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Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…
We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their…
Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis.…
A change points detection aims to catch an abrupt disorder in data distribution. Common approaches assume that there are only two fixed distributions for data: one before and another after a change point. Real-world data are richer than…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…
Optimal algorithms are developed for robust detection of changes in non-stationary processes. These are processes in which the distribution of the data after change varies with time. The decision-maker does not have access to precise…
A martingale framework for concept change detection based on testing data exchangeability was recently proposed (Ho, 2005). In this paper, we describe the proposed change-detection test based on the Doob's Maximal Inequality and show that…
We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the…
This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown…
This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general…
We study stochastic approximation procedures for approximately solving a $d$-dimensional linear fixed point equation based on observing a trajectory of length $n$ from an ergodic Markov chain. We first exhibit a non-asymptotic bound of the…
In this paper, I propose a general procedure for multivariate distribution-free nonparametric testing derived from the concept of ranks that are based upon measure transportation in the context of multiple change point analysis. I will use…
In this paper, we study the problem of estimating a Markov chain $X$(signal) from its noisy partial information $Y$, when the transition probability kernel depends on some unknown parameters. Our goal is to compute the conditional…
We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator…
Changepoint models typically assume the data within each segment are independent and identically distributed conditional on some parameters which change across segments. This construction may be inadequate when data are subject to local…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…
This paper examines the joint problem of detection and identification of a sudden and unobservable change in the probability distribution function (pdf) of a sequence of independent and identically distributed (i.i.d.) random variables to…
Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter spaces with independent or Markovian data. Necessary conditions for consistency include the prior putting enough weight on the correct…
We consider the situation where the observed sample contains some observations whose class of origin is known (that is, they are classified with respect to the g underlying classes of interest), and where the remaining observations in the…
Time-series anomaly detection deals with the problem of detecting anomalous timesteps by learning normality from the sequence of observations. However, the concept of normality evolves over time, leading to a "new normal problem", where the…