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 ...
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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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MLE for initial probability for Hidden Markov Model (supervised learning)
Suppose I have a sequence of observations $\mathbf{o} = (o_1, ..., o_T)$ and a corresponding sequence of states natomiast $\mathbf{q} = (q_1, ..., q_T)$, where $q_i \in \{1,2,...,N\}$
Let $\mathcal{L}(...
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Depmixs4 error: Starting values not feasible; please provide them
I am trying to run a Hidden markov model for my data. When I include more than one response in the formula for a specific part of my data and then try to fit the model I get the following error:
...
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Latent state model - marginal likelihood
Which likelihood do I use to assess model-data-fit for latent space models like e.g. hidden markov models (HMM)?
Let $X$ be the data, $\theta$ the model parameters and $Z$ be the latent variables. My ...
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Finding the most likely point an intermittent failure was introduced
I have a sequence of state changes (changes in computer source code) and a test that I can run on a state that never produces a false positive, but frequently produces a false negative (even incorrect ...
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help me understand a part of the baum welch algorithm for hidden markov models
I am having troubles understanding a crucial part of the baum-welch algorithm in hidden markov models.
When we calculate zhe/digamma representing the probability of being in state i at timestep t and ...
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Could the likelihood increase monotonically in a misspecified EM algorithm?
I am dealing with the estimation of a Gaussian Hidden Markov Model with conditional distribution given the first-order Markov state $S_t = j,\ j=1,...,J$
$$
Y_t|S_t=j\sim N(0,\sigma^2_j)
$$
where the ...
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Creating synthetic data for time series, Hidden Markov Model
Suppose that I have a task of classifying a time series. I decide to use Hidden Markov Model $\lambda(A, B, \pi)$, where $A$ is a transition matrix, $B$ is an emission probability, $\pi$ is an initial ...
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Viterbi algorithm differs between digital communications and more general HMM?
I am self-learning Markov modelling, currently looking at simple
examples of hidden markov models (HMMs) and more specifically,
Viterbi's algorithm. I saw a few uses of Viterbi's algorithm in
simple ...
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HMM estimation (Baum-Welch) with 2 independent state variables
I'm trying to estimate a hidden Markov auto-regressive model with two independent state variables. You can think of one as determining the levels for the mean-reversion and the other determining the ...
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Estimate the HMM parameters (2states), backward
I fitted a 2-states-HMM model last week, and generate a bunch of 1s and 0s, but I forgot to store its parameters (transition matrix). Now, I only got these 1s and 0s, how do I backward/reverse-...
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Reframing a HMM problem as an RNN
Inspired by this question I have been considering how one would reframe a HMM problem as RNN problem.
For HMMs we have some observable timeseries $y(t)$ which corresponds to a set of hidden states $q(...
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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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Observed hidden variables in HMM
I am studying Hidden Markov Models and I'm trying to understand the following exercise:
Consider Hidden Markov Model with hidden states $h_{1:T} = \{h_1,...,h_T\}$ and observed states $v_{1:T}=\{v_1,.....
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Independence in Graphical model of $p(h_{1:T}|v_{1:T})$ of an HMM
I am studying Hidden Markov Models and I'm trying to understand the following exercise:
Consider Hidden Markov Model with hidden states $h_{1:T} = \{h_1,...,h_T\}$ and observed states $v_{1:T}=\{v_1,.....
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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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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 ...
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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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How to create/design a Hidden Markov Model?
I have a rough conceptual understanding of what Hidden Markov Models do.
What I don't understand is how to really create/train one. Let me outline what I'm working on, and then I'll give more specific ...
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