A coarse-grained Markov chain is a hidden Markov model

2020 ◽  
Vol 541 ◽  
pp. 123661 ◽  
Author(s):  
Iain L. MacDonald
Keyword(s):  
Markov Chain ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov ◽  
Coarse Grained

Hidden Markov Processes: Basic Properties

2014 ◽  
Author(s):  
M. Vidyasagar
Keyword(s):  
Markov Chain ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Markov Processes ◽  
Viterbi Algorithm ◽  
Hidden Markov ◽  
Basic Properties ◽  
Deterministic Function ◽  
Hidden Markov Processes ◽  
Chain Type

This chapter considers the basic properties of hidden Markov processes (HMPs) or hidden Markov models (HMMs), a special type of stochastic process. It begins with a discussion of three distinct types of HMMs and shows that they are all equivalent from the standpoint of their expressive power or modeling ability: Type 1 hidden Markov model, or a HMM of the deterministic function of a Markov chain type; hidden Markov model of Type 2, or a HMM of the random function of a Markov chain type; and hidden Markov model of Type 3, or a HMM of the joint Markov process type. The chapter also examines various issues related to the computation of likelihoods in a HMM before concluding with an overview of the Viterbi algorithm and the Baum–Welch algorithm.

scholarly journals A Dependent Hidden Markov Model of Credit Quality

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Małgorzata Wiktoria Korolkiewicz
Keyword(s):  
Markov Chain ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Credit Rating ◽  
Hidden Markov ◽  
Credit Ratings ◽  
The State ◽  
Credit Quality ◽  
The Em Algorithm ◽  
Rating Process

We propose a dependent hidden Markov model of credit quality. We suppose that the "true" credit quality is not observed directly but only through noisy observations given by posted credit ratings. The model is formulated in discrete time with a Markov chain observed in martingale noise, where "noise" terms of the state and observation processes are possibly dependent. The model provides estimates for the state of the Markov chain governing the evolution of the credit rating process and the parameters of the model, where the latter are estimated using the EM algorithm. The dependent dynamics allow for the so-called "rating momentum" discussed in the credit literature and also provide a convenient test of independence between the state and observation dynamics.

scholarly journals The dynamics of social deprivation in Mexico

2021 ◽  
pp. 1-20
Author(s):  
José Carlos Ramírez
Keyword(s):  
Markov Chain ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Similar Pattern ◽  
Social Deprivation ◽  
Hidden Markov ◽  
Sample Period ◽  
First Order ◽  
Order Markov Chain ◽  
Markovian Approach

This paper aims to model the dynamics of social deprivation in Mexico using a Markovian approach. First, we establish a scenario where a list of items characterizing social deprivation evolves as a first-order Markov chain under the sample period (2002-2012). Then, we estimate latent states and ergodic vectors of a hidden-Markov model to verify the strength of the conclusions drawn from such a scenario. After collecting results from both kinds of analyses, we find a similar pattern of impoverishment. The paper's conclusions state that the evolution of Mexico's deprivation profile may slightly worsen soon.

scholarly journals Probability Model Based on Cluster Analysis to Classify Sequences of Observations for Small Training Sets

2020 ◽  
Vol 8 (1) ◽  
pp. 296-303
Author(s):  
Sergey S Yulin ◽  
Irina N Palamar
Keyword(s):  
Markov Chain ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Short Term Memory ◽  
Hidden Markov ◽  
Probability Model ◽  
Training Data ◽  
Training Dataset ◽  
Experimental Comparison ◽  
Self Organizing Map

The problem of recognizing patterns, when there are few training data available, is particularly relevant and arises in cases when collection of training data is expensive or essentially impossible. The work proposes a new probability model MC&CL (Markov Chain and Clusters) based on a combination of markov chain and algorithm of clustering (self-organizing map of Kohonen, k-means method), to solve a problem of classifying sequences of observations, when the amount of training dataset is low. An original experimental comparison is made between the developed model (MC&CL) and a number of the other popular models to classify sequences: HMM (Hidden Markov Model), HCRF (Hidden Conditional Random Fields),LSTM (Long Short-Term Memory), kNN+DTW (k-Nearest Neighbors algorithm + Dynamic Time Warping algorithm). A comparison is made using synthetic random sequences, generated from the hidden markov model, with noise added to training specimens. The best accuracy of classifying the suggested model is shown, as compared to those under review, when the amount of training data is low.

scholarly journals Modelling the Dynamics of Biological Systems with the Geometric Hidden Markov Model

2017 ◽  
Author(s):  
Borislav Vangelov ◽  
Mauricio Barahona
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Time Series Data ◽  
Hidden Markov ◽  
Stem Cell Differentiation ◽  
Coarse Grained ◽  
Genetic Circuit ◽  
Series Data ◽  
Biological Processes

ABSTRACTMany biological processes can be described geometrically in a simple way: stem cell differentiation can be represented as a branching tree and cell division can be depicted as a cycle. In this paper we introduce the geometric hidden Markov model (GHMM), a dynamical model whose goal is to capture the low-dimensional characteristics of biological processes from multivariate time series data. The framework integrates a graph-theoretical algorithm for dimensionality reduction with a latent variable model for sequential data. We analyzed time series data generated by an in silico model of a biomolecular circuit, the represillator. The trained model has a simple structure: the latent Markov chain corresponds to a two-dimensional lattice. We show that the short-term and long-term predictions of the GHMM reflect the oscillatory behaviour of the genetic circuit. Analysis of the inferred model with a community detection methods leads to a coarse-grained representation of the process.

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