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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Hidden Markov Model - Baum Welch algorithm initialization

Currently I'm working on a problem where I have a multidimensional, continuous sequence of observations $X$ that model my response variable $y$ with two states $0$ and $1$. I assume that this sequence ...
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Hidden Markov Model observing sequences

I have been trying to understand Hidden Markov Models but I often find myself confused. I have discussed with my tutor for further help however, he is often rude and does not help and so I have ...
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Which Significance test to apply to compare number of occurences of multiple events across multiple groups?

Our dataset is composed of time-series data (recordings) collected for 18 different groups (test conditions G0 to G17). The number of recordings per group can vary (30-600). For each of these ...
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Equal Error Rate in Hidden Markov Models for Speaker Recognition

I was asked to report the Equal Error Rate (EER) for my speaker recognition proposal. I trained one HMM for each speaker. To evaluate, I introduce the input of an speaker in both models and classify ...
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Calculate probabilities given hidden markov model

Consider a disease D with incidence rate of 5 cases per 100 people (i.e., P(D) = 0.05). Let the corresponding boolean variable D refer to a patient “having disease D”, and let another boolean variable ...
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R msm package does not generate estimates

I am trying to use the MSM R-package to estimate a continuous-time hidden Markov model. I do not know why my code does not show the estimates and confidence intervals for the transition intensities ...
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Are Hidden Markov Models the right tool for signal segmentation task?

I have a particular problem, and I would like to know if using a HMM is the correct tool for it. Apologies for the poor wording of the problem, HMMs are definitely not my specialty. I have the ...
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Python: Markov switching model out of sample forecasts

Is there a way to obtain out of sample forecasts for Markov switching models estimated via statsmodels (or any other package)? https://www.statsmodels.org/dev/examples/notebooks/generated/...
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Real-time sequence classification with Markov Chains vs HMM vs CRF

I see that Markov Chains are useful for providing the conditional probabilities for each individual symbol of the test sequence. So this really gives an incremental overview on how the sequence is ...
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How do HHMM (Hierarchical Hidden Markov Models) work and where to learn more?

I recently came across something called Hierarchical Hidden Markov Models. I am familiar with HMMs, but not HHMMs. I have two questions. I can't fully understand the procedure after reading here: ...
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What are the transition functions for RNNs

From what I understand, the hidden states of RNNs are equivalent to the deterministic probability distribution over hidden states in for example a Hidden Markov Model. Thus, just as probabilistic ...
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How to create/design a Hidden Markov Model?

I have a rough conceptual understanding of what Hidden Markov Models do. What I don't understand is how to really create/train one. Let me outline what I'm working on, and then I'll give more specific ...
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Choice between static and time series Bayesian models

This is a methodology question. I have synchronous time series data (5 dimensions, t=0,1,2,3 etc). In this time series, I believe there are some (unlabelled) events of interest that occur maybe 1% of ...
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What should I optimize when applying Hidden Markov Model to classification problem?

My goal is to classify device as 1 of 5 possible types based on timeseries of its power consumption. I am using the following procedure: Initialize 5 instances of Hidden Markov Model with Gaussian ...
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How do Hidden Markov models classify sequential data?

How exactly do HMMs classify sequential data? I understand that this is a generative model, which models the joint probability distribution and provides us with the conditional probability of ...
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The different between $P(O;\lambda)$ and $P(O|\lambda)$ [duplicate]

In hidden markov model (HMM), if I was given a particular observation $O$ and parameter of HMM $\lambda$, I want to compute the likelihood of a particular observation sequence $O$, $P(O|\lambda)$. Why ...
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Is there such a thing as an order-$k$ RNN?

In HMMs it's common to include edges from previous layers of the model. Looking back at the previous $k$ layers creates an order-$k$ Markov model. Is this commonly done in RNNs? Have you ever seen ...
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Hidden Markov Models with continuous observation densities and scaling?

I am attempting to implement Hidden Markov Models that utilize continuous observations. However, in Rabiner's explanation to implement HMM's with continuous observation densities. There is no mention ...
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How to find state-space representation for an estimated HMM model in R

Take the toy (already estimated) HMM model below from the R package MSwM. How do I find a state-space representation for it? Put differently, what are the matrixes: ${G}_t,F_t,R_t,Q_t$ in the ...
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Filling unknowns within a sequence with a sequence-to-sequence LSTM model

Say we have a very simple sequence pattern that associates a state which is always observable, with a state that is sometimes hidden, and that we want to predict when it's hidden. It is assumed that ...
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Hidden Markov Model Exercise BRML 23.3

I am reading "Bayesian Reasoning And Machine Learning" and I'm doing exercise 23.3 (a) on p.490. Here's the exercise: Consider a HMM with 3 states $(M=3)$ and $2$ output symbols, with a ...
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Why is this HMM a wide sense stationary process?

I have the following HMM model with two states: $$X_t \sim N([0,0],\begin{bmatrix} 1 & .9\\ .9 & 1 \end{bmatrix}) \text{ for state 1},X_t \sim N([0,0],\begin{bmatrix} 1 & -.2\\ -.2 & 1 ...
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Baum-Welch Algorithm and Viterbi Algorithm

Given a sequence of actual states which is assumed to be the sequence that has the maximum likelihood of causing an observed sequence of states, is it possible to find the parameters such that when ...
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Using Hidden Markov Models to Cluster of Time Series, trend Data?

I have time series data of 60 observations per country, across 2 variables of interest, for 20 countries. In my case, Y depends on X, but my data is scaled. I am interested in conducting a cluster ...
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How should I score probability data to clearly highlight good/bad results, in a way that doesn't converge on zero?

I'm looking at a problem right now where we see probability data across many results, and I want to take this data and provide an eventual score, which we can then use to judge the overall probability/...
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Hidden Markov Model with Probabilistic Observations

I have an HMM with $N$ states and $T$ possible obsevations where $A \in \mathbb{R}^{N \times N}$ is transition probability matrix and $B \in \mathbb{R}^{N \times T}$ is emission probability matrix. I ...
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Choosing the best model for Hidden Markov Model

How do I determine the best model from the Baum-Welch algorithm if I know the number of hidden states? Every time I insert a different initial estimation matrix, I will get a different model from the ...
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Definition of a probability in forward-backward method for HMM

I am confused about the way that the Jurafsky and Martin book (Appendix A, page 6) explains the relationship between the observations and hidden states: Each cell of the forward algorithm trellis $...
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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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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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