相关论文: Minimax State Observation in Linear One Dimensiona…

In this article we consider a priori error and pointwise estimates for finite element approximations of solutions to semilinear elliptic boundary value problems in d>=2 space dimensions, with nonlinearities satisfying critical growth…

Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…

In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. Recently, many flexible machine learning methods have been developed for instrumental variable estimation. However, these methods have at least one…

This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…

In this paper we develop a theory of matrix completion for the extreme case of noisy 1-bit observations. Instead of observing a subset of the real-valued entries of a matrix M, we obtain a small number of binary (1-bit) measurements…

In this paper we propose a bilevel optimization approach for the placement of space and time observations in variational data assimilation problems. Within the framework of supervised learning, we consider a bilevel problem where the…

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…

We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…

Consider a remote estimation problem where a sensor wants to communicate the state of an uncertain source to a remote estimator over a finite time horizon. The uncertain source is modeled as an autoregressive process with bounded noise.…

The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…

We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on…

Stochastic minimax optimization has drawn much attention over the past decade due to its broad applications in machine learning, signal processing and game theory. In some applications, the probability distribution of uncertainty depends on…

A simple third order compact finite element method is proposed for one-dimensional Sturm-Liouville boundary value problems. The key idea is based on the interpolation error estimate, which can be related to the source term. Thus, a simple…

The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and…

We derive a reduced-order state estimator for discrete-time infinite dimensional linear systems with finite dimensional Gaussian input and output noise. This state estimator is the optimal one-step estimate that takes values in a fixed…

Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure:…

We consider tracking control of linear minimum phase systems with known arbitrary relative degree which are subject to possible output measurement losses. We provide a control law which guarantees the evolution of the tracking error within…

In this paper we study an infinite-horizon persistent monitoring problem in a two-dimensional mission space containing a finite number of statically placed targets, at each of which we assume a constant rate of uncertainty accumulation.…

In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…

The problem of state estimation for a system of coupled hyperbolic PDEs and ODEs with Lipschitz nonlinearities with boundary measurements is considered. An infinite dimensional observer with a linear boundary injection term is used to solve…