相关论文: Guaranteed Estimations for Linear Difference Descr…

For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally…

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…

Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its…

Fairness has become a central issue for our research community as classification algorithms are adopted in societally critical domains such as recidivism prediction and loan approval. In this work, we consider the potential bias based on…

This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…

Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…

We investigate the approximation and estimation rates of conditional diffusion transformers (DiTs) with classifier-free guidance. We present a comprehensive analysis for ``in-context'' conditional DiTs under four common data assumptions. We…

We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…

Stochastic optimization often involves calculating the expected value of a first-order max or min function, known as a first-order loss function. In this context, loss functions are frequently approximated using piecewise linear functions.…

In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…

The paper presents analytic expressions of minimax (worst-case) estimates for solutions of linear abstract Neumann problems in Hilbert space with uncertain (not necessarily bounded!) inputs and boundary conditions given incomplete…

We investigate a state estimation problem for the dynamical system described by uncertain linear operator equation in Hilbert space. The uncertainty is supposed to admit a set-membership description. We present explicit expressions for…

Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…

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.…

We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate…

Prediction error and maximum likelihood methods are powerful tools for identifying linear dynamical systems and, in particular, enable the joint estimation of model parameters and the Kalman filter used for state estimation. A key…

This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…

In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…

In this paper, approximate Linear Minimum Variance (LMV) filters for continuous-discrete state space models are introduced. The filters are obtained by means of a recursive approximation to the predictions for the first two moments of the…

Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…