# Tagged Questions

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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### Estimating state transition matrix in HMM

Given a sequence of observation O and P (Q|v), I want get the model v=(A,B,w). I have the observation matrix B and resulting probability P (Q|v), but I don't have state transition matrix A. I have 4 ...
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### What it takes to teach an HMM?

I am reading about Hidden Markov Model and I am curious on how it learns. I mean we have: z1 ... zn -- hidden states x1 ... xn -- observations My question is: ...
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### Training HMM for classifying a DNA region as telomeric or non-telomeric

This is the problem setting: I have a large set of strings (sequences of characters A,T,G,C) of length 100. These sequences are either from a telomeric region of a chromosome or non-telomeric. For ...
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### HMMs - Viterbi algorithm alternative

In standard Viterbi, we have $v_t(j)=max(v_{t-1}(i)a_{ij}b_j(o_t))$. What if we define it to be $v_t(j)=sum(v_{t-1}(i)a_{ij}b_j(o_t))$ And then to do decoding, for every $t$, you take the state $i$ ...
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### Markov model for Chanel Attribution

I recently found a package ChannelAttribution which is pretty cool for attributing the marketing channels used during customer's journey (I exported data from Google Analytics). The package is super ...
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### Learn a HMM with fixed emission probabilities constraint

Suppose we want to learn a HMM with the emission matrix is fixed. Can I use the Baum-Welch to estimate the transition probabilities $a_{ij}$ by skipping the $b_{ik}$ values update step at each ...
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### Baum-Welch algorithm variation for Hidden Markov model with reward

Following my previous question on the subject I would like to get your feedback on the following alternative solution. (The original solution to this question is the usage of the POMDP model proposed ...
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### Stock Price Prediction using Forward or Viterbi?

I've run a simulation with my data (using the Hidden Markov Model) and obtained my transition matrix, my hidden states and parameters. I am now wondering which algorithm would be able to predict (and ...
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### HMM with random process that determines how long you stay in a state

I have a situation that is reasonably well-modelled by a discrete Hidden Markov Model (HMM), but with one twist: when you enter a state, the amount of time that you spend there is given by some ...
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### Hidden Markov model with reward

I am looking for a Hidden Markov model that incorporates rewards, i.e., in which the transition between states is dependent on the feedback from the environment (reward). For instance, it could be ...
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### Data Training for HMM Detection in Wavelet Domain

Watermarking using Haar Wavelet Transform and HMM I've been implementing Watermark Extraction in Haar Wavelet Coefficients using HMM likelihood detection. The watermarks I embed into wavelet domain ...
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### Statistical Approaches for Uncertain Target Variable

Let me first explain what I have tried to mean by uncertain target variable. Consider the following scenario: Illegal immigrant behavior: Suppose you want to interdict with illegal immigrants to ...
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### Randomly generating transition probabilities for Markov chains

I'm trying to simulate a person moving through a household using a Markov chain. Each state would be a room in the house. The issue I'm running into is that I have no existing data telling me what a ...
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### HMM Training: Testing convergence

What is the best way to test for convergence while training an HMM? I understand that we need to iterate till the change in parameters ( transition matrix, emission matrix ) is less than the threshold....
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### HMM for fitting multiple time series with covariates

I have a large number of possibly correlated time series with multiple covariates that have the potential to affect them all. I'd like to approach them using HMM but I am not sure about the following:...
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### Re-estimation of Hidden Markov Model Parameters without Knowing Hidden States

I have been working on Hidden Markov Models (HMM) for a while. I thought that I understood the basics of HMM, however, recently I have confused about a point. Here is the issue: Recall the 3rd ...
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### Best way to tackle heterogeneity in oncologic models

I need to model the health outcomes from an immuno oncologic treatment to which patients are responding differently depending on their immune condition, which is unknown to the investigator. I was ...
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### HMM for sequence classification in R

I have a dataset which includes sequence of DNA nucleotides (A,C,G,T) and each sequence has a gene index that is binary. i.e I'm trying to classify unknown sequence by using a hidden markov model ...
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### HMM with skipping

Is there a model of HMM with a probability that the next "item" in the list doesn't fit the criteria for the model and needs to be skipped or do I need to figure out how to remove these myself and ...
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### Interpretation of hidden states in HMM in the part-of-speech tagging task

Let me begin with a part-of-speech tagging task. The ultimate goal: given a sentence, what is the most probable part-of-speech tag for each word in the sentence? We want to answer this question by ...
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### Relation between number of states and Gaussians in HMM GMM chain and window size of Feature Extraction Algorithm

I am using HMM-GMM tool for Matlab by Kevin Murphy.My Frame work has a feature extraction Algorithm (MFCC,Spectrogram) followed by a HMM-GMM classifier. I am trying to set the the number of states ...
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### What are the best packages for HMM sequence analysis?

I have a sequence of events and I want to learn discrete probabilities of transitions between them and to predict next item in a sequence. Can you point me on good papers and Python or R package for ...
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### Likelihood of observations for HMM with continuous state and observation distributions

I have a "real" and estimated HMM model given as $(\pi,\mu, \nu)$ and $(\pi^{\text{est}},\mu^{\text{est}}, \nu^{\text{est}})$, where $\pi$ is initial state distribution of Markov chain, $\mu$ is state ...
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### Convergence in hidden markov model

I have a HMM where forward-backward probability increases in Iteration 1, then it decreases and then increases (as well as converges). Probability values after iterations 0,1,2,3,4 are: ...
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### Hidden Markov Model to calculate market share

I'm currently working on a HMM where I need to predict market share of a medicine (Let's call this J). My output sequence is the market share of J in 12 consecutive months. Market share is influenced ...
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### Hidden Markov Model and Naive Bayes similarity

I understand Naive Bayes classifier and already have made a few implementaions. What i dont understand is, considering that i have a train set with all the X observations and Y states, what stops me ...
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### Calculating Emission Probability values

I'm new to HMM and still learning. I'm currently using HMM to tag part-of-speech. To implement the viterbi algorithm I need transition probabilities ($a_{i,j} \newcommand{\Count}{\text{Count}}$) and ...
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### Baum welch: how to handle last observation while calculating transition probabilities

Using Baum-Welch to estimate the transition probabilities Si->Sj, the probabilities are calculated by the following formula: = (ForwardProbability(t, Si)* P(Si->Sj) * P( Obs_t+1| sj) * ...
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### Baum Welch:Calculating transition probability

I am trying to understand the Baum Welch algorithm by implementing it in xls. I have chosen a simple example of observations from a loaded (L) vs fair (F) die. I calculate the forward and backward ...
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### Hidden states that have never observed in the dataset!

I have been working on a dataset that has 5 discrete predictors and 1 binary response variable. Here is how to data looks like: ...
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### Conditional Distribution of Hidden Markov Model

I am trying to implement a Gibbs sampling algorithm for a toy Hidden Markov Model, but I am having trouble deriving the target conditional distribution. I am generating data through the following ...
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### General HMM training procedure?

I am new to EM algorithm, studying Hidden Markov Model. During training my HMM by EM, I am very confused on the data setting. (text processing) Please confirm whether my EM usage is okay or not. At ...
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### HMM prior on stationary probability

I am trying to model a sensor that when mis-calibrated tends to vibrate alot (or atleast high varying readings). I used a HMM to model these vibrations. It is known that the sensor was calibrated ...
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### How large a training set do I need for an English POS tagger?

I'm trying to implement a POS tagger for English using the Viterbi algorithm on an HMM model. Right now, my results are poor and I'm not sure whether it's due to a bug or due to lack of training data. ...
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### Transition/emission probabilities POS tagger English

is there an freely available online version of transition and emission probabilities for an HMM model used for POS tagging English text? It seems like there are many powerful existing taggers out ...
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### HMM toolbox matlab - joint distribution

I would like to use the HMM toolbox from matlab, but in the example of function hmmestimate they use only one variable distribution but I need to use joint distribution since I have multiple emission ...
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### Finding a pattern in time series data

I have time series data. I am looking for a procedure to find if a particular pattern exists in the time series. To make it more clear, suppose I have a base time series in which the check for the ...
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### Proof that Markov Property is not Satisfied at any Order?

My textbook has this figure in it: The textbook then says, Using d-separation, we can see there is always a path connecting $x_n$ and $x_{m}$ via the latent variables. This makes sense to me because ...
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### Hidden Markov model - Time Granularity

Is Hidden Markov model sensitive on time granularity? I mean if I train HMM parameters on dataset which time granularity is 1 minute. May I use the transition matrix and emissions distributions for ...
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### Hidden Markov model and regime detection on historical data

I use depmixs4 package for stock market regime detection. Here is my code: ...
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### HMM with variable length input

My task is to calculate the likelihood of a word belonging to to a certain group. My training set is comprised of words that are variable in length. If the length of words was equal , I would have ...
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### Is this a correct explanation of the markov assumption?

Here is a description of a the markov assumption (taken from http://di.ubi.pt/~jpaulo/competence/tutorials/hmm-tutorial-1.pdf) : Given W = word is this also a valid explanation of the markov ...
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### Time series pattern recognition tools

I have a matrix of 500 X 12 of time series, represented by each row. The columns being the 12 sampling times. I have also another matrix of 500 X 1 corresponding to 500 time series of which we only ...
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### EM vs. direct numerical optimization of likelihood function in high-dimensional Markov-Switching / HMM

I am currently estimating a Markov-switching model with many parameters using direct optimization of the log likelihood function (through the forward-backward algorithm). I do the numerical ...
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### sample size to train HMM

what the sample size is needed to train HMM? Is there a common method used to determine how many training samples are required to train a HMM , I am asking because I have a large dataset for training ,...