Related papers: Efficient Aggregated Kernel Tests using Incomplete…
We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence…
A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting,…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…
Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…
Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the…
The ability to identify useful features or representations of the input data based on training data that achieves low prediction error on test data across multiple prediction tasks is considered the key to multitask learning success. In…
We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…
The Maximum Mean Discrepancy (MMD) is a widely used multivariate distance metric for two-sample testing. The standard MMD test statistic has an intractable null distribution typically requiring costly resampling or permutation approaches…
A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…
The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot…
Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in…
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…
We study the problem of distributional approximations to high-dimensional non-degenerate $U$-statistics with random kernels of diverging orders. Infinite-order $U$-statistics (IOUS) are a useful tool for constructing simultaneous prediction…
We propose a simple and intuitive test for arguably the most prevailing hypothesis in statistics that data are independent and identically distributed (IID), based on a newly introduced off-diagonal sequential U-process. This IID test is…
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches…
Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do…
This paper investigates the robustness and optimality of the multi-kernel correntropy (MKC) on linear regression. We first derive an upper error bound for a scalar regression problem in the presence of arbitrarily large outliers and reveal…