Related papers: Optimal Rates for Regularized Conditional Mean Emb…

We consider a stochastic optimization problem involving two random variables: a context variable $X$ and a dependent variable $Y$. The objective is to minimize the expected value of a nonlinear loss functional applied to the conditional…

Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations, and discuss what kind of regularization gives a favorable predictive accuracy. Our main target in this paper…

Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works…

In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…

Standard meta-learning for representation learning aims to find a common representation to be shared across multiple tasks. The effectiveness of these methods is often limited when the nuances of the tasks' distribution cannot be captured…

We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) called conditional…

We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of…

We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with…

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

We propose to analyse the conditional distributional treatment effect (CoDiTE), which, in contrast to the more common conditional average treatment effect (CATE), is designed to encode a treatment's distributional aspects beyond the mean.…

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…

This paper proposes a consensus-based distributed nonlinear filter with kernel mean embedding (KME). This fills with gap of posterior density approximation with KME for distributed nonlinear dynamic systems. To approximate the posterior…

Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…

We prove minimax optimal learning rates for kernel ridge regression, resp.~support vector machines based on a data dependent partition of the input space, where the dependence of the dimension of the input space is replaced by the fractal…

Many problems in causal inference and economics can be formulated in the framework of conditional moment models, which characterize the target function through a collection of conditional moment restrictions. For nonparametric conditional…

In this paper, we study the minimax estimation of the Bochner integral $$\mu_k(P):=\int_{\mathcal{X}} k(\cdot,x)\,dP(x),$$ also called as the kernel mean embedding, based on random samples drawn i.i.d.~from $P$, where…