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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Maximum Likelihood in the Markov Switching GARCH(1,1) Model

In the standard GARCH(1, 1) model with normal innovations: $${\displaystyle ~\epsilon _{t}=\sigma _{t}z_{t}},$$ $$\sigma^2_t=\omega+\alpha\epsilon^2_{t-1}+\beta\sigma^2_{t-1}.$$ The (negative) log-...
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Learning HMM parameters by counting?

In 8.4.3 of the book Speech and Language Processing: An introduction to natural language processing, the two matrices transition probabilities and emission probabilities can be learned by counting as ...
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Compute likelihood of state given multiple observations?

I am trying to use Bayes formula to compute the likelihood of a given state given a collection of independent but not sequenced observations - knowing the priors and knowing the probabilities of being ...
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How to use bootstrap method to compute confidence interval for HMM parameters?

I have known how to estimate parameters in hidden Markov model by Baum-Welch algorithm. And then I was curious about how to compute the confidence interval, but I found that few articles discuss about ...
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Differenciate between two distributions using gibbs sampling [closed]

This question is relate to the post : " Conditional distribution for Gibbs sampling for Gaussian mixture " but is a little bit different. My objective is to know why the algorithm (which is ...
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Next event prediction - approach

I have a problem that I do not know how to solve reasonably. I need predict date and amount of next (future) order of product. So my data looks like this: ...
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Identifiability of discrete HMM with categorical observations

My setup is simple. I have two categorical distributions with probabilities $p$ and $\tilde{p}$ that generate an observation depending on whether the hidden state is 1 or 0, respectively. In other ...
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Understanding emission probability in HMM definition

This is rather basic question. I was going through Speech and Language Processing by Jurafsky and Martin. In the book, they define a Hidden Markov Model (HMM) as follows: An HMM is specified by the ...
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Recreating research paper with HMM and K-S test

I am trying to recreate this research: https://www.mdpi.com/1911-8074/13/12/311/htm My first question is when they present the regime breakdown: ...
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How to verify if a graphical model has the markov property?

If I draw the computational graph of an HMM and an RNN from an architectural point of view they look very similar. The main difference is that an RNN gets some input $x$ and the HMM only operates on ...
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Calculating the degrees of freedom of a hidden Markov model (HMM)

I am curious if there is a straightforward explanation for calculating the degrees of freedom of a hidden Markov model (HMM). For example, take a simple HMM with a 1st-order Markov chain and 2 hidden ...
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Number of free parameters of a hidden Markov model with emission prob. as Gaussian mixture model?

If there are $K$ components (or HMM states) and there is $D$ dimensional GMM is the number of free parameters is: HMM: $K(K-1)$ for transition matrix $K-1$ for prior GMM: $D(D+1)K/2$ for ...
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What is the prior probability in a Dynamic Naive Bayes classifier?

For a Hidden Markov process with multiple types of emissions, it is possible to perform current state classification using the Naive Bayes likelihood estimation: $ p(j|b,d) \propto p(b|j) \cdot p(d|j) ...
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MDP in Predictive Maintenance sample implementation

I am searching for a sample python implementation of Reinforcement Learning, Markov Decision Process in the domain of predictive maintenance. I have tried on my own, but either found sample related to ...
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Hidden Markov models in Speech Recognition

My first question here. So I am trying to build a sign language translator(from signs to text) and noticed that the problem itself is quite similar to speech recognition, so I started to research ...
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Predicting events - seizures in epilepsy. A question about time series models matching with observations

I've been keep a diary of epilepsy seizures, and would like to attempt prediction modelling as an help for better management of anti consultant therapy. Could you help to suggest models that fit with ...
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Why do we need unary terms in Ising model (pairwise Markov random field)?

Ising model contains both $\phi(i,j)$ and $\phi(i)$. For example, consider a Markov random field with only two nodes $i$ and $j$, if $P=\phi(i,j) * \phi(i) * \phi(j)$, then we can also write $P=\phi(i,...
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Terminal State Classification with Hidden Markov Models

The Viterbi algorithm predicts the most likely sequence of hidden states. But what if the variable of interest is the final hidden state? For example, predicting if a friend (whom you can't visit due ...
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Does it make sense to study a Hidden Markov Model with an identity transition matrix?

Let's say I have a huge number of samples describing relatively long sequences of a high number of observable states, but whose 2 possible hidden states are constant inside a sequence. (Practically, ...
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HMM, probability of a short state sequence starting at an arbitrary time?

So, I'm going through some course literature on my own and don't have peers to discuss with. The question is "How will you find the probability of a short state sequence starting at an arbitrary ...
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What is the minimum time steps for training hidden markov model?

I'm working with hidden markov model. And I wonder what is the minimum time steps for training hidden markov model. For example, I have weight data with 3 years of 100 people like following ...
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Fix state labels of HMM in depmixS4

Everytime I fit my HMM, the obtained labels of states that I get are different. Sometimes State 1 is of negative mean and high std. deviation response parameters and sometimes State 2 is of negative ...
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Training a layered HMM

I am currently planning on training a layered Hidden Markov Model. I have 3 stages with the following structures. The first stage is a 3-state HMM with the State X: can emit insertion errors State Y: ...
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How do I establish which Hidden Markov Models generates better samples?

I have a time-serie and I fit different HMMs on it, each with a different number of hidden states. Now after sampling from the models , I'd like to compare the results with the ground truth data and ...
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HMM with emission probability being hidden state

I've been working on this problem for a while but cannot think of any solution. So here's the problem explained in the context of HMM. The hidden state is a probability that is updated given ...
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How to perform likelihood ratio hypothesis test between two hidden markov models

I'm currently working on a problem posed as follows: given some data $\mathbf{x}$, what's the appropriate way to accept/reject between two hypotheses which are hidden markov models that could have ...
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Solving for the parameters of a discrete markov state model

I have some observations $y_t \in \mathbb{R}_+, t\in 0 \dots n$, and I'd like to fit the following model: a vector of initial states $p_0 \in \mathbb{R}^s_+$, transition probabilities $K \in \mathbb{R}...
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Interpretation of "log-likelihood" in hidden Markov model, and requisite computations involved

I am currently debugging a hand-coded implementation of a hidden Markov model, and as part of this, am scrutinising whether I have appropriately specified the log-likelihood computation algebraically. ...
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Getting started with Bayesian Dynamic Networks?

Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden ...
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HMM continuous x, discrete y

I'm curious about whether an HMM variant is appropriate when I have a continuous x (time series) and a discrete y (emission class.) In context, I have multiple ships, which could be located in one of ...
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Local independence vs global independence in markov network

I am having a hard time understanding the basic differences between the local independence and global independence of a markov network. Please help me illustrate with a graph or any example
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Using Forward Backward algorithm to find posterior probability of all possible states

I understand that Viterbi finds the most probable sequence of states. However, I want the probability of all possible sequences of states. I understand that FB algorithm can be used to find the ...
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Comparing if obseration sets come from the same HMM

I am using a recurrent network to try and "play" stock data. I want to ask the statistical question "is my model behaving randomly?" I have two Markov chains. Both have 3 states ...
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A problem of likelihood function in a dynamic setting?

I'm having a problem regarding perhaps conditional maximum likelihood problem, but I'm not sure. Suppose time horizon we consider is $T=4$, our goal is to minimize the loss function $$ \sum_{t=2}^T L(...
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Viterbi Algorithm - Most likely sequence vs sequence of most likely states

I'm trying to understand why the following pseudo-code function is correct: ...
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Hidden Markov Model library to study animal movement (preferably in R)

I want to describe the behaviour of whales using data of their vertical movement. Besides the time-depth profile of tagged whales, I calculated several variables for each dive performed (e.g. maximum ...
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Latent Transition Analysis vs Latent Class Growth Analysis

I am curious, what are the main differences between latent transition analysis and latent class growth analysis? I am wanting to model latent classes and probabilities of changes between the classes ...
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Graphical Representation of Dynamic Bayesian Network

Some tourists visiting a cabin are interested in finding out if there are animals nearby. They can observe outside of their window every day whether there are animal tracks and whether the food they ...
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Hidden Markov Model, Particle Filtering: determining an importance density

I am working on implementing particle filtering on the following Hidden Markov Model: $$ X_1 \sim N(0,5) $$ $$ X_n = \dfrac{X_{n-1}}{2} + 25 \dfrac{X_{n-1}}{1+X^2_{n-1}} + 8\cos(1.2n) + V_n, \quad V_n\...
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How do shared weight vectors work for CRF?

I am going through two materials regarding Conditional Random Fields. The first one is this (referred to as [1]) material by Charles Sutton and Andrew McCallum and the second one is this (referred to ...
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Logistic probabilities of state variable in a hidden Markov model always has variance of zero

Here is a simplified version of a more complicated problem that I have. Imagine a hidden Markov model where the state is $X_t\sim N(\mu,\sigma^2)$. The observed variable is $Y_t\sim Bin(N, p_t)$ ...
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Optimizing this log-likelihood

I have a HMM which emits an observation Z. The parameters of the HMM are $\boldsymbol\theta$. $$\boldsymbol\theta = {\boldsymbol{A},\boldsymbol{B},\pi}$$ Where $\boldsymbol{A}$ is the transition ...
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Generating Error Data

I am currently doing a project on finding the HMM parameters for a channel which takes a DNA sequence as an input and aims to output the same sequence. However, the channel has insertion, deletion, ...
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Correlation between two consecutive observed states in a simple Hidden Markov Model with Gaussian emission

Backgrounds Suppose a Hidden Markov process with Gaussian emission and two possible latent states: $s \in \{0,1\}$. I have a observed sequence $\mathcal{X} = \{X_1, X_2, \cdots, X_T \}$, where $X_i$: $...
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Use HMM for time series classification in python - define initial states

I have a time series of locations. I want to use HMM for classification of path, by using the knowledge I have on the locations. I know that locations [0,100] should be state A , [100,200] are state B ...
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Hidden Markov Models and How to Interpret Probability of the Overall Sequence?

What can I do to improve the probability of a sequence given my data? Consider the following MWE: ...
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Interpreting viterbi decoding and posterior probabilities

I am wondering why the last state of the predicted probabilities does not match the viterbi decoding sequence. Consider this MWE: ...
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How do I find Schwartz criterion (or Bayesian Information Criterion) for these three models?

I have to find the schwarz criterion for each of the models in this maths question using RStudio but I don't know where to start. I know I need to find the free parameters but don't know how to find ...
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JAGS the precision parameter accidentally falls on 0

I am using JAGS to create an HMM model and I get stuck with a weird problem. Most of the time, the code works, but sometimes it fails and the failure is about invalid parent values of node: ...
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Hidden Markov Model - Dealing with observation lags

I have a Hidden Markov Model with a "publication lag" (i.e. the observation "published" in period $t$ is actually measured in period $t-1$). For example, a survey asking about ...

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