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This is a technical report which explores the estimation methodologies on hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random Field. In first section, we briefly investigate a theoretical framework on…
We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete…
A model for network panel data is discussed, based on the assumption that the observed data are discrete observations of a continuous-time Markov process on the space of all directed graphs on a given node set, in which changes in tie…
In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…
We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main difficulty in estimating the condition number is the estimation of…
Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the…
The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…
We propose a penalized pseudo-likelihood criterion to estimate the graph of conditional dependencies in a discrete Markov random field that can be partially observed. We prove the convergence of the estimator in the case of a finite or…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…
Complexity is a fundamental concept underlying statistical learning theory that aims to inform generalization performance. Parameter count, while successful in low-dimensional settings, is not well-justified for overparameterized settings…
We consider the parameter estimation of a 2D sinusoid. Although sinusoidal parameter estimation has been extensively studied, our model differs from those examined in the available literature by the inclusion of an offset term. We derive…
Learning the structure of Markov random fields (MRFs) plays an important role in multivariate analysis. The importance has been increasing with the recent rise of statistical relational models since the MRF serves as a building block of…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
Graph pooling compresses graphs and summarises their topological properties and features in a vectorial representation. It is an essential part of deep graph representation learning and is indispensable in graph-level tasks like…
In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best…
This paper deals with parameter estimation when the data are randomly right censored. The maximum likelihood estimates from censored samples are obtained by using the expectation-maximization (EM) and Monte Carlo EM (MCEM) algorithms. We…
Linear regression models are useful statistical tools to analyze data sets in several different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally…
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,…
Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood…
We consider the problem of evaluating representations of data for use in solving a downstream task. We propose to measure the quality of a representation by the complexity of learning a predictor on top of the representation that achieves…