# 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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### Main event time prediction based on different sub events

As the title says, I want to predict the time (with a wide error range) of a main event’s first occurrence based on previous sub events that are vary in importance. These previous ‘predictor’ events ...
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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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### Is there a way to learn/mine a process from continuous values and no actions?

I have following data: value1, value2, valuen, reward 0.2, -0.2, 3.0, 0.22 ..., ..., ..., ... I would like to mine a process from this where I can find most ...
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### Is it ok to just use Add One Smoothing for any sufficient statistics on Counts/Probabilities?

I know that Add-one smoothing is due to $$\theta_{\text{MAP}}=\arg\max_\theta \log(P(\theta|D))$$ when the posterior is a Binomial/Bernoulli with a $\text{Beta}(2,2)$ prior. Now, I am implementing ...
1 vote
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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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### Is there a Hidden Markov Model compression scheme for time series?

Hidden Markov Models (HMMs) are very useful for time series analysis and inference. At the same time, probability distributions over a data type are used in finding compression schemes for data of ...
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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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### Hidden Markov Model with Gaussian distribution emissions

I run HMM for genetics data in java. For emissions, It just generates the mean of the Gaussian distribution. Can I conclude that any of the observed variables that have a higher mean belong to that ...
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### How to incorporate real-valued multi-observations into Hidden Markov Model?

I want to perform Voice Activity Detection (VAD) application which decides whether there exists human voice in the audio signal or not. I want to train a HMM using Baum-Welch algorithm. The states ...
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### How to train HMM using two different time series of the same feature?

I am using hmmlearn (Gaussian HMM) for classification of data. I want to train my model using 4 features, but I want to use two time series for each feature. I don't think combining the two time-...
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### How to efficiently caclulate probability of a state in HMM when a random shuffle operation happens on emitted observations

The problem setup is as follows(it's from a book and may not be tied to reality): Suppose we have some speakers s_1, s_2..s_k seated around a table speaking at ...
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### Hidden Markov Model: 'Warning: Sequence is impossible'

I am using Hidden Markov Model to predict the state of rain based on observed rainfall in centimeters. The three states are ' little rain' 'some rain' and 'a lot of rain'. For the prediction, when I ...
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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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### Confusion about names of algorithms used in Hidden Markov Models (Baum-Welch vs Forward-backward vs Forward)?

Copy of this question on DS SE 2 of 3 fundamental problems in Hidden Markov Models are: (1) estimate model parameters given just the observations (2) compute likelihood of observations given model ...
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### How to map states between two different Hidden Markov Models (HMM) for a classification problem?

I am currently working on a classification problem for timeseries analysis which uses two different Hidden Markov Models. I fit a model to the sample of subjects belonging to class A, model A, and ...
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### Comparing time series classification with Hidden Markov Model vs Dynamic Time Warping - which model should I use to generate data?

Copy of this question on DataScience SE I am writing a thesis which compares two approaches to time series classification: Hidden Markov Models and Dynamic Time Warping combined with 1-NN. I'll apply ...
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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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### Memorylessness by way of additional dimensions

This is a somewhat broad question that occurred to me regarding the nature of memorylessness. Namely: Is there utility in considering systems which are themselves not memoryless, but then expanding ...
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### Find "seasonality" in a categorical time series in python

I have the following sequence: ...
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### How to calculate the equilibrium (initial probability) for second order HMM in python?

I have a transition matrix looks like: ...
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### When using Markov models for attribution modeling,what information does the transition matrix have,that causes the steady state vector not to be used?

I've just finished my msc thesis in attribution modeling, comparing higher order Markov models and the heuristic approaches. The professor's question is what information does the transition matrix ...
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### AIC vs BIC for time series clustering and descriptive purposes

I'm in the process of fitting a hidden markov model with gaussian mixtures to time series health data. The primary purpose of this is descriptive, not predictive – I'm using the fitted model to give a ...
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### Computing conditional distribution of hidden state given observed states?

I am interested in the following Gaussian linear system that describes a Hidden Markov Model (HMM): x_{k+1}=Ax_k + u_k + \xi_k, \xi_k \sim N_2((0,0), 0.01I_2)\\ y_{k+1}=C^tx_{k+1}+\eta_k, \eta_k \...
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### Hidden Markov Model - Baum Welch algorithm initialization

Currently I'm working on a problem where I have a multidimensional, continuous sequence of observations $X$ that model my response variable $y$ with two states $0$ and $1$. I assume that this sequence ...
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### Hidden Markov Model observing sequences

I have been trying to understand Hidden Markov Models but I often find myself confused. I have discussed with my tutor for further help however, he is often rude and does not help and so I have ...
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### Which Significance test to apply to compare number of occurences of multiple events across multiple groups?

Our dataset is composed of time-series data (recordings) collected for 18 different groups (test conditions G0 to G17). The number of recordings per group can vary (30-600). For each of these ...
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### Equal Error Rate in Hidden Markov Models for Speaker Recognition

I was asked to report the Equal Error Rate (EER) for my speaker recognition proposal. I trained one HMM for each speaker. To evaluate, I introduce the input of an speaker in both models and classify ...
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### Calculate probabilities given hidden markov model

Consider a disease D with incidence rate of 5 cases per 100 people (i.e., P(D) = 0.05). Let the corresponding boolean variable D refer to a patient “having disease D”, and let another boolean variable ...
1 vote
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### R msm package does not generate estimates

I am trying to use the MSM R-package to estimate a continuous-time hidden Markov model. I do not know why my code does not show the estimates and confidence intervals for the transition intensities ...
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### Are Hidden Markov Models the right tool for signal segmentation task?

I have a particular problem, and I would like to know if using a HMM is the correct tool for it. Apologies for the poor wording of the problem, HMMs are definitely not my specialty. I have the ...
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### Python: Markov switching model out of sample forecasts

Is there a way to obtain out of sample forecasts for Markov switching models estimated via statsmodels (or any other package)? https://www.statsmodels.org/dev/examples/notebooks/generated/...
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### Real-time sequence classification with Markov Chains vs HMM vs CRF

I see that Markov Chains are useful for providing the conditional probabilities for each individual symbol of the test sequence. So this really gives an incremental overview on how the sequence is ...
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### How do HHMM (Hierarchical Hidden Markov Models) work and where to learn more?

I recently came across something called Hierarchical Hidden Markov Models. I am familiar with HMMs, but not HHMMs. I have two questions. I can't fully understand the procedure after reading here: ...
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### What are the transition functions for RNNs

From what I understand, the hidden states of RNNs are equivalent to the deterministic probability distribution over hidden states in for example a Hidden Markov Model. Thus, just as probabilistic ...
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