Related papers: Functional Autoregression Without Truncation: A Co…
In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. While recent advancements in machine learning have introduced flexible methods for IV estimation, they often encounter one or more of the following…
Numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments. A common practice is to normalize all the cutoffs to zero and estimate one effect. This procedure identifies the average…
In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…
Rapid prediction of the aeroacoustic response is a key component in the design of aircraft and turbomachinery. While it is possible to achieve accurate predictions using direct solution of the compressible Navier-Stokes equations,…
This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA…
Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^{\gamma}$ for some $\gamma > 0$.…
This paper describes the procedure to estimate the parameters in mean reversion processes with functional tendency defined by a periodic continuous deterministic function, expressed as a series of truncated Fourier. Two phases of estimation…
We propose an optimal algorithm for estimating conditional average treatment effects (CATEs) when response functions lie in a reproducing kernel Hilbert space (RKHS). We study settings in which the contrast function is structurally simpler…
Functional principal component analysis (FPCA) is a widely used technique in functional data analysis for identifying the primary sources of variation in a sample of random curves. The eigenfunctions obtained from standard FPCA typically…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
We study the minimax settings of binary classification with F-score under the $\beta$-smoothness assumptions on the regression function $\eta(x) = \mathbb{P}(Y = 1|X = x)$ for $x \in \mathbb{R}^d$. We propose a classification procedure…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
Adapting models pre-trained on large-scale datasets is a proven way to reach strong performance quickly for down-stream tasks. However, the growth of state-of-the-art mod-els makes traditional full fine-tuning unsuitable and difficult,…
This paper presents an error analysis of classical and learned Tikhonov regularization schemes for inverse problems. We first demonstrate, both theoretically and numerically, that using a fixed regularization parameter across varying noise…
We consider Tikhonov regularization of control-constrained optimal control problems. We present new a-priori estimates for the regularization error assuming measure and source-measure conditions. In the special case of bang-bang solutions,…
We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…
This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…
Online Continual Learning (OCL) models continuously adapt to nonstationary data streams, usually without task information. These settings are complex and many traditional CL methods fail, while online methods (mainly replay-based) suffer…
In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…