相关论文: Efficiency of Z-estimators indexed by the objectiv…

We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…

Test-time adaptation (TTA) aims to improve model robustness under distribution shifts by adapting to unlabeled test data, but most existing methods rely on backpropagation (BP), which is computationally costly and incompatible with…

The primary objective of this paper is to investigate the orthonormal Strichartz estimates at the critical summability exponent for the Schr\"odinger operator $e^{it\Delta}$ with initial data from the homogeneous Sobolev space $\dot{H}^s…

Test-Time Adaptation (TTA) addresses distribution shifts during testing by adapting a pretrained model without access to source data. In this work, we propose a novel TTA approach for 3D point cloud classification, combining sampling…

This paper deals with functions that defined in metric spaces and valued in complete paranormed vector spaces or valued in Banach spaces, and obtains some necessary and sufficient conditions for weak convergence of finite measures.

We study lower bounds for the Riemann zeta function $\zeta(s)$ along vertical arithmetic progressions in the right-half of the critical strip. We show that the lower bounds obtained in the discrete case coincide, up to the constants in the…

For an integer $n$ and the parameter $\gamma\in(0,n)$, the Riesz potential $I_\gamma$ is known to take boundedly $L^1(\mathbb{R}^n)$ into $L^{\frac{n}{n-\gamma},\infty}(\mathbb{R}^n)$, and also that the target space is the smallest possible…

The research is about a systematic investigation on the following issues. First, we construct different outcome regression-based estimators for conditional average treatment effect under, respectively, true (oracle), parametric,…

The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Riemann zeta function is defined as a sum of the infinite number…

We prove an inequality related to questions in Approximation Theory, Probability Theory, and to Irregularities of Distribution. Let $h_R$ denote an $L ^{\infty}$ normalized Haar function adapted to a dyadic rectangle $R\subset [0,1] ^{3}$.…

We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…

The concept of a profile decomposition formalizes concentration compactness arguments on the functional-analytic level, providing a powerful refinement of the Banach-Alaoglu weak-star compactness theorem. We prove existence of profile…

We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_1,Y_1),...,(X_n,Y_n)$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric…

The goal of this study is to investigate the local convergence of a three-step Newton-Traub technique for solving nonlinear equations in Banach spaces with a convergence rate of five. The first order derivative of a nonlinear operator is…

Test-time adaptation (TTA) refers to adapting neural networks to distribution shifts, with access to only the unlabeled test samples from the new domain at test-time. Prior TTA methods optimize over unsupervised objectives such as the…

We propose a novel algorithm for large-scale regression problems named histogram transform ensembles (HTE), composed of random rotations, stretchings, and translations. First of all, we investigate the theoretical properties of HTE when the…

We address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)=\int_0^z f(\zeta)g'(\zeta)\,d\zeta$ acting from a Banach space $X$ into $H^\infty$. We obtain a collection of general…

Online Test-Time Adaptation (OTTA) has emerged as an effective strategy to handle distributional shifts, allowing on-the-fly adaptation of pre-trained models to new target domains during inference, without the need for source data. We…

This paper is a close follow-up of Kaltenbacher and Tomba 2013 and Jin 2012, where Newton-Landweber iterations have been shown to converge either (unconditionally) without rates or (under an additional regularity assumption) with rates. The…

In this work, we study the weighted empirical risk minimization (weighted ERM) schema, in which an additional data-dependent weight function is incorporated when the empirical risk function is being minimized. We show that under a general…