Related papers: Kernel-based function learning in dynamic and non …

Many machine learning algorithms can be interpreted as procedures for estimating functions defined on the data distribution. In this paper we present a conceptual framework that formulates a wide range of learning problems as variational…

As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of…

Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…

Feature learning is widely regarded as the key mechanism distinguishing neural networks from fixed-kernel methods, yet its impact on the induced function space remains poorly understood. In this work, we precisely characterize how the…

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like…

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

Many algorithms in computer vision and robotics make strong assumptions about uncertainty, and rely on the validity of these assumptions to produce accurate and consistent state estimates. In practice, dynamic environments may degrade…

Reinforcement learning (RL) algorithms find applications in inventory control, recommender systems, vehicular traffic management, cloud computing and robotics. The real-world complications of many tasks arising in these domains makes them…

Kernel ridge regression, KRR, is a generalization of linear ridge regression that is non-linear in the data, but linear in the model parameters. Here, we introduce an equivalent formulation of the objective function of KRR, which opens up…

We consider the problem of function estimation in the case where the data distribution may shift between training and test time, and additional information about it may be available at test time. This relates to popular scenarios such as…

We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient descent (GD) and stochastic gradient descent (SGD) with…

The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…

Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

We address the problem of causal effect estimation in the presence of unobserved confounding, but where proxies for the latent confounder(s) are observed. We propose two kernel-based methods for nonlinear causal effect estimation in this…

Learning from examples is one of the key problems in science and engineering. It deals with function reconstruction from a finite set of direct and noisy samples. Regularization in reproducing kernel Hilbert spaces (RKHSs) is widely used to…

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…

While balancing covariates between groups is central for observational causal inference, selecting which features to balance remains a challenging problem. Kernel balancing is a promising approach that first estimates a kernel that captures…