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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forwards algorithm - derivation

I am self-studying hidden markov models, and am struggling to with the derivation of the forward algorithm, and especially the definition of $\alpha_t$ as the hadamard product. It would be much ...
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What is the difference between a conditional random field model and a particle filter?

Please can any one explain the difference between a CRF model and a particle filter?
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Hidden Markov model - formulas

I am self-studying Kevin Murphy's book, and trying to understand the math behind the HMM. I am struggling with the following derivation. Why can we in 17.46 cross out the $X_{1:t-1}$ term? my guess ...
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Relation between AR(1) and Vasicek model

The discrete time version of a Vasicek model is equivalent to an AR(1) model with opportunely chosen parameters, as showed in this paper: http://www.damianobrigo.it/toolboxweb.pdf. Following this ...
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Real Data Sets Examples

I have a set of observations $\mathcal{Y} = {Y_1, \cdots, Y_T}$. I am running EM algorithm to fit the observations to the following Hidden Markov Model $$A = [a_{ij}]_{N \times N}, a_{ij} = P(X_{k+1} ...
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Calculating BIC for a HMM without any training data

I need to evaluate my HMM models, that are trained using EM algorithm, since I don't have any training data. In order to evaluate with BIC or with most of the other criterions I need the log ...
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Varying transition probabilities by position

I'm still very new to Bayesian Tables, Hidden Markov Models and the likes, but have an otherwise solid computational and linguistics background. I've been diving into NLTK (Natural Language Toolkit) ...
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What software estimates hidden Markov models?

I am trying to estimate a hidden Markov model (HMM) for a research project. Suppose that I observe a sequence of emissions, but I do not know the sequence of states the model went through to generate ...
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best offtheshelf MATLAB hidden markov model toolbox

Whats the best,current off the shelf hidden markov model toolbox to use for MATLAB? I came across this http://bnt.googlecode.com/svn/trunk/docs/usage_dbn.html but it seems a bit old. there are ...
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A question on mixture model

I'm a bit confused by the conception of "mixtrue model" I'm studying hidden markov model, which is frequently referred to as a "mixture model". But I don't know what the term "mixture" implies. ...
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How do I use Hidden Markov Model Viterbi algorithm for sequence labeling?

with my current small experience of HMM. Given that i have some patterns (sequence of interest for example gestures or words in spoken language) if i need to use HMM for sequence classification ...
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Test cases for HMM implementation

I've written some simple code to fit Hidden Markov Models with discrete emission probabilities (similar to this implementation, which follows Rabiner's tutorial very closely). I'd like to extend my ...
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difference between forward backward, alpha beta, sum product, baum welsh

For Hidden Markov Models, what the difference between forward backward, alpha beta, sum product, baum welsh?
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How is prior knowledge of letter/word patterns incorporated into handwriting (or speech) recognition?

Using handwriting recognition as an example, we can train various models to recognise individual characters but to actually be useful we must incorporate prior knowledge of common character sequences, ...
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How to reestimate GMMs in a HMM-GMM

Context: Automatic Speech Recognition I understand the training of a pure HMM with Baum-Welch: Expectation step compute $\gamma_t(i) = P(q_t=i |O,\lambda)$ //p(passing state $i$ at frame ...
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How can I train HMM for continuous sign language recognition?

Currently I can recognize isolated words using HMM (Hidden Markov Model) through training an HMM model for each sign, and for a new word I take the sign for the model giving the highest likelihood. ...
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How is $\sum\limits_{t=1}^{T-1} \xi_t(i,j)$ the expected number of transitions in Baum Welch

Context: Baum-Welch Algorithm, Maximization step Serveral tutorials, e.g. this one say that $\sum\limits_{t=1}^{T-1} \xi_t(i,j)=\sum\limits_{t=1}^{T-1}\frac{P(q_t=i, O | \lambda)}{P(O|\lambda)}$ can ...
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hmmtrain default prior vector

I am using hmmtrain as follow: [trans,emiss]=hmmtrain(symbol_seq,trans0,emiss0); My question is: What is the default prior vector (pi) that used in hmmtrain.m ...
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Sensitivity to scaling of multivariate data with HMM

I have some multivariate data, say 40 features. Some features are scaled between 0 and 1, and some are scaled between 0 and 1e8. For reference, I am using sci-kit learn's HMM implementation (yes, I ...
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Connection between Hidden Markov models and logistic regression?

This question is inspired by a comment below this question on Hidden Markov models: "Have you considered logistic regression? For non longitudinal data, they are practically the same thing." My ...
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Material on plate notation of bayesian hidden markov model

Does any one know some materials on plate notation of Bayesian Hidden Markov Model? Say, given multiple observed sequences, how to infer the posterior distribution of the parameters, and the ...
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hmm variable number states

I have looked around for a while but cant seem to find any literature on this but can't seem to find a treatment. I have a set A of observations at time $t_n$ $A = \{A_1... A_n\}$ Further I know that ...
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Ttests for DNA sequences

Let's say I have two sets(1000 sequences in each set: set1 and set2) of independent DNA sequences of length 30. I created a HMM model by using DNA sequences in set1 which calculate Prob(Seq/Model). It ...
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Impulse Response Analysis for Markov-Switching Models

I've estimated a bivariate Markov-Switching VAR(1). I am interesting in understanding how an error/ 'shock' would propagate through the system. I've been stuck on how this could be done? Thank you!
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Markov models that with several active states

Are there any Markov-like models that can have several active states? So say if trying to determine (the chance) when the person will wake up based on two variables (weather and the time the person ...
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How to choose between VOMs and Predictive models, e.g., ARIMA?

In time series prediction, there is a lot of work that uses predictive models (e.g., ARIMA). On the other hand, there's also a lot of work that uses Variable Order Markov models (e.g., context ...
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Reference request: EM algorithm and hidden Markov model books with solutions

I am studying missing data problems and the applications of the EM algorithm to missing data problems, like mixture models and hidden Markov models. We have been using Schafer's book Analysis of ...
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What are good tutorial on Weighted Finite Automata?

I would especially appreciate papers, books or tutorials with source code already available. Currently I'm reading "Spectral Learning Techniques for Weighted Automata, Transducers, and Grammars" by ...
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Hidden markov model multivariate regression with time-series data

I am working with a dataset that includes the trajectories of various car trips and would like to be able to predict their destinations using only a subset of the trip trajectory. For instance, if in ...
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How to use a Hidden Markov Model to detect state in a time series?

Questions Am I right in assuming that the emission probabilities will not be following a gaussian distribution for my particular problem? Obviously, I will need to train the model for state ...
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disease progression R markov chains

hello i have a dataframe, some of the columns include: remission,height,weight,time from diagnosis, age ethnicity, age, patient id remission is 1 or 0 just to be clear i want to fit an appropriate ...
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Markov chains vs. HMM

Markov chains makes sense to me, I can use them to model probabilistic state changes in real life problems. Then comes the HMM. HMMs are said to be more suitable to model many problems than MCs. ...
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Estimate core state transition probability matrix in partially observable Markov decision processes

I have a longitudinal data set of patients who have been monitored by a medical test over a year. The results of this test have false positive and false negative, so the system is partially ...
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Implications of using fixed effects to account for hierarchical data structure

I am currently implementing a hidden Markov model in R, using the msm package. The data I am using are drawn from a cluster-randomized trial; i.e. there is a ...
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Hidden Markov model question; pseudo time series?

I apologize that the title of this question isn't super specific, but I am having a very difficult time exactly and succinctly describing the problem I am facing in my implementation of a hidden ...
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Implementation of bag-of-features HMM?

I'm trying implement a word-spotting paper that uses a Hidden Markov Model where the emissions are a bag of words/features. I have found HMM implementations, but I haven't seen functionality to ...
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time series based classification

I want to classify some data. Basically the data is time series in nature. The target variable is categorical. I know there are so many algorithms for predicting the time series model. However, I have ...
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Observation Likelihood in hidden Markov models

As far as I understand, in discrete HMM, the observation symbol probability distribution $b_{i}(O_{t})$ is always a probability less than 1, e.g. $\frac{1}{6}$ for each side when rolling a dice. But ...
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Values of PDF in Bayes Classifier

I'm new here and also a beginner in statistics. I'm implementing a Bayes classifier for two classes but get confused with the value of likelihood (pdf). $$P(c|o) = p(o|c)\cdot P(c)/p(o);$$ Here ...
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Good library for Switching Autoregressive Hidden Markov Model (SAR-HMM)

can you recommend a good library for SAR-HMM? (Switching Autoregressive Hidden Markov Model) Apparently only MATLAB can be recommended. ...
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Hidden Markov models with state transitions conditioned on some node

I'm lacking some clarity related to HMM's Suppose I have a binomial state node and another binomial observation node, In this node the conditional probability table will be state transition matrix ...
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How to evaluate the goodness of Fit of parameters obtained from EM algorithm

I have a set of observations $\mathcal{Y} = {Y_1, \cdots, Y_T}$. I am running EM algorithm to fit the observations to the following Hidden Markov Model $$A = [a_{ij}]_{N \times N}, a_{ij} = P(X_{k+1} ...
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How to fit a stochastic matrix to given data.?

Given a data sequence of noisy observations of a 3-state Markov chain $X$ -- $y_1$,$y_2$,...$y_n$, with two transition matrices $A_1$ and $A_2$ corresponding to different regions (**) in the (unit) ...
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Hidden Markov Model For Text Classification

I have a question about HMMs being used to classify an entire text body under examination. This is as opposed to classifying a subset of a text body under examination. For example, classifying a news ...
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Selecting the number of mixtures / hidden states / latent variables

My question is regarding 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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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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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 ...