相关论文: Parametric error bounds for convex approximations …

This paper is concerned with a posteriori error bounds for linear transport equations and related questions of contriving corresponding adaptive solution strategies in the context of Discontinuous-Petrov-Galerkin schemes. After indicating…

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and…

We consider a two-level discrete-time control framework with real-time constraints where a central controller issues setpoints to be implemented by local controllers. The local controllers implement the setpoints with some approximation and…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution $u \in H^s$…

We consider a parabolic-parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin-Robin splitting method analyzed in [J. Numer. Math., 31(1):59--77, 2023]. We show that the errors of the…

We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…

Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM…

We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…

In this paper the problem of selecting $p$ out of $n$ available items is discussed, such that their total cost is minimized. We assume that costs are not known exactly, but stem from a set of possible outcomes. Robust recoverable and…

Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…

Probabilistic rounding error analysis can yield much sharper bounds than classical worst-case theory, but existing results typically rely on zero-mean rounding errors and often leave the confidence parameter implicit. This work revisits…

We derive error estimates for a linear-quadratic elliptic distributed optimal control problem with pointwise control constraints that can be applied to standard finite element methods and multiscale finite element methods.

This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…

Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…

Consider the standard linear regression model $\y = \Xmat \betastar + w$, where $\y \in \real^\numobs$ is an observation vector, $\Xmat \in \real^{\numobs \times \pdim}$ is a design matrix, $\betastar \in \real^\pdim$ is the unknown…

In QM/MM indirect free energy simulation, QM/MM corrections can be obtained from integration of partial derivatives of alchemical Hamiltonians or from perturbation-based estimators including free energy perturbation (FEP) and acceptance…

We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…

For practical model-based demands, such as design space exploration and uncertainty quantification (UQ), a high-fidelity model that produces accurate outputs often has high computational cost, while a low-fidelity model with less accurate…