Related papers: Optimal Estimation of Recurrence Structures from T…
We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot based analysis for…
We consider the problem of estimating the asymptotic variance of a function defined on a Markov chain, an important step for statistical inference of the stationary mean. We design a novel recursive estimator that requires $O(1)$…
This paper is concerned with fundamental limits on the approximation of nonlinear dynamical systems. Specifically, we show that recurrent neural networks (RNNs) can approximate nonlinear systems -- that satisfy a Lipschitz property and…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
Although the notion of diagnostic problem has been extensively investigated in the context of static systems, in most practical applications the behavior of the modeled system is significantly variable during time. The goal of the paper is…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
We consider the problem of optimizing time averages in systems with independent and identically distributed behavior over renewal frames. This includes scheduling and task processing to maximize utility in stochastic networks with variable…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
In this study, we employ the recently developed recurrence microstate probabilities as features to improve accuracy of several well-established machine learning (ML) algorithms. These algorithms are applied to classify discrete and…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
In this study, we present a method for classifying dynamical systems using a hybrid approach involving recurrence plots and a convolution neural network (CNN). This is performed by obtaining the recurrence matrix of a time series generated…
This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework…
We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network…
We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with…
In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
Learning from temporally-correlated data is a core facet of modern machine learning. Yet our understanding of sequential learning remains incomplete, particularly in the multi-trajectory setting where data consists of many independent…