We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions unit ball of reproducing kernel Hilbert space (RKHS), called maximum mean discrepancy (MMD).We present distribution free based on large deviation bounds MMD, third asymptotic this statistic. The MMD can be computed quadratic time, although...

Abstract Motivation: Many problems in data integration bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernel-based statistical test for this problem, based on fact that distributions are different if and only there exists at least function having expectation distributions. Consequently we use maximum discrepancy between means basis statistic. The Maximum Mean Discrepancy (MMD) take advantage kernel trick,...

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This represents any measure as a mean element in reproducing kernel (RKHS). pseudometric on the of can be defined distance between distribution embeddings: we denote this γk, indexed by function k that defines inner product RKHS. We present three theoretical properties γk. First, consider question determining...

Local field potentials (LFPs) reflect subthreshold integrative processes that complement spike train measures. However, little is yet known about the differences between how LFPs and spikes encode rich naturalistic sensory stimuli. We addressed this question by recording from primary visual cortex of anesthetized macaques while presenting a color movie. then determined power at different frequencies represents features in found most informative LFP frequency ranges were 1–8 60–100 Hz. range...

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, energy distances distance covariances from literature; other, maximum mean discrepancies (MMD), that is, between embeddings distributions to reproducing kernel Hilbert spaces (RKHS), as established machine learning. In case where is computed with semimetric negative type, positive definite kernel, termed may be defined such MMD corresponds exactly distance....

We introduce a framework for filtering features that employs the Hilbert-Schmidt Independence Criterion (HSIC) as measure of dependence between and labels.The key idea is good should maximise such dependence.Feature selection various supervised learning problems (including classification regression) unified under this framework, solutions can be approximated using backward-elimination algorithm.We demonstrate usefulness our method on both artificial real world datasets.

Given two probability measures, $\mathbb{P}$ and $\mathbb{Q}$ defined on a measurable space, $S$, the integral metric (IPM) is as $$\gamma_{\mathcal{F}}(\mathbb{P},\mathbb{Q})=\sup\left\{\left\vert \int_{S}f\,d\mathbb{P}-\int_{S}f\,d\mathbb{Q}\right\vert\,:\,f\in\mathcal{F}\right\},$$ where $\mathcal{F}$ class of real-valued bounded functions $S$. By appropriately choosing $\mathcal{F}$, various popular distances between $\mathbb{Q}$, including Kantorovich metric, Fortet-Mourier dual-bounded...

We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions unit ball of reproducing kernel Hilbert space (RKHS). present based on large deviation bounds statistic, while third asymptotic distribution this statistic. The can be computed quadratic time, although efficient linear time approximations available....

While kernel canonical correlation analysis (CCA) has been applied in many contexts, the convergence of finite sample estimates associated functions to their population counterparts not yet established. This paper gives a mathematical proof statistical CCA, providing theoretical justification for method. The uses covariance operators defined on reproducing Hilbert spaces, and analyzes empirical rank counterparts, which can have infinite rank. result also sufficient condition regularization...

We investigated whether it is possible to infer spike trains solely on the basis of underlying local field potentials (LFPs). Using support vector machines and linear regression models, we found that in primary visual cortex (V1) monkeys, spikes can indeed be inferred from LFPs, at least with moderate success. Although there a considerable degree variation across electrodes, low-frequency structure (in 100-ms range) reasonable accuracy, whereas exact positions are not reliably predicted. Two...

Many modern applications of signal processing and machine learning, ranging from computer vision to computational biology, require the analysis large volumes high-dimensional continuous-valued measurements. Complex statistical features are commonplace, including multimodality, skewness, rich dependency structures. Such problems call for a flexible robust modeling framework that can take into account these diverse features. Most existing approaches, graphical models, rely heavily on...