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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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Does this problem satisfy markov properties to be modeled as HMM?

I want to model a chemical reaction network which is defined by a stoichiometric matrix $\nu^{s\times m} $ where $s$ is the number of participating species and $m$ the number of chemical reactions. If ...
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50 views

ARMA and HMM equivalence

The question might be trivial, but I am confused. Assume, one has $$ x_{t} = s_{t} + v_{t},\\ s_{t} = \phi s_{t-1} + w_{t}, $$ where $v_{t}$ and $w_{t}$ are two independent white noise sequences with ...
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hidden markov model fit with an absorbing state

Do the HMM Baum-Welch and Viterbi algorithms assume the underlying states are recurrent? I'm trying to fit an HMM where one of the states is an absorbing state, and I'm not sure if I need to change ...
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Bigram model with checkpoint sequence

I have co-occurence statistics for pairs of words and want to fill-in a sentence given a start word and another word placed in the sentence. Note that my training set never contains anymore than two ...
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Constrained parameters update during hidden Markov model forward-backward algorithm

I want to train a Gaussian hidden Markov model. I currently use the Python package hmmlearn. I looked thouroghly at the code to see how parameters are updated after each training iteration, but I ...
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Markov Chain Attribution Model: Calendar periods VS Sliding Window?

I'm trying to utilize Markov Chains in order to analyze and attribute online conversions of b2b users browsing on a company web. The key question mark I'm facing is on which period length to apply the ...
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25 views

How to represent an HMM whose observations are a continuous vector?

I have usually read about HMMs with observation spaces that we can somehow encode as a finite number of observations. How could I use HMM fitting if my observation at each time step is an $n$-...
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Face Recognition using HMM

I had learnt some of the research papers of Face Recognition using Hidden Markov Model. Can you help me how Hidden Markov model is applied to face recognition?Also can you please give some numerical ...
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HMM - Deal with Baum-Welch emission never observed

If I train a HMM with a given sequence of observations among n possible emissions, how do I deal with an emission that is never observed? For example, if in a 100 long observation sequence the ...
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How to work out the global maximum of the likelihood of a hidden Markov model?

I have generated some data based on a transition matrix and emission parameters that I have set. I want to test whether the optimisation algorithm I am using will find the global maximum of the log-...
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What is an appropriate threshold for the EM algorithm?

I am implementing the Baum-Welch algorithm (special case of the EM algorithm) on a hidden Markov model and I now have to pick an appropriate stopping criteria $\epsilon$ so that the algorithm ...
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Convergence of EM algorithm

I am aware that EM eventually converges. However, I still have some confusions regarding this property: 1: As far as I am aware, HMM, Gaussian mixture model and MCMC can converge and all of them use ...
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Hidden-Markov Model for Markov-Chain with Sequential Bernoulli State Sampling

Consider a finite discrete-time Markov chain whose state is sampled at the times determined by the outcome of a Bernoulli process. That is, in each time period I flip a biased coin. If it comes up as "...
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HMM with hidden state of unequal interval

I am constructing a HMM model. However, the hidden states are of unequal interval. Take the rainy / sunny scenario as example. The hidden states I am about to infer is the 1st day, 2nd day, 5th day, ...
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Why do the non-informative a priori distributions give better results than the frequentist estimate?

For example, in the specific case of Markov-Switching GARCH models why is a non-informative prior distribution chosen for GARCH models with Bayesian estimation and why is this approach better than the ...
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Suggest a model for segmenting a time series

Hi all, I have a time series that looks like above. I'm interested in segmenting it into the numbering listed. I've tried using a hidden Markov model, but the versions I can find with multiple ...
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What kind of a priori distribution for the Markov Switching models?

Why in the Markov-Switching models is chosen as prior distribution for the probability of the transaction as follows: $$f(P) \propto \prod_{i=1}^K \left(\prod_{j=1}^K p_{i,j}\right) I \left\{0 < ...
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Suggest a model for this dataset

I have a time series data set (the Old Faithful geyser data available here: http://www.gatsby.ucl.ac.uk/teaching/courses/ml1-2012/geyser.txt). Plotting the eruption duration on the x axis and the ...
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Observations correction using HMM

I don't know if this is even a good idea, but I am trying to implement a HMM such that my hidden states are the same as my output states. So given a sequence of discrete, time-series observations: $$O ...
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Convergence of HMM Training

HMMs are commonly trained using the forward/backward algorithm. But there is an alternative approach using the Viterbi algorithm. The difference is that, in the E step of EM (Baum/Welch), instead of ...
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What are the differences between Bayesian filters and adaptive filters?

I am learning about state estimation and I am having difficulty understanding the difference between Bayesian filters such as Kalman filter and particle filters compared to adaptive filters. According ...
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1answer
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Notation for conditional probability when the conditioned event is observed

I am trying to understand proper notation for functions related to state transition models (e.g., a HMM). There are two indexing variables $t$ (time step) and $i$ (state). Such that it matters, in my ...
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How to use Hidden Markov Model for predicting the last state in set of sequences? [duplicate]

I have a dataset consisting of a set of sequences as follows: ...
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HMM rolling estimation different from batch estimation

I'm using the GuassianHMM from the python package hmmlearn and after fitting the hmm to the data the predictions that are done in one batch ...
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What is the point of doing simulation on Markov Chain?

I am studying Markov Chain and I am currently reading about simulation on Markov Chain but I can't see the point of simulation on Markov Chain. What does simulation mean in Markov Chain and what can ...
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can the prior probability change with time?

I was reading Markov Models for sequence modeling and stuck with my understanding(hypothesis). In Baye's theorem, can the prior probabilities change with time? If the prior probability at t=3 is 0.05,...
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HMM training of multiple observations corresponding to different hidden states

Given a set of states $\{q_1,q_2,..,q_n\}$, I am considering the following problem. Corresponding to a sequence of hidden states, I have some observations. first sequence of hidden states ; first ...
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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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What are the relationships among Markov Property, Stationarity, and Time Invariance

I am wondering if there is or are any relationship among those. I have understood Markov Property by reading Wikipedia, but it is still confusing to figure out if there is any relationship among those ...
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Model to Bootstrap/ simulate hourly shape from daily data

How do I simulate/boot strap hourly shape from daily data ? $\mathbf {Data set:}$ My first data has hourly granularity, its hourly temperature, $T_1$ through $T_{24}$ and but I have no means to ...
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1answer
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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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To say my model is a stochastic model,what assumptions do I need to make?

I am trying to understand what a stochastic model is and assumptions to be able to say my model is a stochastic model. I am new to it, so I may confuse you. I have gone through Markov chain, Markov ...
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80 views

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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39 views

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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Models for interdependent finite sequences?

I have a large set S of pairs of (short) sequences (, )_i where the first sequence of each pair comes from sequence set A and the second sequence of each pair comes from the sequence set B. Sequences ...
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Applicability of Markov Models for predicting user input

I am trying to predict user action based on the shown content of different modules. Lets assume the user sees a page where several content may be shown or not. The next action of the user depends on ...
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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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1answer
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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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Baum-Welch algorithm and link to EM algorithm [duplicate]

What is the exact link between Baum-Welch in HMM and EM? In EM, we usually calculate: $$Q(X) = P(X|Y,\theta)$$ and then maximize $$\mathbb{E}_{~Q}[ log(\frac{P(Y, X, \theta)}{Q(X)})].$$ I read the ...
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Training Hidden Markov model with GMM, nan appears after some iterations

Problem During the training process of my continuous observation sequence data using HMM with GMM mixtures, the cost function reduces gradually and it becomes NaN ...
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1answer
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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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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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41 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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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 ...