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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Hidden state models vs. stateless models for time series regression

This is a quite generic question: assume I want to build a model to predict the next observation based on the previous $N$ observations ($N$ can be a parameter to optimize experimentally). So we ...
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2answers
2k views

Scaling the backward variable in HMM Baum-Welch

I am just trying to implement the scaled Baum-Welch algorithm and I have run into a problem where my backward variables, after scaling, are over the value of 1. Is this normal? After all, ...
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700 views

Computing Standard Errors in EM algorithm

I'm applying the EM to a hidden markov chain (the $\mathbf{Z}=\{Z_1,...,Z_n\}$ variable), with observations(the $\mathbf{Y}=\{Y_0,...,Y_n\}$ variable) dependent not only on the hidden markov chain, ...
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513 views

Learning hidden Markov model where transition/emission/initial probabilities aren't independent

I'm working on a problem that I've cast as an HMM, except that unlike the "traditional" case where the transition probabilities $a(i,j) = p(s_i = j \,|\, s_{i-1}=i)$, emission probabilities $b(j,o) = ...
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486 views

Number of states and symbols in multi class Hidden Markov Model classifier

I'm designing a multi class classifier (for 4 classes) using Discrete HMMs with States N and Symbols M for each of the HMM. However, I found that recognition performance(i.e highest log likelihood) ...
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102 views

Can I use HMM to predict the spread of Ebola?

1) Can Hidden Markov Model be used across both a large number of categories (districts) and cases (weeks)? 2) Is HMM appropriate for trying to model such a problem? 3) Would I need to develop a ...
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3k views

Use of Hidden Markov Models for Clustering

I would like to ask whether Hidden Markov Models can be used for clustering and if so, in what cases. I have found somewhere, references like this but practically I haven't found a way to do this. Is ...
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100 views

Is there any way to define a distance metric given a Hidden Markov Model?

Let's say I've gotten a HMM that describes user search strings for my e-commerce website. Let's also say that I've just received a search string from a customer that doesn't have any search results. ...
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684 views

Anomaly detection in user behaviour using hidden Markov models

I would like to detect user anomalies or mal-behavior on a web site. For each user I monitor the web browser used, IP (and thus ISP & geo-location) of the user as well as users' activities on the ...
4
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1answer
497 views

Semi-supervised method for identifying states and state durations in a time series for anomaly detection

I am developing a semi-supervised method for identifying anomalies in a time series with multiple states. Let's consider this example time series in which there are two states e.g. state 1 and 2 with ...
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1answer
146 views

Gibbs Sampling vs. Using Raw Probability in Contrastive Divergence

In Hinton's Practical Guide to Training Restricted Boltzmann Machines, Section 3, he discusses different situations in which one should take a sample from the Gibbs sampling process, and other ...
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344 views

Hidden Markov Model with several observations

I am a little bit familiar with Hidden Markov Models. I have always seen cases with only one layer of hidden states and one layer of observations. Now I wonder to see if there is a possibility to add ...
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145 views

Offline Hidden Markov Model for time series analysis

One of the main principles of HMM is that the future state is dependent on previous state. This method is widely used for time series segmentation. However, for offline segmentation one can run HMM ...
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276 views

how to write down dynamical state space models with deterministic variables in PyMC?

is it possible to write down this simple dynamical system in pymc? $R_0 \sim Normal(\mu_r, \sigma_r)$ $Z_0 \sim Normal(\mu_z, \sigma_z)$ $R_t \sim Normal(R_{t-1}, \sigma_r)$ $Z_t = Z_{t-1} + R_{t-...
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Applying HMM to time series data

I have times series data from accelerometer that was attached to a person that was doing different type of exercises. I have a feature matrix that is basically a table with 3 columns (3-axis ...
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323 views

Why isn't a gaussian mixture prone to overfitting?

Consider a Gaussian mixture of 2 components and a dataset of size $N$. The EM algorithm use the data to estimate: the model parameters: the means $\mu_1, \mu_2$ (say the covariances matrices are ...
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How is prior knowledge of letter/word patterns incorporated into handwriting (or speech) recognition?

Using handwriting recognition as an example, we can train various models to recognise individual characters but to actually be useful we must incorporate prior knowledge of common character sequences, ...
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HMM library, different length sequences training

I'm using the Kevin Murphy's HMM library in MATLAB(http://www.cs.ubc.ca/~murphyk/Software/HMM/hmm.html) There is a section called 'How to use the toolbox'. There is this example for GMM ouputs: <...
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How can you use HMMs and ANNs for on-line handwriting recognition?

I've asked this question on cs.stackexchange before. It has a 20-hours remaining bounty there. On-line handwriting recognition is the task of converting a series of $(x(t),y(t))$ coordinates to ...
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The state-of-the-art methods for speech recognition?

Recently I noticed that Google and Apple have really high quality speech-recognition services. I was wondering about the state-of-the-art methods and techniques they are/might be using to achieve such ...
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540 views

Filtering with HMM

I want to use HMM for filtering, i.e. to find $p(x_t|y_{1:t})$. I see that the forward algorithm calculates the forward variable as a joint probability; $\alpha_t(i) = p(y_{1:t},x_t=S_i|\lambda)$, ...
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961 views

Using R and hidden Markov models to predict pseudorandom binary sequences better than P > .5?

I would to predict a pseudo-random binary sequence of 0's and 1's. I am thinking of using the HMM package in R. I have a binary sequence like ... 0 1 0 0 1 1 0 1 x(n+1)? with thousands of values. ...
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264 views

How to generalize Particle Filters (w.r.t. multiple states)

I'm using particle filters for inference in a hidden markov model with an infinite state-space. My current state-variable is multidimensional and there are interdependencies between some dimensions. I ...
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447 views

How do sudden spikes affect hidden Markov models

I have some data that has two sudden spikes (almost like extreme masses or Dirac delta functions) within my time series data and I was wondering if that is a problem when building hidden Markov models....
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720 views

Baum-welch algorithm: probabilities after each step

In an effort to understand machine learning, at least to some degree, I've been implementing the various algorithms to solve the three problems in a Hidden Markov Model. I've been using Rabiner's ...
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1answer
663 views

HMM ever better than CRF?

For classifying a sequence of instances, are there any specific circumstances that make Hidden Markov Models (HMMs) more accurate than Conditional Random Fields (CRFs)? I have seen several papers ...
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1answer
428 views

Observation symbols for training a set of HMMs

If we are to classify 2 separate classes/actions using HMMs, we design 2 separate HMMs (one for each class). Do they share same set or a different set of observations-symbols for each of the HMM? If ...
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75 views

Best way to find non-randomness regions in these or similar count data?

Let say I have data in a shape: [0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,2,0,0,0,....] - so mainly zeros.... However I know how long is my 'signal' and how many counts are they. Is it possible ...
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1answer
186 views

Logistic probabilities of state variable in a hidden Markov model always has variance of zero

Here is a simplified version of a more complicated problem that I have. Imagine a hidden Markov model where the state is $X_t\sim N(\mu,\sigma^2)$. The observed variable is $Y_t\sim Bin(N, p_t)$ ...
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53 views

Optimizing this log-likelihood

I have a HMM which emits an observation Z. The parameters of the HMM are $\boldsymbol\theta$. $$\boldsymbol\theta = {\boldsymbol{A},\boldsymbol{B},\pi}$$ Where $\boldsymbol{A}$ is the transition ...
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36 views

Particle Filtering: Derivation that mean of weights is the marginal likelihood

I see everywhere the following (for the Bootstrap Filter) $$ p(y_t \mid y_{1:t-1}) \approx \frac{1}{N} \sum_{i=1}^N W(x_{0:t}^i) $$ where $W(x_{0:t}^i)$ are the normalized weights defined as $$W(x_{...
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Combining probability and density with Bayes theorem

I have prior density $f(x)$, prior probabilities $p(y=0), p(y=1)$ and two conditional densities: $$f(x|y=0) = \mathcal{N}(x, \mu_0, \sigma^2)$$ $$f(x|y=1) = \mathcal{N}(x, \mu_1, \sigma^2)$$ Where $y \...
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92 views

Initialisation strategies for learning Hidden Markov Models

I used hmmlearn library to initialize an HMM (Hidden Markov Model). sampled observations from the HMM, and used the sampled data to re-estimate the parameters of ...
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49 views

Particle Filter for structural credit risk model

Kwon (2012)* proposes a structural credit risk model where the asset value process and the noise are estimated based on the observed equity prices: $S$ - equity prices $V$ - value of the assets $Z$ - ...
2
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1answer
596 views

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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36 views

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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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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0answers
145 views

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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0answers
52 views

Machine Learning on Sequential Data Reperesenting Events

Would you please recommend which model should I use for modeling user activity observing certain events that happen to them in time. I want to make sense of the history of events (just a presence of ...
2
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1answer
265 views

How to initialize and train a Hidden Markov Model to improve the classification produced by a previous classifier?

Say we've previously used a neural network or some other classifier C with $N$ training samples $I:=\{I_1,...I_N\}$ (that has a sequence or context, but is ignored by C) the, belonging to $K$ classes. ...
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356 views

A Hidden Markov model with covariates in the transition probabilities

I would like to construct a Hidden Markov model with data about online customer journeys. A well-known concept related to the customer journey literature is the sales funnel. Consumers walk through ...
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359 views

Hidden Markov Models as Dynamic Bayesian Networks

I'm working on a project where I'm trying to classify violent events into different latent states (e.g., low, medium, and high). Each series is distributed Poisson and I'm controlling for population ...
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0answers
798 views

HMM (Baum-Welch) - convergence rate differences between the transition and output matrices

I am trying to learn more about the convergence properties of the Baum-Welch algorithm for estimating the HMM parameters. I ran a test comparing the convergence of both the transition and output ...
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602 views

Predicting next event time

Problem definition: Predict user's next event date, based on previous event occurrences. The aim is to inter-corporate time dependent and time independent features. Data: +10 year transactional data ...
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804 views

Using HMM or depmixS4 package to find log-likelihood values

I am trying to implement a Hidden Markov Model. In my studies we used the package HMM as well as wrote our own functions. Here is a slight modification of the example from the HMM package. ...
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0answers
418 views

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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0answers
964 views

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 in ...
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0answers
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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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164 views

Hidden Markov Model prior

Suppose I have a set of time sequences, and that each time sequence is representative of a class. I can train several HMMs using Baum-Welch, one HMM per class. Let all HMMs have the same number of ...
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160 views

Predicting Trend using Hidden Markov Model

I am trying to predict exchange rates trend using Hidden Markov model (Viterbi Algorithm). For 2 state trending, I use A = [0.9 0.1; 0.1 0.9] as transition matrix and B = [1/N 1/N ....1/N; 1/N 1/N .....

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