arXiv research

We introduce a new GP kernel based on the sinc function for band-limited signals.

New classifier combines locally linear kernels for fast and accurate non-linear classification.

Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of data points. We provide a new analysis of a class of approximate kernel methods…

Characterizes kernel interpolation in large dimensions, revealing optimal and sub-optimal regions.

New research shows Manturov-Nikonov map fails for large k values.

The paper explores identifiability and stability in drifting fields using companion-elliptic kernels.

Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending func…

We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical $M$-estimation. We interpret the KDE based on a radial, positive semi-definite ke…

Paper studies identifiability and stability of drifting fields in generative modeling.

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological summaries, most noticeably the Persistence Diagram, are typically defined in comple…

Paper introduces RKHM and KME for richer data analysis.

Kernel-Gradient Drifting improves generative modeling for non-Euclidean data.

We construct near-optimal coresets for kernel density estimates for points in $\mathbb{R}^d$ when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size $O(\sqrt{d}/\varepsilon\cdot \sqrt{\log 1/\varepsilon} )$, and we show a near-matching lower bound of size $Ω(\min\…

New sparse GP model learns compositional kernels efficiently.

Regularized approaches have been successfully applied to linear system identification in recent years. Many of them model unknown impulse responses exploiting the so called Reproducing Kernel Hilbert spaces (RKHSs) that enjoy the notable property of being in one-to-one correspondence with the class of positive semidefi…

Deep kernel learning improves performance on complex tasks.

A method for interpreting SVMs using polynomial kernels, revealing model complexity.

New research optimizes HSIC estimation rate for translation-invariant kernels.

Unified framework for spectral methods, kernel learning, and manifold unfolding.

KQT-EWMA monitors multivariate data streams online with flexible and practical change detection.

Gaussian Process Hydrodynamics approximates fluid flow equations using probabilistic kernels.

SKI accelerates GP inference with sparse grids to handle higher dimensions.

Improves probability distribution compression with KT algorithm.

Kernel k-Means algorithm improves clustering of non-linear data.

Quantum kernels can be efficiently embedded into classical feature spaces.

We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding. Since GPTMs w…

Novel Newton method for large-scale kernel methods using random features.

Proposes a new CNN for meshes that can handle orientation.

In kernel methods, the kernels are often required to be positive definite, which restricts the use of many indefinite kernels. To consider those non-positive definite kernels, in this paper, we aim to build an indefinite kernel learning framework for kernel logistic regression. The proposed indefinite kernel logistic r…

Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind t…

A fast algorithm speeds up training of pairwise kernels.

A new Mean Shift variant converges after a finite number of iterations for specific kernel shapes.

Identifying significant subsets of the genes, gene shaving is an essential and challenging issue for biomedical research for a huge number of genes and the complex nature of biological networks,. Since positive definite kernel based methods on genomic information can improve the prediction of diseases, in this paper we…

While tree methods have been popular in practice, researchers and practitioners are also looking for simple algorithms which can reach similar accuracy of trees. In 2010, (Ping Li UAI'10) developed the method of "abc-robust-logitboost" and compared it with other supervised learning methods on datasets used by the deep …

New spectral mixture representation for isotropic kernels simplifies random Fourier features.

New robustness test for kernel goodness-of-fit tests.

We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space, using random features of the kernel's Fourier transform. The advantage is that, the …

The paper explores how kernel eigenalignments affect generalization in KRR.

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy measures that provably determine the convergence of a sample to its target dist…

This work addresses two main issues of the standard Kernel Entropy Component Analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of by variance as in K…

We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by th…

We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape for the various scalings of $d = n^α$, $α\in(0,1)$, for the input dimension $d$ and sample size $n$. Empirical evidence supports our finding that minimum-norm interpo…

Paper advances sparse regularisation theory for measures with new kernel insights.

Bayesian model merges multi-view latent models and kernel methods.

Advances in deep learning for spatio-temporal event modeling.

PRS improves rejection sampling by learning better proposals.

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the…

Efficient kernel methods for large datasets using GPU acceleration.