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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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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37 views

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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Optimal sampling rate for forward algorithm

I have a system with a binary-state. The system state is estimated by an HMM forward-algorithm. Also, the system allows a varying sampling rate. Considering that the system state transition takes a ...
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1answer
24 views

Hidden Markov Model: How to define the state observation matrix B for continuous (Normal) observations?

I am having a hard time understanding how to use the observation matrix B for continuous HMM assuming the observation of each hidden state Normal. So far I defined the matrix B as an Nx2 matrix where ...
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Is an HMM an appropriate model for a case like this? If not, what is?

I hope to build a fully empirical model of Total Daily Energy Expenditure (TDEE), i.e. the number of calories an individual must eat in order to neither lose nor gain weight. As data, I have ...
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Help with state-space Markov-switching models

I am new to state-space models with Markov-switching, but the reason I am interested in this is because I want to model trend productivity in the fashion of Kahn & Rich (2007). In general, I am ...
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Is statistical machine translation similar in many ways to Hidden Markov Model? How can we justify it?

Came across this question but didn't know the correct answer, if anyone could clear this out would be of great help. 'If we say we Statistical machine translation is similar in many ways to Hidden ...
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Dirichlet Process vs Hierarchical Dirichlet Process: coupling among transitions on infinite HMM

I'm new to nonparametric Bayesian, and I am reading a paper about beam sampling for the infinite hidden Markov model. In the paper, it is mentioned that since there is no coupling among the ...
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Efficiency of Viterbi Algorithm

Considering that we have a sequence of observed states $\{y_1, y_2, \dots, y_T \}$ of length $T$. We want to generate a path $\{x_1, x_2, \dots, x_T\}$, which is a sequence of states $x_n \in S = \{...
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What model to use when examining subject specific control variables on the outcome?

I want to study whether a trader will buy or sell a stock from a given set of stocks =[1,2,3,...,n], based on the sentiment scores of these stocks [sent_1, sent_2, sent_3, ..., sent_n]. So basically I ...
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HMM or RNN for modeling and prediciting deep sleep

I have created a hidden markov model (HMM) that predicts if a drosophila is awake, in light sleep, or in deep sleep using binary movement data as the input / observable. However, I was wondering if a ...
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Browser history topic clustering

I have a detailed browser history where each event has a visit time, visit duration, URL, and page title. For example let's consider this browser history (page titles only): is Thailand open for ...
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165 views

Forward algorithm vs Forward–backward algorithm

Both the forward algorithm and the forward-backward algorithm are expected to provide a probability for the hidden states. For a live estimate of the state, does it pay to add latency to the output ...
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Hidden Markov Model

For part b, would the answer be p = 7/10 since the left hand is biased, we would look at every q that has L and check the observation for every L that has H?
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1answer
52 views

Number of states in HMM

I am testing a HMM model by generating data from a 3x3 transition matrix and 3x4 emission matrix and then trying to train a HMM model against this data with different initializations. When I plot the ...
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Separating random and correlated errors

When running the ping command over a IP network for a period of time, I assume the packet loss will be a combination of: Random, uncorrelated failures where the ...
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1answer
27 views

Predicting Graph Edge Connections

I have a set of nodes in 3d physical space. Some of those nodes are connected to one another by a graph edge, while others are not. Just because two nodes are physically close doesn't necessarily mean ...
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Viterbi Algorithm [closed]

Can someone explain why Is it because for the left argument, we would find the most likely sequence of states given observations and for the right argument, we would eventually find the most likely ...
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Tensorflow Hidden Markov model

A decoding HMM has 3 parameters. But I am bit confused in tensorflow's HMM parameters and I'm not clear with docs https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/...
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Update the Emission Matrix in Baum-Welch Algorithm for HMM: Numerical Example

I am trying to manually implement a numerical example of the Baum-Welch Algorithm from the following Tutorial https://handwiki.org/wiki/Baum%E2%80%93Welch_algorithm. I do not understand how the ...
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HMM/Linear Dynamical System - How do I incorporate observation lags?

I'd like to use a Linear Dynamical System to model economic time series (e.g. Total Non-Farm Payroll), as observed in economic releases from the BLS, BEA, etc. There are two stylized facts about the ...
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How do I model state transitions, but conditioned on extra features?

I'm trying to model a dataset in which the goal is to predict the path of users through a series of states. The state space is very simple, with just three states, and I have plenty of sequence ...
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How to interpreting the log-likelihood values of Hidden Markov Model?

I have working with Hidden Markov Models for prediction purposes. I have used 8-HMMs each with 3,4,5 and 6 hidden states for a dataset. So, I have 4 sets: ...
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Best way to get a single sequence of states using Viterbi algorithm in Stan/R

I am writing this up because it seems like there should be a standard, easy way to do this and I just haven't found it. I wrote up my Viterbi algorithm in Stan as shown here in the Stan User's Guide, ...
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2answers
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Understanding Bishop on EM for HMM's

I'm reading page 616 of Bishop's PRML (pdf), which introduces EM for hidden markov models with categorical hidden states and arbitrary emission distributions. Bishop defines $z_n$ as the hidden state ...
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Difference between Infinite HMM and Latent Variable Model with Sequential Chinese Restaurant Prior?

What is the difference between an infinite HMM (http://mlg.eng.cam.ac.uk/zoubin/papers/ihmm.pdf) and a latent variable model where the latent states are given by a distance-dependent Chinese ...
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Understanding how to calculate removal effects in a markov chain

I am currently trying to model a Marketing Multi-Channel Attribution. All the articles and the packages I have come across use a special "start" state and the removal effect is calculated ...
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imputing high percentage of missing data in multivariate time series

In a dataset with time-series, that is dependant on a given input, which the time-series are given only on an irregular cycle of 10-12 time steps that makes lots of missing observations what is the ...
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32 views

Covariate dependent Markov models? Plot state transition probability along gradient of covariate values

fist post here, came from Stack overflow as it was suggested to me this is more appropriate for the kind of question. So, data consists of 4 variable, id, x1 and x2, continuous variables which are ...
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1answer
68 views

Equivalence between ARIMA and HMM

The question is about the equivalence between ARIMA models and hidden Markov models in the context of time series analysis/prediction. Specifically: Can any ARIMA(p,d,q) model bet represented by an ...
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Markov Decision Process augmented with latent/hidden variables but does not use a belief state distribution (what do we call this?)

I have a Markov Decision Process where packets arrive to a queue which services them. It has a high cost fast setting and a low cost slow setting. Usually the arrival rates are assumed to follow some ...
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Deep markov models

I am reading the following article: https://arxiv.org/pdf/1609.09869.pdf It's a Markov Model in which emissions and transitions are parameterised by neural networks. In section 2 Background, they say ...
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Marginalizing a time-series model in Stan

I'm trying to implement the following model in Stan $$ \theta[i] \thicksim Normal(0,1) \\ b[k] \thicksim Uniform(0.0, 2.5) \\ a[k] \thicksim Normal(0,1) \\ guess[k] \thicksim Uniform(0.0, 0.5) \\ ...
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Time series forecasting: from ARIMA to LSTM

I am looking for resources on the techniques for time series forecasting. It seems that there are three approaches, listed below in the order of their machine learning-ness (and correspondingly their ...
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Packages for autoregressive HMM?

I have data I'd like to fit a generalized HMM on: my observations $\{Y_t\}_{t=1}^N$ and my states $\{X_t\}_{t=1}^N$ are both time series. The specific task I'd like to do is decoding the states given ...
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Solving Markov Switching Autoregressiv (MS-AR) model

I am currently trying to estimate a MS-AR model of the form $$y_t - \mu_{s_t} = \sum_{l=1}^{p}\phi_l(y_{t-l}-\mu_{s_{t-l}}) + \epsilon_t$$ with $p=4$ and $n=3$ regimes. Further, the variance terms are ...
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Why do we fit Recurrent Neural Networks with backprop instead of message passing/expectation propagation?--as with hidden markov models

The form of a Recurrent Neural Network (RNN) seems to resemble that of a hidden markov model. With a hidden markov model we have transitions between discrete states, as well as an emission variable ...
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Training two Hidden markov models vs two state Hidden Markov models

I have a scenario where I have log of events followed by some kind of special event (e.g Failure etc). I have two kind of sequences (events, that are observations, can be common in both sequence), ...
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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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