Related papers: Minimum information Markov model
A model of rank polysemantic distribution with a minimal number of fitting parameters is offered. In an ideal case a parameter-free description of the dependence on the basis of one or several immediate features of the distribution is…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower…
We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning…
We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via minimization of a suitable (empirical) version of the…
The causal Markov condition (CMC) is a postulate that links observations to causality. It describes the conditional independences among the observations that are entailed by a causal hypothesis in terms of a directed acyclic graph. In the…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
We consider missing data in the context of hidden Markov models with a focus on situations where data is missing not at random (MNAR) and missingness depends on the identity of the hidden states. In simulations, we show that including a…
Given the stochastic nature of gene expression, genetically identical cells exposed to the same environmental inputs will produce different outputs. This heterogeneity has been hypothesized to have consequences for how cells are able to…
Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…
The change detection problem is to determine if the Markov network structures of two Markov random fields differ from one another given two sets of samples drawn from the respective underlying distributions. We study the trade-off between…
Majority-vote ensembles achieve variance reduction by averaging over diverse, approximately independent base learners. When training data exhibits Markov dependence, as in time-series forecasting, reinforcement learning (RL) replay buffers,…
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
We want to reconstruct a signal based on inhomogeneous data (the amount of data can vary strongly), using the model of regression with a random design. Our aim is to understand the consequences of inhomogeneity on the accuracy of estimation…
We present a variational principle for the extraction of a time-dependent orthonormal basis from random realizations of transient systems. The optimality condition of the variational principle leads to a closed-form evolution equation for…
Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…
Safety is an essential requirement for reinforcement learning systems. The newly emerging framework of robust constrained Markov decision processes allows learning policies that satisfy long-term constraints while providing guarantees under…
Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable…