Related papers: Functional worst risk minimization
In the financial field, precise risk assessment tools are essential for decision-making. Recent studies have challenged the notion that traditional network loss functions like Mean Square Error (MSE) are adequate, especially under extreme…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
We establish a new concentration result for regularized risk minimizers which is similar to an oracle inequality. Applying this inequality to regularized least squares minimizers like least squares support vector machines, we show that…
We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The…
This manuscript introduces a new optimization framework for machine learning and AI, named {\bf empirical X-risk minimization (EXM)}. X-risk is a term introduced to represent a family of compositional measures or objectives, in which each…
This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…
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…
Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations. Specifically, we introduce a new class of function transformations with the…
A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…
We introduce a new surrogate loss function called orbit loss in the structured prediction framework, which has good theoretical and practical advantages. While the orbit loss is not convex, it has a simple analytical gradient and a simple…
In this paper, we study the functional linear multiplicative model based on the least product relative error criterion. Under some regularization conditions, we establish the consistency and asymptotic normality of the estimator. Further,…
A fundamental assumption of most machine learning algorithms is that the training and test data are drawn from the same underlying distribution. However, this assumption is violated in almost all practical applications: machine learning…
In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…
In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected…
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…
Machine learning systems often experience a distribution shift between training and testing. In this paper, we introduce a simple variational objective whose optima are exactly the set of all representations on which risk minimizers are…
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…
This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our primary goal is to establish central limit theorems for these functionals when mixed estimators are employed. Our study is relevant to the…