Questions tagged [hidden-markov-models]

Question 1

I have a question regarding training HMM and then applying it to new data: Is it possible to train a HMM with several time series as inputs? My point here is that it'd be convenient to have a ...

Question 2

In Chapeter 3 of Speech & language processing, Jurafsky says "We need the end-symbol to make the bigram grammar a true probability distribution. Without an endsymbol,instead of the sentence ...

Question 3

Definition of a a Markov renewal process: Let the states of a process be denoted by the set $E= \{0,1,2, \dots\}$ and let the transitions of the process occur at epochs $t_0 =0,t_1,t_2, \dots$. Let $...

Question 4

I am working through a problem in my textbook regarding Markov chains and hidden Markov models (HMMs). The problem is as follows: Prove that $P(\pi)$ is equal to the product of the transmission ...

Question 5

The question might be trivial or non-sensical but help me understand, please. My understanding so far: The likelihood is given by $$ L_T=\boldsymbol{\delta \text{P}}(x_1)\boldsymbol{\Gamma \text{P}}(...

Question 6

Consider this problem where a machine can be in either of two states (bad or good) and depending on the state with some probabilities (p_1 and p_2) it may produce good products (with probabilities 1-...

Question 7

Is there a formalism for a Hidden Markov model that is : time-discrete with both discrete and continuous states with continuous (gaussian linear) observation (of the continuous space) ? For specifics,...

Question 8

Say I have a HMM system that can be in any of $n$ discrete possible states - say they are numbered $1$ to $n$ and can even actually be these integers. I know the transition matrix between different ...

Question 9

Let $X=(X_i)_{i \ge 1}$ be an irreducible Markov chain started in its stationary distribution, and $Y=(Y_i)_{i \ge 1}$ be such that $Y_i=\phi(X_i)$ for an arbitrary function $\phi$. Note that $X$ is a ...

Question 10

Consider the model $y_t = F_{S_t} x_t + \varepsilon_{S_t}$ and $x_t = A_{S_t} x_{t-1} + \nu_{S_t}$, where $\varepsilon_{S_t}, \nu_{S_t} \sim N(0, R_{S_t})$ and $N(0, Q_{S_t})$ and $S_t$ is Markov ...

Question 11

If we have a $2$-state model (i.e. the simplest non-trivial example) in a hidden markov model, and some generated observation-data $\mathcal{O}$ from the algorithm for generating observations. Is it ...

Question 12

Given two Markov kernels on the same space $\mathfrak X$ and relative to the same dominating measure, $K_0(\cdot,\cdot)$ and $K_1(\cdot,\cdot)$, both ergodic with respective stationary distribution ...

Question 13

I'm struggling to understand the statistic relation referring the observations of an HMM. That's clear for me: Output Independence My problem is how this equation can be derived: probability of an ...

Question 14

I'm struggling to understand the reasoning between moving between two steps in a reaction scheme for a paper I am reading. For this (from the description), the probabilities over different paths are ...

Question 15

I am trying to understand the derivation of the Viterbi algorithm for hidden Markov models. I understand that the motivation is to find the maximum probability path estimate, i.e., \begin{equation} ...

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Questions tagged [hidden-markov-models]

Hidden Markov model (HMM) for multiple time series

Jurafsky Speech & language processing Chapter 3 "end-symbol to make the bigram grammar a true probability distribution"

Property of a Markov renewal process

Proving Termination Properties of a Markov Chain with Non-Constant Transition Probabilities

Hidden Markov Model Likelihood when Marginal Density Isn't avaliable?

Hidden Markov Model with Multiple Agents

Hidden Markov with both discrete and continuous states

Discrete Hidden Markov Model with continuous observation

Hidden Markov Model of a stationary Markov chain is a stationary process.

EM algorithm for Markov switching models.

Likelihood computation for hidden markov models.

When do mixtures of ergodic Markov kernels remain ergodic?

Hidden Markov Model - Observations [closed]

First-passage time distribution in Laplace space?

Derivation of Viterbi Algorithm

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