Related papers: From univariate to multivariate coupling between c…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
We present a general method to detect and extract from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality. Our central result is derived from the theory of free random…
The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…
We study the asymptotic behaviour of sequences of multivariate random variables representing the number of occurrences of a given set of symbols in a word of length $n$ generated at random according to a rational stochastic model. Assuming…
We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used…
We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously, and we explore them…
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…
Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…
This article considers the problem of analyzing associations between power spectra of multiple time series and cross-sectional outcomes when data are observed from multiple subjects. The motivating application comes from sleep medicine,…
We propose a two-stage approach Spec PC-CP to identify change points in multivariate time series. In the first stage, we obtain a low-dimensional summary of the high-dimensional time series by Spectral Principal Component Analysis…
The estimation of the covariance function of a stochastic process, or signal, is of integral importance for a multitude of signal processing applications. In this work, we derive closed-form expressions for the variance of covariance…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…
Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. For probabilistic models in the Bayes optimal setting, general…
This paper is concerned with elucidating a relationship between two common coupling methods for the continuous time Markov chain models utilized in the cell biology literature. The couplings considered here are primarily used in a…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…