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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Extended Hidden Markov Models (HMM) parameter estimation

For simpler HMMs, we can use algorithms like Viterbi training (not decoding) or Baum Welch to estimate the parameters that best describe the observed data. How do we do the same when using a more ...
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What is the effect of sampling rate on parameter estimation when fitting a markov state model to timeseries data?

Let us say that I have some timeseries data, which can be described by a markov state model. And the time series has been sampled every $\Delta t$ time units. The sampling rate ($1/\Delta t$) must ...
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Do I use $P(y_t|y_{1:t-1})$ instead of $P(y_t|z_{t},y_{1:t-1})$ for prediction in a Hidden Markov Model?

I am confused what to sample for getting the prediction $y_{t}$ if I have access to the previous observations $y_{1:t-1}$ and the hidden states $z_{1:t}$. I want to predict the observation at time $t$ ...
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Help with Gambler's ruin problem, can't solve abstraction [duplicate]

I'm having difficulty solving this exercise. When I assume that p=0.4 and player A's fortune is 99 dollars and B's fortune is 1 dollar, I can find that the probability of player A losing to player B ...
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HMM probability of sequence of observations using forward and backward probabilities

I've come across this statement whilst reading about HMMs: Given $\alpha_{n}(j) = P(Y_{0}^{n}, X_{n} = j)$ and $\beta_{n}(j) = P(Y_{n+1}^{N} | X_{n} = j)$, then $$P(Y_{0}^{N}) = \sum_{j} \alpha_{n}(j)\...
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Hidden Markov Model: Robustness and `Forbidden` Transitions

I have an issue while using a HMM to estimate the state of a system where the state-transition matrix is a block-diagonal matrix. Specifically I have an issue with robustness and the HMM keeps ...
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Help interpreting normalized HMM (or otherwise) results

I have run a hidden markov model with five variables on very different scales. Because of this I normalized the input data beforehand using Carets preprocessing: ...
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How to feed multi-channel spectrograms to Deep Neural Network?

I am using a 14 channel EEG device. To do away with the need for any handcrafted features, I wish to implement an ML classification task with the EEG data collected using deep neural networks (such as ...
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Data scaling for hidden Markov models?

I understand that scaling data is important for certain machine learning algorithms, and the idea makes sense. I've found this great description of the processes here https://ourcodingclub.github.io/...
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Mean and covariance kernel for the posterior GP of a Hidden Markov Model

In a hidden Markov model (HMM) we have a process $X_k$ that evolves according to: $$ X_{k+1} = X_k + W_{k+1}, \quad W_{k+1} \sim N(0, \sigma_{W}^2), $$ where $\{W_k \}$ are IID and $X_0 = W_0$. We can ...
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Parameter estimation for HMM with different emission distribution for different states

I am trying to solve a parameter estimation problem where a HMM have different emission distribution for different states (i.e. Gaussian for one state and exponential for the other). However most ...
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Identifying states (or clusters) in multivariate mixed-type time series

I have multivariate time series with mixed data types, which includes continuous variables, binary variables, and variables with bimodal distributions. I need to identify distinct states or epochs in ...
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Interpretation of covariates HMM depmixS4

I would like advice on correctly interpreting the covariates for a hidden markov model I have run, using Depmixs4. I'm really struggling to find any examples at all that actually interpret covariates. ...
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Scaling forward variable in Inhomogeneous Hidden Markov Model

Background Ordinary HMM Consider an ordinary Hidden Markov Model $\lambda = (\pi, A, B)$ with $N$ hidden states $\{1, 2, ..., N\}$ and $M$ observation symbols $\{v_1, ... v_m\}$. Let's denote a state $...
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Q function in Baum-Welch algorithm

Assume there's a hidden Markov Model $\lambda=(\pi, \mathbf{A}, \mathbf{B})$, where $\pi$ is an initial distribution, $\mathbf{A}$ is a transition matrix and $\mathbf{B}$ is an emission matrix. Also, ...
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Improve HMM state estimation in latest data

I have a time-series dataset that is poisson-distributed, where each day I get a new additional datapoint. If I input all the data into a HMM (I am using code I found from hmmlearn in python) it does ...
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Inferring Hidden States in Hidden Markov Models

To decode an HMM, the usual approach is use the Viterbi algorithm where the probability of the most likely sequence of hidden states $z_1,..,z_n$ generating the observations $y_1,..,y_n$ is given by: \...
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Inhomogeneous Hidden Markov Model

I've recently been working on Inhomogeneous Hidden Markov Model (IHMM) as defined in this article. In short, the whole idea distinguishing IHMM from typical HMM is that a transition matrix $A = \{a_{...
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Calculate posterior distribution and full conditional of a HMM

Set up a Bayesian analysis of an hidden Markov model and calculate the posterior distribution and the full conditionals, given this assumptions: The state space of the hidden process has size m $Z_t|...
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Time Duration Modelling for Hidden Markov Models

As we know, one of the major weakness of conventional HMMs is related to the modelling of state duration, as the probability of state occupancy decreases exponentially with time. There are multiple ...
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Block sampling hidden state using forward algorithm only

In a hidden Markov model, I can't get my mind around why I can't sample the full hidden state $\vec x$ using only a forward sampling algorithm. Let $\vec y$ be the observed data and $\theta$ the model ...
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LMest for cluster membership over time

I have a dataset of 18 continuous variables measured over 3 time points for 90 patients. I hypothesise that there are clusters of patients with similar characteristics and that cluster membership may ...
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Efficient method to detect large probability shifts in HMM model output

I am using an HMM model, the specifics of which I cannot disclose. However, my objective is to detect significant transitions in the model's output probability distribution. This probability ...
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HMM matching a string as mosaic of two strings from a larger panel

I have a problem which I think can be solved by an appropriately structured (“constrained?) HMM, but I’m not sure how to structure it, and what the prior art is. Any help such as implementations, ...
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Canonical references for HMMs with covariates

What is/are the canonical reference(s) for HMMs with covariates? I'm coding some up and I'd like to follow the standard notations, if they exist.
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EM algorithm "maximization step" for product of two independent Bernoulli variables

We are given the following model, where the event $C=1$ is defined using two other Bernoulli variables $E$ and $R$: $$P(C=1|q,d,k)=P(E=1|k)\cdot P(R=1|q,d)$$ Which we denote as: $$\theta_k=P(E=1|k), \...
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Baum Welch algorithm for Semi-Continuous (Tied-Mixture) Hidden Markov Model

I'm currently implementing Baum-Welch algorithm for Semi-Continuous Hidden Markov Model (SCHMM) as described in Huang, Xuedong. Semi-continuous hidden Markov models for speech recognition, 1989, pages ...
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Extension of Markov Model with Time Dependence and Emissions

I am interested in a continuous time system with $n$ observable factors $s_1(t),\ldots,s_n(t)$ and a discrete process $z(\tau_i)\in\{0,1\}$ with random emission times $\tau_1,\ldots,\tau_m$. The ...
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ML Modeling Recommendation for Predicting Snake Encounters in Historical Journey Data

I have a dataset consisting of historical journey data where individuals travel from point A to point B. During their journeys, they may encounter varying numbers of animal sightings, including snakes....
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HMM model training issue in implementation

I am attempting to train an HMM on a series of sequences but the resulting prediction of the hidden states returns no change over the time series. My dataset is structured where the state begins in a ...
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Inferring a random walk from noisy "images"

I'm interested in the following inference / filtering problem in a hidden Markov model setting. Suppose we have a simple random walk $x_t\in\mathbb{Z}$ and observations are "images" ...
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inequality constraints in mixture models using conrows in depmixS4

I would like to fix the states identified by depmixS4 in a certain order to prevent label switching. This question was asked here (Fix state labels of HMM in depmixS4), and the answer given ...
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What is the difference between hidden states and mixture components in a continuous Hidden Markov Model?

I'm trying to understand how a continuous Hidden Markov Model works and I am confused by the difference of the hidden states of the discrete latent variables and the mixture components in the emission ...
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Understanding stage 2 of the PYIN algorithm [closed]

I am reading the PYIN[1] research paper, and I am having difficulty understanding stage 2. I have looked at the Librosa[2] implementation, however, I would like to clarify my understanding. From ...
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Amortized complexity of viterbi algorithm for first-order HMM

The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results ...
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Trouble with understanding alpha and beta in HMM

I'm implementing HMM myself and I'm stuck with this concept. Let T be the total time steps. $\pi$ be the initial probabilities. A be the transition matrix. B be emission matrix. $\alpha_{t,i}$ ...
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How to use Forwards algorithm for HMM with Continuous Observation model $P(y|z_t=k)$

I have implemented a Forwards-Backwards algorithm for discrete latents HMM given the observed distribution matrix $B$. Now if the observed distribution matrix is a Gaussian instead of finite ...
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How to calculate the variance of importance sampling estimate

I am given the following Hidden Markov Model: $X_{k+1} = \alpha X_{k} + b W_{k+1}$ $Y_{k} = cX_{k} + dV_{k}$ Also, $V_{k}$ and $W_{k}$ are independent and iid following $N(0, 1)$ I am required to ...
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Can the observation function in a POMDP be a function of the previous state?

I would like to model my problem with a Partially Observable Markov Decision Process (POMDP) but I have as an observation the previous state $o_t = s_{t-1}$. However, I see in all formal definitions ...
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MLE for initial probability for Hidden Markov Model (supervised learning)

Suppose I have a sequence of observations $\mathbf{o} = (o_1, ..., o_T)$ and a corresponding sequence of states natomiast $\mathbf{q} = (q_1, ..., q_T)$, where $q_i \in \{1,2,...,N\}$ Let $\mathcal{L}(...
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Latent state model - marginal likelihood

Which likelihood do I use to assess model-data-fit for latent space models like e.g. hidden markov models (HMM)? Let $X$ be the data, $\theta$ the model parameters and $Z$ be the latent variables. My ...
Carol Eisen's user avatar
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help me understand a part of the baum welch algorithm for hidden markov models

I am having troubles understanding a crucial part of the baum-welch algorithm in hidden markov models. When we calculate zhe/digamma representing the probability of being in state i at timestep t and ...
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Could the likelihood increase monotonically in a misspecified EM algorithm?

I am dealing with the estimation of a Gaussian Hidden Markov Model with conditional distribution given the first-order Markov state $S_t = j,\ j=1,...,J$ $$ Y_t|S_t=j\sim N(0,\sigma^2_j) $$ where the ...
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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 ...
thesecond's user avatar
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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-...
user3222184's user avatar
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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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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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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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