Related papers: Equations for hidden Markov models

Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in the development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there…

The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate.…

The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…

As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…

The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…

Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov…

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.

Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a…

We consider novel phylogenetic models with rate matrices that arise via the embedding of a progenitor model on a small number of character states, into a target model on a larger number of character states. Adapting representation-theoretic…

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…

Infinite hidden Markov models provide a flexible framework for modelling time series with structural changes and complex dynamics, without requiring the number of latent states to be specified in advance. This flexibility is achieved…

This paper reports on recent results related to audiophonic signals encoding using time-scale and time-frequency transform. More precisely, non-linear, structured approximations for tonal and transient components using local cosine and…

We propose a new flexible tensor model for multiple-equation regression that accounts for latent regime changes. The model allows for dynamic coefficients and multi-dimensional covariates that vary across equations. We assume the…

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…

Latent space models are popular for analyzing dynamic network data. We propose a variational approach to estimate the model parameters as well as the latent positions of the nodes in the network. The variational approach is much faster than…

In an effort to aid communication among different fields and perhaps facilitate progress on problems common to all of them, this article discusses hidden Markov processes from several viewpoints, especially that of symbolic dynamics, where…

The paper studies optimal coding of hidden Markov sources (HMS), which represent a broad class of practical sources obtained through noisy acquisition processes, beside their explicit modeling use in speech processing and recognition, image…

An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with…

Hidden Markov model (HMM) has been successfully used for sequential data modeling problems. In this work, we propose to power the modeling capacity of HMM by bringing in neural network based generative models. The proposed model is termed…

Markov decision processes are a ubiquitous formalism for modelling systems with non-deterministic and probabilistic behavior. Verification of these models is subject to the famous state space explosion problem. We alleviate this problem by…