

Hidden Markov process

I've been reading about hidden Markov models, and I'm interested in both discrete and continuous time models (and discrete states). I have found many papers on the discrete time HMM, but not the ...
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48 views

Concavity of log likelihood for hidden markov models

Could you give me a good link where the concept of concavity of the log likelihood related to hidden markov model EM algorithm is clarified? Thank you in advance.
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HIdden Markov model training Baum Welch, concavity log likelihood

Hi i'm developing an hidden markov model algorithm training with multiple sequences. The recognition rate is good but i have doubts about the shape of the curve of log likelihood obtained from the ...
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64 views

Example on Hidden Markov Model

I was studying Hidden Markov Model(HMM) recently. I was looking to cross check what I understood. I found a code on Forward-Backward and Viterbi is given in simple Python terms in Wikipedia. I ...
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22 views

Forward Sampling for HMM

Is it reasonable to use forward sampling to compute the probability of P(X_1=x_1, ..., X_N=x_n) in an HMM where is the observation variable? Is the forward sampling algorithm related to the ...
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26 views

Distance between a transition matrix and an instance

I am trying to put a number to the distance of a sequence and how close it is to the original training corpus. From the original training data, I got a markov transition matrix (TM). So from the ...
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37 views

How to find log-likelihood of multiple sequences for hmm using Kevin Murphy toolkit for MATLAB

I have an observation sequence of TPM, EPM and prior. I want to find the log-likelihood of around 100 sequences of length 10 at a time. How can I do this using a forward algorithm?
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32 views

Why Baum-Welch algorithm is an instantiation of EM algorithm?

$\newcommand{\E}{\mathrm{E}}$ I don't understand why Baum-Welch algorithm is an instantiation of EM algorithm. Indeed, why computing $\alpha_t(i)$ and $\beta_t(i)$ corresponds to Expectation step. ...
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142 views

Hidden state models vs. stateless models for time series regression

This is a quite generic question: assume I want to build a model to predict the next observation based on the previous $N$ observations ($N$ can be a parameter to optimize experimentally). So we ...
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430 views

Training a Hidden Markov Model, multiple training instances

I've implemented a discrete HMM according to this tutorial http://cs229.stanford.edu/section/cs229-hmm.pdf This tutorial and others always speak of training a HMM given an observation sequence. ...
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42 views

Hidden Markov Models methods for selecting optimal number of states

Package RHmm (R) I have a vector which I fit into a hmm model in an attempt to select an optimal number of states for a hidden markov model. ...
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55 views

Hidden Markov Model: Predict observation sequence from state sequence

Given a transition matrix, starting probability, means and covariances Is it possible to predict the most likely observed sequence for a given state sequence using the above details? If yes, how? ...
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HMM learning from video data?

I am having a problem understanding how to learn the parameters for the HMM from observed data. Let's say that my HMM model has one hidden variable for affect(emotion) with three values/states (anger, ...
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25 views

How tho choose the number of components in a Bayesian Hidden markov model

I'm implementing a bayesian Hidden markov model. I now face the problem of how to choose the number of components. I have two problems: 1) which index is better to use? 2) suppose i decide to use the ...
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Markov Switching and Hidden Markov Models

Are the two interchangeable terms? I have been reading about markov-switching models and am struggling to see the difference with HMM models.
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What should be done to deal with missing observations ( or outlier observation ) for Viterbi?

I want to use Viterbi algorithm, to decode an HMM sequence, but very few observations are missing in some of the steps or outliers. The hidden states in these steps are assumed to be the same as ...
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233 views

How do I train HMM's for classification?

So I understand that when you train HMM's for classification the standard approach is: Separate your data sets into the data sets for each class Train one HMM per class On the test set compare the ...
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Why are after training 5-state HMM only few entries of transition matrix left greater than zero?

I try to create the speech recognition system based on 5-state HMM + Multivariate Gaussian function. I use my own feature vector derived from MFCC (Mel-frequency cepstral coefficients). The problem is ...
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33 views

Exact inference in a Factorial HMM with 2 hidden state chains

I am trying to understand the process of exact inference in Factorial HMM models. While it is explained here (Appendix B, page 20). I think my goal is slightly different and I am struggling to fill in ...
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28 views

Confidence interval for hidden markov model (MATLAB preferred)

I'm trying to uncover the transition parameters of data of a hidden Markov Model using MATLAB. Using the built in hmmtrain function, I can estimate the parameters quite well (I already know what they ...
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How to combine states of viterbi path?

I am using HMM in my project. After Viterbi, I can get a sequence, such as 0000000000011111011111100000000000111111111111....... The 0 in subsequence 111110111111 may be wrongly decoded. Because in ...
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24 views

Markov model for time series, going back n periods?

I realise there are a lot of questions about markov here, but as we say in Dutch, I couldn't see the threes through the forest. I have a sequence of intervals between subsequent notes (pitches). ...
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29 views

Computing Standard Errors in EM algorithm

I'm applying the EM to a hidden markov chain (the $\mathbf{Z}=\{Z_1,...,Z_n\}$ variable), with observations(the $\mathbf{Y}=\{Y_0,...,Y_n\}$ variable) dependent not only on the hidden markov chain, ...
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74 views

Scaling the backward variable in HMM Baum-Welch

I am just trying to implement the scaled Baum-Welch algorithm and I have run into a problem where my backward variables, after scaling, are over the value of 1. Is this normal? After all, ...
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66 views

How to incorporate per-observation emission priors into HMM

I have a two-state HMM, in which my belief in emission probabilities depends on the observation. Basically, in addition to the two vectors of emission spectra (one for each state), I also have two ...
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70 views

The state-of-the-art methods for speech recognition?

Recently I noticed that Google and Apple have really high quality speech-recognition services. I was wondering about the state-of-the-art methods and techniques they are/might be using to achieve such ...
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Does this graphical model describe a hidden Markov model?

I'm facing the problem of visual tracking in computer vision. I have some observation (image blobs by background subtraction) produced by some moving object, and the task is to infer the state ...
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105 views

Confusion about hidden Markov models definition?

In Wiki the following diagram has been sketched and the following text has been written: From the diagram, it is clear that the conditional probability distribution of the hidden variable x(t) ...
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128 views

Initial Probabilities of an HMM

I have a learned Hidden Markov Model (HMM) from a certain sequential data using Gibbs sampling. I have managed to obtain the transition probabilities (transition matrix) of the Markov chain and the ...
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150 views

scikit learn HMM training results in non-positive definite covariance matrix

I have a observation sequence of around 1000 samples, each observation is a 10 dim vector. I am trying to learn an HMM model based on this. Specifically I am using the GaussianHMM based on this ...
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130 views

Scikit-Learn GaussianHMM decode vs score [closed]

What Exactly is the difference between decode and score? The documentation seems pretty sparse regarding this. My guess is that: decode represents the probability of the best sequence of states for a ...
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130 views

Graphical models for correlation of random variables and prediction of hidden observations

I am studying about Graphical Models and I came up with a simple example but I am not sure which kind of technique (HMM, DGM, MRF) would be able to help me with that. Imagine we have three balls that ...
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Restrictions on the type of HMM observations

I am working on developing an HMM (or DBN) to detect vigilance from time-series observations of eye-closure. Vigilance is defined as a binary variable (vigilant or non-vigilant). While I understand ...
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52 views

Optimal lookback period and standard deviation level for determining in which state of Hidden Markov model with Gaussians

I am trying to solve the following task analytically, yet can only come up with heuristical solution for special cases based on monte carlo simulations: Given a Hidden Markov model with two states ...
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Trouble understanding posterior probabilities

I'm having trouble understanding what this problem is asking for. Could someone clarify how to obtain posterior probabilities using backward/forward probabilities?
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Filtering with HMM

I want to use HMM for filtering, i.e. to find $p(x_t|y_{1:t})$. I see that the forward algorithm calculates the forward variable as a joint probability; $\alpha_t(i) = p(y_{1:t},x_t=S_i|\lambda)$, ...