Related papers: Super-Samples from Kernel Herding
In recent years, transfer learning has garnered significant attention. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
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,…
Kernel ridge regression (KRR) is widely used for nonparametric regression over reproducing kernel Hilbert spaces. It offers powerful modeling capabilities at the cost of significant computational costs, which typically require $O(n^3)$…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and…
Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…
One of the most fundamental aspects of any machine learning algorithm is the training data used by the algorithm. We introduce the novel concept of $\epsilon$-approximation of datasets, obtaining datasets which are much smaller than or are…
Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering…
Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…
Random forests are notable learning algorithms first introduced by Breinman in 2001, they are widely used for classification and regression tasks and their mathematical properties are under ongoing research. We consider a specific class of…
The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as…
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…