Related papers: A Permutation-free Kernel Two-Sample Test
As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However,…
The mean shift (MS) is a non-parametric, density-based, iterative algorithm with prominent usage in clustering and image segmentation. A rigorous proof for the convergence of its mode estimate sequence in full generality remains unknown. In…
The modelling of data on a spherical surface requires the consideration of directional probability distributions. To model asymmetrically distributed data on a three-dimensional sphere, Kent distributions are often used. The moment…
The measurement-device-independent quantum key distribution (MDI-QKD) can be immune to all detector side-channel attacks. Moreover, it can be easily implemented combining with the matured decoy-state methods under current technology. It…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
We study the problem of quickest detection of a change in the mean of an observation sequence, under the assumption that both the pre- and post-change distributions have bounded support. We first study the case where the pre-change…
In this paper, we bound the error induced by using a weighted skeletonization of two data sets for computing a two sample test with kernel maximum mean discrepancy. The error is quantified in terms of the speed in which heat diffuses from…
This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally…
This paper considers the change point detection problem under dependent samples. In particular, we provide performance guarantees for the MMD-CUSUM test under exponentially $\alpha$, $\beta$, and fast $\phi$-mixing processes, which…
Exploring the free-energy landscape along reaction coordinates or system parameters $\lambda$ is central to many studies of high-dimensional model systems in physics, e.g. large molecules or spin glasses. In simulations this usually…
Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and…
We revisit extending the Kolmogorov-Smirnov distance between probability distributions to the multidimensional setting and make new arguments about the proper way to approach this generalization. Our proposed formulation maximizes the…
To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly…
We study query time bounds for the fundamental problem of estimating the kernel mean $\frac1{|X|}\sum_{x\in X}\mathbf{k}(x,y)$ of a query $y$ in a finite dataset $X\subset\mathbb{R}^d$ up to a prescribed additive error $\varepsilon$. The…
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…
The standardized mean difference (SMD) is a widely used measure of effect size, particularly common in psychology, clinical trials, and meta-analysis involving continuous outcomes. Traditionally, under the equal variance assumption, the SMD…