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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Creating synthetic data for time series, Hidden Markov Model

Suppose that I have a task of classifying a time series. I decide to use Hidden Markov Model $\lambda(A, B, \pi)$, where $A$ is a transition matrix, $B$ is an emission probability, $\pi$ is an initial ...
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Viterbi algorithm differs between digital communications and more general HMM?

I am self-learning Markov modelling, currently looking at simple examples of hidden markov models (HMMs) and more specifically, Viterbi's algorithm. I saw a few uses of Viterbi's algorithm in simple ...
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HMM estimation (Baum-Welch) with 2 independent state variables

I'm trying to estimate a hidden Markov auto-regressive model with two independent state variables. You can think of one as determining the levels for the mean-reversion and the other determining the ...
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Estimate the HMM parameters (2states), backward

I fitted a 2-states-HMM model last week, and generate a bunch of 1s and 0s, but I forgot to store its parameters (transition matrix). Now, I only got these 1s and 0s, how do I backward/reverse-...
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Reframing a HMM problem as an RNN

Inspired by this question I have been considering how one would reframe a HMM problem as RNN problem. For HMMs we have some observable timeseries $y(t)$ which corresponds to a set of hidden states $q(...
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How to get the probability of number t element in HMM?

Suppose I have 3 hidden states. I want to get the probability of the last element belongs to state 2. How do I achieve this probability? I have looked at the forward algorithm, It doesn't seem like ...
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Confusion about names of algorithms used in Hidden Markov Models (Baum-Welch vs Forward-backward vs Forward)?

Copy of this question on DS SE 2 of 3 fundamental problems in Hidden Markov Models are: (1) estimate model parameters given just the observations (2) compute likelihood of observations given model ...
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Observed hidden variables in HMM

I am studying Hidden Markov Models and I'm trying to understand the following exercise: Consider Hidden Markov Model with hidden states $h_{1:T} = \{h_1,...,h_T\}$ and observed states $v_{1:T}=\{v_1,.....
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Independence in Graphical model of $p(h_{1:T}|v_{1:T})$ of an HMM

I am studying Hidden Markov Models and I'm trying to understand the following exercise: Consider Hidden Markov Model with hidden states $h_{1:T} = \{h_1,...,h_T\}$ and observed states $v_{1:T}=\{v_1,.....
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How to map states between two different Hidden Markov Models (HMM) for a classification problem?

I am currently working on a classification problem for timeseries analysis which uses two different Hidden Markov Models. I fit a model to the sample of subjects belonging to class A, model A, and ...
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Comparing time series classification with Hidden Markov Model vs Dynamic Time Warping - which model should I use to generate data?

Copy of this question on DataScience SE I am writing a thesis which compares two approaches to time series classification: Hidden Markov Models and Dynamic Time Warping combined with 1-NN. I'll apply ...
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Parameter estimation of state-space models with hidden variables

I have a time-series analysis problem, that I am having trouble finding a suitable regression technique for. I have a coupled linear three dimensional system \begin{align*} X_{t} & =\left(1+J\...
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Memorylessness by way of additional dimensions

This is a somewhat broad question that occurred to me regarding the nature of memorylessness. Namely: Is there utility in considering systems which are themselves not memoryless, but then expanding ...
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Find "seasonality" in a categorical time series in python

I have the following sequence: ...
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How to calculate the equilibrium (initial probability) for second order HMM in python?

I have a transition matrix looks like: ...
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When using Markov models for attribution modeling,what information does the transition matrix have,that causes the steady state vector not to be used?

I've just finished my msc thesis in attribution modeling, comparing higher order Markov models and the heuristic approaches. The professor's question is what information does the transition matrix ...
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AIC vs BIC for time series clustering and descriptive purposes

I'm in the process of fitting a hidden markov model with gaussian mixtures to time series health data. The primary purpose of this is descriptive, not predictive – I'm using the fitted model to give a ...
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Computing conditional distribution of hidden state given observed states?

I am interested in the following Gaussian linear system that describes a Hidden Markov Model (HMM): $$x_{k+1}=Ax_k + u_k + \xi_k, \xi_k \sim N_2((0,0), 0.01I_2)\\ y_{k+1}=C^tx_{k+1}+\eta_k, \eta_k \...
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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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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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