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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HMMs "difficulty" compared to a Markov model
Given an HMM, it is easy to compute the best approximating $n$-gram model over the observations. For example, for $N=1$, we have $p(w_i|w_{i-1}) = \sum_{s_i,s_{i-1}}p(w_i,s_i|w_{i-1},s_{i-1})=\sum_{...
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Dynamic Bayesian Network with Temporal Hidden State
Can someone direct me to papers or Python packages which I can use to develop a dynamic bayesian network with temporal hidden states. I found packages that can handle discrete hidden states. But that'...
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Time Series Prediction with Hidden Variables [closed]
I have time series data sampled every 10 seconds. I want to predict a target variable 𝑦 for 5 steps ahead using the input variable at the current time along with 10 past lags. My problem is that ...
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Are correlated variables in hidden markov model tolerated?
I have two weakly correlated variables (r2=0.66). I want to include these in a hidden markov model (HMM) alongside other uncorrelated variables. I cannot find anything in the assumptions of HMM's ...
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Forward-Backward Algorithm for Autoregressive HMMs
I am currently studying HMMs, and covered the Forward-Backward Algorithms as well as the smoothing and filtering process. Recently, we were posed a question on Autoregressive HMMs which I've been ...
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Extended Hidden Markov Models (HMM) parameter estimation
For simpler HMMs, we can use algorithms like Viterbi training (not decoding) or Baum Welch to estimate the parameters that best describe the observed data.
How do we do the same when using a more ...
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What is the effect of sampling rate on parameter estimation when fitting a markov state model to timeseries data?
Let us say that I have some timeseries data, which can be described by a markov state model. And the time series has been sampled every $\Delta t$ time units. The sampling rate ($1/\Delta t$) must ...
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Do I use $P(y_t|y_{1:t-1})$ instead of $P(y_t|z_{t},y_{1:t-1})$ for prediction in a Hidden Markov Model?
I am confused what to sample for getting the prediction $y_{t}$ if I have access to the previous observations $y_{1:t-1}$ and the hidden states $z_{1:t}$.
I want to predict the observation at time $t$ ...
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Help with Gambler's ruin problem, can't solve abstraction [duplicate]
I'm having difficulty solving this exercise. When I assume that p=0.4 and player A's fortune is 99 dollars and B's fortune is 1 dollar, I can find that the probability of player A losing to player B ...
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HMM probability of sequence of observations using forward and backward probabilities
I've come across this statement whilst reading about HMMs:
Given $\alpha_{n}(j) = P(Y_{0}^{n}, X_{n} = j)$ and $\beta_{n}(j) = P(Y_{n+1}^{N} | X_{n} = j)$, then
$$P(Y_{0}^{N}) = \sum_{j} \alpha_{n}(j)\...
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Hidden Markov Model: Robustness and `Forbidden` Transitions
I have an issue while using a HMM to estimate the state of a system where the state-transition matrix is a block-diagonal matrix. Specifically I have an issue with robustness and the HMM keeps ...
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Help interpreting normalized HMM (or otherwise) results
I have run a hidden markov model with five variables on very different scales. Because of this I normalized the input data beforehand using Carets preprocessing:
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How to feed multi-channel spectrograms to Deep Neural Network?
I am using a 14 channel EEG device. To do away with the need for any handcrafted features, I wish to implement an ML classification task with the EEG data collected using deep neural networks (such as ...
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Data scaling for hidden Markov models?
I understand that scaling data is important for certain machine learning algorithms, and the idea makes sense. I've found this great description of the processes here https://ourcodingclub.github.io/...
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Mean and covariance kernel for the posterior GP of a Hidden Markov Model
In a hidden Markov model (HMM) we have a process $X_k$ that evolves according to:
$$ X_{k+1} = X_k + W_{k+1}, \quad W_{k+1} \sim N(0, \sigma_{W}^2), $$
where $\{W_k \}$ are IID and $X_0 = W_0$. We can ...
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