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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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Biased viterbi training result

I try to use GMM-HMM model to infer the topic of sentences in a short paragraph. While instead of using normal Baum-Welch optimization, I use viterbi training as follows. I use average of word ...
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Why does HMM model for POS tagger works better with less data

The following is the result of using an HMM model for POS tagging a corpus. The following shows the size of training data and the precision on 1000 words test data: ...
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Modelling probability distribution of a set of sequences (to calculate Entropy)

Let $T$ be a set of trajectories $\tau$, where $\tau=\{\mathbf{x}_1,\mathbf{x}_2,...\mathbf{x}_N\}$ with $\mathbf{x}_i\in\mathbb{R}^k$ being a vector of observations. I am looking for an efficient ...
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Markov Chain for Different Groups of Time Series

I would like to use (hidden) Markov Chain to predict $X[t+1]$ stock price. Historical data for top biggest 500 companies for last 10 years will be used for training. The error would be sum of $...
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17 views

Normalizing output of Viterbi algorithm

Viterbi algorithm can be used to solve problems in belief networks of the following kind: $$argmax_{x_{1:t}}P(x_{1:t}| e_{1:t})$$ where $e_{1:t} \in E^t$ are evidence variables and $x_{1:t} \in S^t$ ...
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33 views

What are the differences between Bayesian networks and hidden Markov models?

Bayesian networks and HMMs are both probabilistic graphical models and they are both represented by DAGs. What else do they have in common? What are their differences, both in terms of architecture ...
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10 views

How to model this as a POMDP?

I would like to fit a DLM to a dataset in R but I don't know the underlying transition matrices between states nor do I have a guess for the emission matrix (given a state, what responses should I see)...
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23 views

Hidden Markov Models states

i have a simple question, let's imagine we have a system with 3 states, room 1, room 2 and corridor. Thanks to some bluetooth receiver i'm able to understand if somebody is in the room 1 or 2, not in ...
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32 views

How do you find the most probable state path given an observed sequence with infinite emissions values in MATLAB?

I have created code to output observed values of a Hidden Markov Model. I see that 'hmmviterbi' would give you the most probable state sequence given an observed sequence, transmission matrix, and ...
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40 views

Data exploration methods for noisy time series

I have time series data from NanoPore sequencing (Attached is a illustrative figure and short explanation) which I'd ultimately like to use in order to find various methylation patterns in the input ...
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1answer
38 views

What happens if the observations are connected in a hidden Markov model (HMM)?

Suppose that we have an HMM with hidden variables $X_t$ and observed variables $Y_t$. Why do we always assume $p(Y_t|X_t)$? What happens if we have $p(Y_t|X_t, Y_{t-1})$? Is it because that wouldn't ...
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Hidden Markov Model probability of producing a sequence

Suppose that we have two models for a 2-state HMM and both have two output symbols: $A$ and $B$. Model 1: Transition probabilities: $a_{11}=0.6$, $a_{12}=0.4$, $a_{21}=0.0$, $𝑎_{22}=1.0$. Output ...
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25 views

Deciding length of units in sound recognition for training HMMs

I am working on creating a method to detect changes from one song to another. Namely, I hope to use a Hidden Markov Model (HMM) in order to model a part of a song and check to see if it accurately ...
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12 views

Model selection with this model of a large number of components

I have a discrete time Markov Chain $\{X_n: n \in \mathbb{N}_0\}$ with unknown transition matrix $P \in \mathbb{R}^{M \times M}$ on the state space $\mathcal{S}_X = \{1,2, \dots, M\}$, with $M \geq 2$....
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Kalman/HMM for (short) multivariate time series from a sample with missing values

The problem in short: I want to estimate (?) a lag-1 Markovian hidden process for offline multi-variate discrete-time time series with continuous distributions via smoothing, with no dimensionality ...
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39 views

Hidden Markov Model for classification

I have fitted a Gaussian mixture model to my data. This Gaussian mixture model is the combination of two Gaussian distributions. I call the first Gaussian distribution state 1 and the second Gaussian ...
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37 views

How to use the Expectation Maximization (EM) algorithm for Part of Speech (POS) tagging?

I want to know how can we use the EM algorithm for Part of Speech (POS) tagging. The data is a set of sentences Xs and their POS tags Ys i.e. a sentence X is a sequence of words $(X_1,X_2,\ldots, ...
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1answer
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Viterbi and forward-backward algorithm in HMM

I am learning HMM recently and got confused with the training problem (training model parameters and hidden state given outcome sequence). As far as I know, both Viterbi learning and Baum-Welch (...
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56 views

Combining a neural network and hidden Markov models

I am reading a paper where authors use neural networks to produce emission and transition probabilities. And I am confused about the way they've described their emission architecture and transition ...
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1answer
32 views

Are e2e DL systems better than DNN-HMM models in speech recognition?

End-to-end deep learning systems for automatic speech recognition (ASR) have been around for a while now since Deep Speech (2014), but I noticed that DNN-HMM based methods are still performing well ...
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1answer
29 views

What's the proper name for these chain structured PGMs?

I'm trying to find previous work that has dealt with this type of PGMs, but don't know what to call them: a) "recurrent HMM"? $y_i$ are scalars and $x_i$ are discrete b) "triangle HMM"? again, $y_i$ ...
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28 views

Time-Series Test Statistics

We have observed a time-series of number of occurrences of a process over time (discrete time steps). We assume a hidden Markov model ($k$ states) governing the rate of occurrence of points in each ...
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Baum-Welch (EM) algorithm for non-homogeneous Hidden Markov Models

Is there a way of applying the Baum-Welch (or more general, EM) algorithm for non-homogenous Hidden Markov Models, i.e. if the Markov chain depends on covariates?
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Imposing constraints on observation model in a HMM

I have $N$ observations ($x_1, x_2,.. ,x_N$) from a HMM with $K$ latent states. The M step for computing the observation model $\mu_k$ involves maximizing the expression: $$ L = \sum_{n=1}^{N}{ln \...
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Testing Baum Welch algorithm

I am looking for a working example of the Baum Welch algorithm of a form like this: Define the true model $\lambda=$(A,B,$\pi$) (transition probabilities, emission probabilities, initial distribution)...
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1answer
41 views

Why are discrete state Hidden Markov Models far more popular than continuous state HMMs?

I am planning to use a Poisson HMM to model the long-memory serial correlation in my data, and my first thought was to use a mean-reverting continuous state, something like a univariate Ornstein-...
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Calculate Transition Probabilities Interest rate data

I came across a paper by Rodda (2004), who simulates interest rates with a Markov sequence. To simulate changes in the interest rates, they used the historical transition probabilities. Their ...
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15 views

Sequence Prediction with noise / gap using markov models

I'm trying to understand if Markov models can account for a "noise event" when predicting the next item in a sequence. For instance, if i have very frequently occurring (noise) event "F", can a ...
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49 views

Markov Models for time series prediction

I am student conducting an experiment with different models for time series prediction. In my experiment, I am going to use ARIMA, a Recurrent Neural Network, a Long-Short Term Memory network, and a ...
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1answer
25 views

Why does different factorisation matter in Markov networks?

I have been reading about Markov Networks that given some set of factors we can construct a unique graph G but not the other way around: "It should also be noticed that, given a set of factors, the ...
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Hidden markov models for phoneme recognition in continuous speech

I know how to apply hmm when I have an isolated phoneme. I'd just have to create several models of hmm (with al leats 3 states per model), one for each phoneme, compute forward algorithm on all of ...
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1answer
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Forward algorithm for ZIP - Hidden Markov model

I'm trying to adjust a Zero Inflated Poisson Hidden Markov Model with Stan. For the Poisson-HMM in a past forum this setting was shown. see link. While to adjust the ZIP with the classical theory is ...
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1answer
40 views

Combining probabilities to find most probable window

I have a series of observations, with an associated probability that an event is occuring at timestep t, something like: [0.8, 0.8, 0.3, 0.9, 0.2] Events can ...
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27 views

Finding Probability of a digit given a sequences?

I have a n sequences of numbers ranges from 1 to 4, say sequence s1 = [1,3, 1, 4] and s2 = [2,1,3,4] up to s(n). My question is how can i find probability of a number coming right after a sequence, ...
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42 views

How to train HMM for ECG beat types generation?

I've read papers on using a regular Markov Model to do this, manually defining the transition matrix. I wanted to use a Hidden Markov Model to more accurately capture these transition probabilities ...
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Bayes Factor Poisson-Hidden Markov Model

I am following the Hidden Markov Models guide text for Time Series An Introduction Using R (Walter Zucchini). Chapter 7. Bayesian inference for Poisson-hidden Markov models. Specifically in section 7....
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1answer
30 views

Kalman filter-ish model, is this identifiable?

Time series of observations $y_t$. The proposed model is that there's unobservable scalar series $x_t$: $$x_t=\phi x_{t-1}+B_tu_t+w_t$$ where $u_t$ - vector predictirs and $w_t$ - noise. Then there's ...
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24 views

HMM: Efficiently calculating a probability of a subsequence given the next hidden state

The forward-backward algorithm offers an efficient way to calculate the joint probability of a subsequence of observed states y1...yt and a hidden state xt = i (via alpha values). However, I am ...
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How can I use (modify) the Forward algorithm to calculate the probability of a subset observation?

For usual HMM problems, observations are generated for all time steps. But let's suppose that we only observe a subset of the outputs: $x_{t1},...x_{tk}$ at the time steps $t1,...tk$. How can we ...
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Notation in different articles about HMM

I'm studying hidden Markov models, especially the articles by Stamp (2018) and Rabiner (1989). Please let me check with you that I got this right: Especially the last observation is my own, about the ...
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25 views

build a macine learning model, using Hidden Markov Model

I have a task to predict student retention by modelling student behavior by observing observable states (such as interaction with log data that contain accessing lectures,discussion, problem and so on)...
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24 views

Way build a ML model with dynamic dataset have dependencies between feasuers- python or node

I need build a model has to predict for the director of a treatment institute What is the recommended treatment for a new patient according to his Personal Information and Difficulty diagnosed: the ...
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43 views

Viterbi Algorithm vs Maximum of Variational Posterior for HMM

I have a HMM with observed values $x$ and latent values $z$, upon which I've performed variation inference to get an approximate posterior distribution $q(z|x)$. If I want to calculate a "most likely ...
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32 views

What is the relationship between the EM-algorithm, forward-backward alrgorithm and Viterbi algorithms for Hidden Markov Model?

I know procedure of viterbi, EM-algorithm, and forward-backward independently for Hidden Markov Model. But what the relationship between them?
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51 views

How to infer the number of states in a Hidden Markov Model with Gaussian mixture emissions

I have a time series made up of an unknown number of hidden states. Each state contains a set of values unique to that state. I am trying to use a GMM HMM (as implemented in Python's ...
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35 views

Autocorrelated time series analysis

I have a set of observations $X_1, ...,X_n$. They can be generated with a simple Markov chain with $k$ states - in theory, in practice there are covariances between observations from different time ...
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1answer
263 views

Examples of state space models where the filtering problem can be solved analytically

Background A discrete-time, Markovian state space model takes the form \begin{align} \mathbf{y}_t&\sim p(\mathbf{y}_t\,|\,\mathbf{s}_t,\,\boldsymbol{\theta})\\ \mathbf{s}_t&\sim p(\mathbf{s}...
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HMMs: How to Interpret The Average Likelihood Of My Data

I have recently trained an HMM using R's depmixS4 package, and am evaluating its performance via the average likelihood of my data. The equation is provided below: However, I noticed the average ...
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1answer
143 views

HMM - Difference between forward and backward case

In the HMM formulation where z is hidden state and x is observed In the forward case, I see it represented as such: $\alpha_{k}(z_{k})=P(z_{k},x_{1:k})=\sum_{z_{k-1}}P(z_{k},z_{k-1},x_{1:k})$ but ...
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2answers
40 views

Trouble understand HMM Forward Algorithm

Referencing: https://en.wikipedia.org/wiki/Forward_algorithm I understand most of the expansion of the forward algorithm, but the very first step is confusing to me: Why does the joint probability ...