Related papers: Nystr\"om landmark sampling and regularized Christ…

The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel…

Indefinite similarity measures can be frequently found in bio-informatics by means of alignment scores, but are also common in other fields like shape measures in image retrieval. Lacking an underlying vector space, the data are given as…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise…

Learning the principal eigenfunctions of an integral operator defined by a kernel and a data distribution is at the core of many machine learning problems. Traditional nonparametric solutions based on the Nystr{\"o}m formula suffer from…

Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require…

Determinantal point processes (DPPs for short) are a class of repulsive point processes. They have found some statistical applications to model spatial point pattern datasets with repulsion between close points. In the case of DPPs on…

The Nystr\"{o}m method is an effective tool to generate low-rank approximations of large matrices, and it is particularly useful for kernel-based learning. To improve the standard Nystr\"{o}m approximation, ensemble Nystr\"{o}m algorithms…

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…

In large-scale regression problems, random Fourier features (RFFs) have significantly enhanced the computational scalability and flexibility of Gaussian processes (GPs) by defining kernels through their spectral density, from which a finite…

Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine…

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…

In this paper we present new algorithms for training reduced-size nonlinear representations in the Kernel Dictionary Learning (KDL) problem. Standard KDL has the drawback of a large size of the kernel matrix when the data set is large.…

Statistical Relational Learning (SRL) models have attracted significant attention due to their ability to model complex data while handling uncertainty. However, most of these models have been limited to discrete domains due to their…

Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with…

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…

Determinantal point processes (DPPs) have received significant attention as an elegant probabilistic model for discrete subset selection. Most prior work on DPP learning focuses on maximum likelihood estimation (MLE). While efficient and…

The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…

A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a…

We introduce a general framework for active learning in regression problems. Our framework extends the standard setup by allowing for general types of data, rather than merely pointwise samples of the target function. This generalization…