Related papers: On Distributional Autoregression and Iterated Tran…
We study the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e. sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges…
This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples…
In the fields of sociology and economics, the modeling of matrix-variate integervalued time series is urgent. However, no prior studies have addressed the modeling of such data. To address this topic, this paper proposes a novel…
Given a sequence of i.i.d. random functions $\Psi_{n}:\mathbb{R}\to\mathbb{R}$, $n\in\mathbb{N}$, we consider the iterated function system and Markov chain which is recursively defined by $X_{0}^{x}:=x$ and…
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…
We consider a distributed estimation method in a setting with heterogeneous streams of correlated data distributed across nodes in a network. In the considered approach, linear models are estimated locally (i.e., with only local data)…
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…
Most optimal routing problems focus on minimizing travel time or distance traveled. Oftentimes, a more useful objective is to maximize the probability of on-time arrival, which requires statistical distributions of travel times, rather than…
We propose a multiscale approach to time series autoregression, in which linear regressors for the process in question include features of its own path that live on multiple timescales. We take these multiscale features to be the recent…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
We review autoregressive models for the analysis of multivariate count time series. In doing so, we discuss the choice of a suitable distribution for a vectors of count random variables. This review focus on three main approaches taken for…
The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…
We study the problem of learning the transition matrices of a set of Markov chains from a single stream of observations on each chain. We assume that the Markov chains are ergodic but otherwise unknown. The learner can sample Markov chains…
We propose a factor network autoregressive (FNAR) model for time series with complex network structures. The coefficients of the model reflect many different types of connections between economic agents ("multilayer network"), which are…
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…
Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing the return time entropy of a Markov chain, subject to a graph topology with travel times and stationary distribution. The return time entropy…
We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…
Contemporary time series analysis has seen more and more tensor type data, from many fields. For example, stocks can be grouped according to Size, Book-to-Market ratio, and Operating Profitability, leading to a 3-way tensor observation at…