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In modern scientific experiments, we frequently encounter data that have large dimensions, and in some experiments, such high dimensional data arrive sequentially rather than full data being available all at a time. We develop multiple…
Aleatoric and Epistemic uncertainty have achieved recent attention in the literature as different sources from which uncertainty can emerge in stochastic modeling. Epistemic being intrinsic or model based notions of uncertainty, and…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
The problem of sequential anomaly detection and identification is considered, where multiple data sources are simultaneously monitored and the goal is to identify in real time those, if any, that exhibit ``anomalous" statistical behavior.…
We consider the problem of sequential anomaly identification over multiple independent data streams, under the presence of a sampling constraint. The goal is to quickly identify those that exhibit anomalous statistical behavior, when it is…
The problem of sequential anomaly detection is considered, where multiple data sources are monitored in real time and the goal is to identify the "anomalous" ones among them, when it is not possible to sample all sources at all times. A…
Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…
This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the…
Personalized optimal decision making, finding the optimal decision rule (ODR) based on individual characteristics, has attracted increasing attention recently in many fields, such as education, economics, and medicine. Current ODR methods…
With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attention in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize…
The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress…
This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…
Multiple hypothesis testing is a central topic in statistics, but despite abundant work on the false discovery rate (FDR) and the corresponding Type-II error concept known as the false non-discovery rate (FNR), a fine-grained understanding…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
Within a Bayesian decision theoretic framework we investigate some asymptotic optimality properties of a large class of multiple testing rules. A parametric setup is considered, in which observations come from a normal scale mixture model…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
The goal of this paper is to develop methodology for the systematic analysis of asymptotic statistical properties of data driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…