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We present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt…

Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…

We consider kernel based learning methods for regression and analyze what happens to the risk minimizer when new variables, statistically independent of input and target variables, are added to the set of input variables; this problem…

In this paper, we investigate the supremum-norm generalization error and the uniform inference for a specific class of kernel regression methods, namely the kernel gradient flows. Under the widely adopted capacity-source condition framework…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

Localized support vector machines solve SVMs on many spatially defined small chunks and one of their main characteristics besides the computational benefit compared to global SVMs is the freedom of choosing arbitrary kernel and…

In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this…

We obtain sharp oracle inequalities for the empirical risk minimization procedure in the regression model under the assumption that the target Y and the model F are subgaussian. The bound we obtain is sharp in the minimax sense if F is…

Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure…

The expected signature kernel arises in statistical learning tasks as a similarity measure of probability measures on path space. Computing this kernel for known classes of stochastic processes is an important problem that, in particular,…

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…

Recent advances in machine learning have shown promising results for financial prediction using large, over-parameterized models. This paper provides theoretical foundations and empirical validation for understanding when and how these…

We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…

We consider the problem of estimating the expected value of information (the knowledge gradient) for Bayesian learning problems where the belief model is nonlinear in the parameters. Our goal is to maximize some metric, while simultaneously…

Under covariate shift, training (source) data and testing (target) data differ in input space distribution, but share the same conditional label distribution. This poses a challenging machine learning task. Robust Bias-Aware (RBA)…

We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as…

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings…

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…

Expected Shortfall (ES), also known as superquantile or Conditional Value-at-Risk, has been recognized as an important measure in risk analysis and stochastic optimization, and is also finding applications beyond these areas. In finance, it…

Abundant literature has been published on approximation methods for the forward initial margin. The most popular ones being the family of regression methods. This paper describes the mathematical foundations on which these regression…