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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1answer
108 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
35 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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8 views

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
25 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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1answer
15 views

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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Learning the number of chains in an infinite hidden Markov Model

I have a model whereby the first order Markov process $\{X_n: n \in \mathbb{N}\}$ has a transition probability matrix $P$ (unknown). This process spits out $\{Y_n: n \in \mathbb{N}\}$ with emission ...
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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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1answer
26 views

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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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
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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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9 views

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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30 views

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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2answers
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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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1answer
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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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1answer
36 views

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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9 views

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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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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24 views

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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0answers
51 views

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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1answer
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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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11 views

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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0answers
11 views

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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24 views

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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2answers
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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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0answers
9 views

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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25 views

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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0answers
123 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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