相关论文: Three Asymptotic Regimes for Ranking and Selection…

Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…

Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample…

We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…

This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning…

In this paper the asymptotic distribution of estimators is derived in a general regression setting where rank restrictions on a submatrix of the coefficient matrix are imposed and the regressors can include stationary or I(1) processes.…

Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…

The statistical analysis of Randomized Numerical Linear Algebra (RandNLA) algorithms within the past few years has mostly focused on their performance as point estimators. However, this is insufficient for conducting statistical inference,…

We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…

An asymptotically optimal sampling-based planner employs sampling to solve robot motion planning problems and returns paths with a cost that converges to the optimal solution cost, as the number of samples approaches infinity. This…

We study a class of iterated empirical risk minimization (ERM) procedures in which two successive ERMs are performed on the same dataset, and the predictions of the first estimator enter as an argument in the loss function of the second.…

Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly-exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong…

The superiority of symplectic methods for stochastic Hamiltonian systems has been widely recognized, yet the probabilistic mechanism behind this superiority remains incompletely understood. This paper studies the superiority of symplectic…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and…

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

Semisupervised learning has emerged as a popular framework for improving modeling accuracy while controlling labeling cost. Based on an extension of stochastic composite likelihood we quantify the asymptotic accuracy of generative…

This work analyzes the asymptotic performances of fully distributed sequential hypothesis testing procedures as the type-I and type-II error rates approach zero, in the context of a sensor network without a fusion center. In particular, the…

We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…

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…

Voting and assignment are two of the most fundamental settings in social choice theory. For both settings, random serial dictatorship (RSD) is a well-known rule that satisfies anonymity, ex post efficiency, and strategyproofness. Recently,…