Related papers: Minimum information Markov model
We propose a method to construct a joint statistical model for mixed-domain data to analyze their dependence. Multivariate Gaussian and log-linear models are particular examples of the proposed model. It is shown that the functional…
Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian…
We study an information-theoretic minimax problem for finite multivariate Markov chains on $d$-dimensional product state spaces. Given a family $\mathcal B=\{P_1,\ldots,P_n\}$ of $\pi$-stationary transition matrices and a class $\mathcal F…
In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces,…
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible…
In this work we introduce a new and richer class of finite order Markov chain models and address the following model selection problem: find the Markov model with the minimal set of parameters (minimal Markov model) which is necessary to…
We introduce the Markov missing graph (MMG), a novel framework that imputes missing data based on undirected graphs. MMG leverages conditional independence relationships to locally decompose the imputation model. To establish the…
Traditional hidden Markov models have been a useful tool to understand and model stochastic dynamic data; in the case of non-Gaussian data, models such as mixture of Gaussian hidden Markov models can be used. However, these suffer from the…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
Developing feature selection algorithms that move beyond a pure correlational to a more causal analysis of observational data is an important problem in the sciences. Several algorithms attempt to do so by discovering the Markov blanket of…
Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types…
Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…
We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space, as well as the problem of finding an optimal partition of coordinates such that the…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
Starting from the Avellaneda-Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on…
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…
We formulate a probabilistic Markov property in discrete time under a dynamic risk framework with minimal assumptions. This is useful for recursive solutions to risk-sensitive versions of dynamic optimisation problems such as optimal…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
The value of plant model information available in the control design process is discussed. We design optimal state-feedback controllers for interconnected discrete-time linear systems with stochastically-varying parameters. The parameters…
We propose a numerical technique for parameter inference in Markov models of biological processes. Based on time-series data of a process we estimate the kinetic rate constants by maximizing the likelihood of the data. The computation of…