Related papers: Learning Deep Kernels for Non-Parametric Two-Sampl…

Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this paper, we consider a semiparametric problem of two-sample hypothesis testing for a class of latent position…

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…

Two-sample tests are important areas aiming to determine whether two collections of observations follow the same distribution or not. We propose two-sample tests based on integral probability metric (IPM) for high-dimensional samples…

Two-sample tests have been extensively employed in various scientific fields and machine learning such as evaluation on the effectiveness of drugs and A/B testing on different marketing strategies to discriminate whether two sets of samples…

A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to…

In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…

We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…

This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel methods tied to the neural tangent kernel theory, the diagonal…

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While…

Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product…

Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…

Deep kernel learning aims at designing nonlinear combinations of multiple standard elementary kernels by training deep networks. This scheme has proven to be effective, but intractable when handling large-scale datasets especially when the…

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…

Multiple kernel learning (MKL) method is generally believed to perform better than single kernel method. However, some empirical studies show that this is not always true: the combination of multiple kernels may even yield an even worse…

We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then…

An exciting recent development is the uptake of deep neural networks in many scientific fields, where the main objective is outcome prediction with the black-box nature. Significance testing is promising to address the black-box issue and…

We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic…

The rise of generative models for scientific research calls for the development of new methods to evaluate their fidelity. A natural framework for addressing this problem is two-sample hypothesis testing, namely the task of determining…

In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…