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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What are the necessary qualifications or assumptions to say that a graph structure is a Markov Chain?
I have a graph structure and want to say it is a Markov Chain. But I am wondering what necessary assumptions or properties that my graph structure need to meet to be called a Markov Chain?
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The difference between forward algorithm used in CRF and the variable elimination?
I found that in the forward algorithm used in the CRF(and perhaps also in the HMM) the mechanism applied is almost the same as that in the variable elimination(VE) except that the emission ...
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Example of manual implementation of baum-welch algorithm in R
Is there any code out there that implements the baum-welch algorithm for a very basic problem? It would be very helpful to actually see the algorithm in action to better understand how it works.
I ...
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Viterbi algorithm for finding most probable path with varying transition probabilities
I'm struggling to apply the Viterbi algorithm to a simple case of inferring hidden states where the transmission probabilities change. I've draw a picture below of the trellis with transition ...
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Generating probability distribution parameters using a neural network
I am new to neural network therefore, my question might be super basic. I am reading this article:
https://arxiv.org/pdf/1609.09869.pdf
In this article they've made a deep Markov Model in which they ...
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Are conditional mean in an AR(1)-GARCH(1,1) equal for different GARCH(1,1) processes of the same data?
I have created a Markov-Switching GARCH model, where the volatility is defined to be switching between two different GARCH(1,1) processes. The data is assumed to have zero mean, where the data is ...
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Hidden States in Hidden Markov Model
I am using Hidden Markov Models, having observations as continuous variable and states as discrete variable. I can use the observations to train HMM model and generate n number of states(say 2 hidden ...
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When to use a Hidden Markov Model vs Markov Model with history?
I'm trying to understand when and why it's useful to use hidden state in a model. The purpose of my modeling is to be able to simulate sequences with features similar to observed data sets.
As a ...
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HMM - state transition depending on amount of time spent in states
Can we have a HMM where state transition is dependent on amount of time spent in states?
Suppose I build a hidden markov model(HMM) with 2 hidden states - S1, S2. In normal HMM, we assume the state ...
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Application of a Hidden Markov Model
I recently began learning about HMMs and wanted to ask about a possible application that would hopefully help me grasp the concepts.
One of the applications for a regular Markov Model is modelling ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Finding Probability of a digit given a sequences? [closed]
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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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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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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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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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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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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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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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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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 ...
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How to sample an unobserved Markov process using the forward-backward algorithm?
The setup
Let $X = (x_1, \ldots, x_T)$ denote a state variable that follows a Markov process, where $x_t \in S$. The transition distribution is denoted by
\begin{equation}
p(x_{t}|x_{t-1}) .
\end{...
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Dynamic Programming vs Hidden Markov Models
I've just been introduced to machine learning, and one of the first topics I'm covering is an introduction to finite state transitions and their models. Specifically, right now, I'm on Hidden Markov ...
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Inference over time index in hidden Markov models
Good evening!
I have been working with HMMs for a while now and a recent addition to my problem space sees me attempt something which I do not quite know how to google.
Assume that we have three ...
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If the Markov assumption is wrong, will a learner still converge to a stable policy?
I'm trying to figure out what guarantees can be made if a learner wrongly assumes a problem obeys the Markov transition property. Assume I have a problem defined by a partially observable Markov ...
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Classification Using The Hidden Markov Model
I am having difficulty understanding certain concepts regarding the classification using HMM. There are numerous post here and in the internet about that, but they never get to detail or they all ...
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Interpretation of the forward algorithm
I was reading the book of Jurafsky about HMM and came along this graphic:
The problem that I have is in the interpretation of the graph. According to the problem the hidden states are the weather ...
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If Bayesian is better than frequentist(and it's tractable) then how can it be as practical?
In a textbook Probability Theory: The Logic of Science written by E. T. Jaynes and others, on page 13 it reads that:
For many years, there has been controversy over ‘frequentist’ versus
‘Bayesian’ ...
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How to penalize change of states in Hidden Markov model?
I'm trying to fit a HMM on a sequence of observations and I would like to introduce some constraints that would penalize an excessive number of changes of state in the complete sequence (where "change"...
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Using Hidden Markov Models for Classification
When we use HMM for classification, we need to train one HMM per class. My question is: How to find the matrices A,B,\pi?? What is the meaning of them?
To clarify: A =[aij] transition matrix, aij ...
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Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states?
I'm trying to model sequence data that has 5 hidden states. Observation data conditional to each state is gaussian except for one state for which mixture of 2 gaussians seems more appropriate. ...
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Interpolating between consecutive weather radar images
I have a series of rainfall intensity images from a weather radar taken every 10 minutes. My goal is to generate intermediate frames in order to create a slow motion video. I've tried using the ...
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Finding maximum likelihood solution of a continuous state HMM
The likelihood of a hidden Markov model (HMM) for states $x_0, \dots, x_N$ and observations $y_1, \dots, y_N$ can be written as
$$ L = f(x_0) \prod_{i=1}^N f(y_i | x_i) f(x_i | x_{i-1} )$$
where we ...
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Predicting probability of next event happening
My Data is:
TimeStamp <- time stamp of the event occurring
Length <- length is the duration of the event
ID <- identifier where the event is occurring ( 25 IDs)
TimeStamp | Length | ID
The ...
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