arXiv research

Quantum kernels can be efficiently embedded into classical feature spaces.

This paper provides a dictionary of closed-form kernel mean embeddings.

This note optimizes distributions using kernel mean embeddings with a new parameterization.

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of kernel mean embeddings of probability measures. For characteristic kernels, which inc…

Kernel embeddings help estimate causal effects from observational data.

New embeddings for manifolds using heat kernels.

A Hilbert space embedding for probability measures has recently been proposed, wherein any probability measure is represented as a mean element in a reproducing kernel Hilbert space (RKHS). Such an embedding has found applications in homogeneity testing, independence testing, dimensionality reduction, etc., with the re…

A new method estimates multi-dimensional value distributions using Hilbert space embeddings.

Kernel embeddings separate distinct probability distributions, simplifying testing.

Kernel discriminant analysis uses nonlinear embeddings to improve classification.

New KQEs improve probability metrics without mean function constraints.

In this paper, we survey some recent results about the asymptotic expansion of Bergman kernel and we give a Bergman kernel proof of Kodaira embedding theorem.

Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the align…

In recent years, there have been significant efforts on mitigating unethical demographic biases in machine learning methods. However, very little is done for kernel methods. In this paper, we propose a new fair kernel regression method via fair feature embedding (FKR-F$^2$E) in kernel space. Motivated by prior works on…

Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying function of interest whose conditional mean was observed is a challenging inferenc…

Faster convergence of kernel mean embeddings using variance information.

IDK improves anomaly detection for points and groups without explicit learning.

Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $μ$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two mapped measures is a semi-metric $d_k$ over $M$. We study three questions. (I) For a…

New recursive algorithm estimates conditional kernel mean embeddings in Hilbert space.

Gaussian kernel fails on circle and related spaces.

New test for conditional independence using kernel embeddings.

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 for the computation of optimal reaction coordinates of such systems that is based …

Paper proposes a new method to learn distribution kernels via entropy maximization.

Paper generalizes kernel mean embedding to von Neumann-algebra-valued measures.

Efficiently approximates kernel mean embeddings using Nyström method.

For any n-dimensional compact Riemannian manifold (M,g), we construct a canonical t-family of isometric embeddings I_{t}: M->R^{q(t)}, with t>0 sufficiently small and q(t)>>t^{-n/2}. This is done by intrinsically perturbing the heat kernel embedding introduced in [BBG]. As t->0, asymptotic geometry of the embedded imag…

A novel kernel-based test detects equality versus singularity of two probability measures.

A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the product of the marginals, in a Reproducing Kernel Hilbert Space (RKHS). It has …

Maps embed manifolds using heat kernels of connection Laplacian.

In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding coordinates are the eigenvectors of a positive semi-definite kernel obtained as the sol…

Conditional kernel mean embeddings are nonparametric models that encode conditional expectations in a reproducing kernel Hilbert space. While they provide a flexible and powerful framework for probabilistic inference, their performance is highly dependent on the choice of kernel and regularization hyperparameters. Neve…

Improved learning theory for kernel distribution regression with two-stage sampling.

A new method embeds data using Gaussian processes based on the heat kernel.

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 computation-efficient kernel embeddings from specific data. In the framework, the h…

Paper introduces RKHM and KME for richer data analysis.

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing kernel Hilbert space (RKHS) in which the whole arsenal of kernel methods can be ex…

We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space embeddings, namely the ``Double Sum'' (DS) kernels recently considered in Bayesian set opt…

Given only information in the form of similarity triplets "Object A is more similar to object B than to object C" about a data set, we propose two ways of defining a kernel function on the data set. While previous approaches construct a low-dimensional Euclidean embedding of the data set that reflects the given similar…

Kernel method embeds noisy datasets, capturing shared structures.

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). A pseudometric on the spac…

Alternative proof of coisotropic embedding theorem for pre-symplectic manifolds.

Estimates class prior for unlabeled data using kernel embedding.

Kernel fusion is a popular and effective approach for combining multiple features that characterize different aspects of data. Traditional approaches for Multiple Kernel Learning (MKL) attempt to learn the parameters for combining the kernels through sophisticated optimization procedures. In this paper, we propose an a…

Proposes estimators for complex dose-response curves using kernel methods.

Kernel-spectral embedding learns low-dim. structures from noisy data.

Paper explores duality in DPPs using embedding structure analysis.

Paper develops a unified framework for measuring differences between conditional distributions.

Paper characterizes embeddability of function spaces into $L_p$-type RKBS via metric entropy.