Questions tagged [hidden-markov-model]

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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Does HMM training data need observed states?

I have been trying to study HMMs and have had some differences in understanding them with a colleague with whom I am working on a project. I would really appreciate some clarification. From what I ...
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How to calculate the probability Matrix (Alpha) for Regular Markov chains

Pardon me for being a novice here. In the image attached, eq 3.1 represents the transition matrix (it's pretty clear). I am not able to comprehend the eq 3.2, alpha*P = alpha, as well as the further ...
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How to learn a Hidden Markov Model with categorical responses in R?

I am looking for a mature library to learn hidden markov models with categorical responses, and I want to be able to learn the HMM from several traces. I tried a few options, but I settled for the ...
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Particle Filtering: Derivation that mean of weights is the marginal likelihood

I see everywhere the following (for the Bootstrap Filter) $$ p(y_t \mid y_{1:t-1}) \approx \frac{1}{N} \sum_{i=1}^N W(x_{0:t}^i) $$ where $W(x_{0:t}^i)$ are the normalized weights defined as $$W(x_{...
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Can I still call a chain a Markov Chain if it is not ergodic, and can I still use it for prediction?

Currently, I am using a Markov Chain to build a predictive model. I have done some research on the Internet, and found that a Markov Chain has a stationary distribution followed by ergodic condition. ...
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Bernoulli process with nonstationary probability

Say we have a process $X_t\vert P_t\sim \mathrm{Bin}(n,P_t)$ where $X_t$ is observable but $P_t$ is not. Also, the success probability $P_t$ might vary over time and I don't assume some ...
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134 views

Predict output when an outcome occurs - Python

I have a dataset containing a continuous time series. There is approx 50,000 continuous samples with 3 columns. ...
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16 views

Regime detection methods to identify habitat transitions

The following figure represents the concentration of a substance (referred to as Element in the code) measured in an organism throughout its life. There are ...
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What are the differences between Smoothed and filtered probabilities in Markov-Switching models?

I am working with a MSM. I have noticed that almost all models present a plot that contains the smoothed and filtered probabilities, but I do not understand the differences between them. I understand ...
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What to do when Bayesian Hidden Markov Model doesn't converge at larger number of hidden states?

I'm learning Bayesian Hidden Markov Model (with Stan). For now I'm fitting a time series data in which hidden states are thought to represent the volatility. This series involves more than 2,500 data ...
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Efficient Gaussian process sampling on grid

I have evenly spaced data, $\vec{x}$, generated from a hidden Markov model where a photon emitter switches between bright, $b$, and dark, $d$, states with transition probability $\pi$, combined with ...
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Combining probability and density with Bayes theorem

I have prior density $f(x)$, prior probabilities $p(y=0), p(y=1)$ and two conditional densities: $$f(x|y=0) = \mathcal{N}(x, \mu_0, \sigma^2)$$ $$f(x|y=1) = \mathcal{N}(x, \mu_1, \sigma^2)$$ Where $y \...
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How to format longitudinal/panal data for HMM [closed]

How should longitudinal data be inputted into a HMMmodel (I don't care if the package is seqlearn, hmmlearn, pomegranate,...)? All these packages don't have a proper documentation on how to input data ...
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How to calculate using probability using hidden Markov model

So a hidden markov model consists of hidden states $H_i \in \{1,2,...,n\}, i \in \{1,...,\infty\}$, observable states $O_j \in \{1,...,p\}, j \in \{1,...,\infty \}$, transition probabilities $P(X_i=x|...
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Clarification on HMM training sequences

I am reading a tutorial on hidden Markov models for speech recognition by Rabiner. He states that for a simple isolated word speech recognizer, we design an N-state HMM for each word. We represent ...
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Initialisation strategies for learning Hidden Markov Models

I used hmmlearn library to initialize an HMM (Hidden Markov Model). sampled observations from the HMM, and used the sampled data to re-estimate the parameters of ...
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Hidden Markov Model with Autoregressive Emissions

So far, all standard HMM implementations I've seen assume some variation of a Gaussian Mixture (GMM) as their emission model. It can of course only have a single mixture component which reduces it to ...
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HMM backward probability question(please help)

Hello my first question here I am was learning nlp, and recently was researching about HMM. Just to make sure I understand it correctly so we have to make two assumptions to simplify everything for ...
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Linear, Gaussian HMM with no Process Noise vs. Linear Model

I have been asked to implement a statistical paper for work. I have no contact with the original author, and I am confused on his approach to the problem. He models the problem as a linear, Gaussian ...
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Evaluating goodness of fit of a model estimated with EM-algorithm (with AIC or BIC)

I am learning a Hidden Markov Model with time varying transition probabilities depending on different features. I do this by estimating the model parameters with the EM-algorithm. Now I would like to ...
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Particle Filter for structural credit risk model

Kwon (2012)* proposes a structural credit risk model where the asset value process and the noise are estimated based on the observed equity prices: $S$ - equity prices $V$ - value of the assets $Z$ - ...
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R alternatives to JAGS/BUGS [closed]

I've recently fit more complex hidden markov models with random effects and covariates etc. JAGS was the only program that could get the job done. Now I want to write my own functions to facilitate ...
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Predicting if an event will or won't occur in a fixed time period

Hypothetically, I have sales data from a shoe store. The store would like a model, which can predict if a customer will purchase a given product (always the same product, thankfully!) within a 1-month ...
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What does 'sampling from an HMM' mean?

I have an understanding of the basics Hidden Markov Models (HMM) - the transition/emission probabilities, as well as an understanding some of the algorithms used in evaluating an HMM, such as the ...
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120 views

Multi-state survival model with potentially correlated independent variables

Consider a market where every item is directly tradable against any other item. Let the set of items traded be Gold (GLD), Silver (SLV), Copper (CPR) and US dollar (USD). Individuals bring their items ...
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37 views

Hidden Markov Model with response and independent variable

I need to fit a HMM for a machine/process that links some input variable to an output variable. When plotting the values, it is clear that there is a time series pattern. This repeating pattern is ...
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What is HMM and Viterbi algorithm?

I have to learn what is HMM and Viterbi alogrithm, I search all pages on Google, but I can't understand what is HMM is and what is Viterbi is, if there is very basic and very simple examples/...
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HMM Bayesian vs. non-Bayesian

I aim to use Hidden Markov Model for regime detection in time series. My question might be a little too blurry: in which cases it is crucial to use Bayesian version of HMM and in which cases it is ...
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48 views

Extending HMM with Gaussian Emissions to GMM

In the notation/language of HMMs, say $h_{1:T_i}^i$ be the hidden states, and $v_{1:T_i}^i$ be the observations where $i=1,\ldots,n$ denote each training set. Let each mutlivariate observation $v_t \...
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Hidden Markov Models - How do you judge the probability that a given sequence of observations is produced by a specific model?

I've been trying to learn about Hidden Markov Models, but am stuck with a certain problem. I have calculated the probability that an observed sequence is produced by a given model as: P(O|λ) = Σ αT(i)...
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explanation of Hidden markov model and its values [duplicate]

So i'm trying to learn about the Hidden Markov Model (HMM) and are solving some problems. Im run into a question that I dont quite understand and are hopeing that someone on here can help me ...
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Seeing a tree graphical model as a Markov model

I have been doing an exercise task and I encountered an issue. Let's imagine that we have a graphical model(binary tree) as in the image below. To every vertex a rv $X_v$ is assigned which obtains ...
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Taking temporal coherence into account: HMM

I would like to detect sleep stages in 30s intervals, given 4 EEG and 1 EMG signals. Since my EEG and EMG data are just timeseries over 24h, they are temporarily coherent. I am currently using Python /...
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Hidden markov random field

I'm working on HMRF in wireless traffic characterization. Please can someone help? If I have 10x10 matrix how can I apply HMRF on this matrix regarding classification of wireless traffic?
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256 views

Difference between GMM and HMM

From what I understand: GMM is a probabilistic model which can model N sub population normally distributed. Each component in GMM is a Gaussian distribution. HMM is a statistical Markov model with ...
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42 views

Hidden Markov Model Training

I am reading more about sequence prediction tasks NLP specifically and am trying to fully understand HMMs and Viterbi. It seems that the latent structure for HMMs is just two matrices one for state ...
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19 views

Markov network, estimating unknown variable with multiple observations

I have this hidden markov model/network with four unknown variables $y_{1:4}$ with the discrete domain $(0,1)$ and four known observations $y^{obs}_{1:4}$ and a potential function $\phi(x_i,x_j)$. $$ ...
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61 views

Hidden markov model estimate p(x | y1, y2, y3, …)

I have this hidden markov model/network with four unknown variables $y_{1:4}$ with the discrete domain $(0,1)$ and four known observations $y^{obs}_{1:4}$ and a potential function $\phi(x_i,x_j)$. $$ ...
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Does this problem satisfy markov properties to be modeled as HMM?

I want to model a chemical reaction network which is defined by a stoichiometric matrix $\nu^{s\times m} $ where $s$ is the number of participating species and $m$ the number of chemical reactions. If ...
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hidden markov model fit with an absorbing state

Do the HMM Baum-Welch and Viterbi algorithms assume the underlying states are recurrent? I'm trying to fit an HMM where one of the states is an absorbing state, and I'm not sure if I need to change ...
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Bigram model with checkpoint sequence

I have co-occurence statistics for pairs of words and want to fill-in a sentence given a start word and another word placed in the sentence. Note that my training set never contains anymore than two ...
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60 views

Constrained parameters update during hidden Markov model forward-backward algorithm

I want to train a Gaussian hidden Markov model. I currently use the Python package hmmlearn. I looked thouroghly at the code to see how parameters are updated after each training iteration, but I ...
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Markov Chain Attribution Model: Calendar periods VS Sliding Window?

I'm trying to utilize Markov Chains in order to analyze and attribute online conversions of b2b users browsing on a company web. The key question mark I'm facing is on which period length to apply the ...
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34 views

How to represent an HMM whose observations are a continuous vector?

I have usually read about HMMs with observation spaces that we can somehow encode as a finite number of observations. How could I use HMM fitting if my observation at each time step is an $n$-...
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17 views

Face Recognition using HMM

I had learnt some of the research papers of Face Recognition using Hidden Markov Model. Can you help me how Hidden Markov model is applied to face recognition?Also can you please give some numerical ...
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HMM - Deal with Baum-Welch emission never observed

If I train a HMM with a given sequence of observations among n possible emissions, how do I deal with an emission that is never observed? For example, if in a 100 long observation sequence the ...
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How to work out the global maximum of the likelihood of a hidden Markov model?

I have generated some data based on a transition matrix and emission parameters that I have set. I want to test whether the optimisation algorithm I am using will find the global maximum of the log-...
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43 views

What is an appropriate threshold for the EM algorithm?

I am implementing the Baum-Welch algorithm (special case of the EM algorithm) on a hidden Markov model and I now have to pick an appropriate stopping criteria $\epsilon$ so that the algorithm ...
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80 views

Convergence of EM algorithm

I am aware that EM eventually converges. However, I still have some confusions regarding this property: 1: As far as I am aware, HMM, Gaussian mixture model and MCMC can converge and all of them use ...
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59 views

Hidden-Markov Model for Markov-Chain with Sequential Bernoulli State Sampling

Consider a finite discrete-time Markov chain whose state is sampled at the times determined by the outcome of a Bernoulli process. That is, in each time period I flip a biased coin. If it comes up as "...

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