Related papers: Large-Scale Kernel Methods for Independence Testin…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…
Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…
We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
The role of complex quantities in quantum theory has been puzzling physicists since the beginnings. It is thus natural to ask whether, in order to describe our experiments, the mathematical structure of complex Hilbert spaces it is built on…
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…
Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…
This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…
We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…
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…
Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean…
Constraint based causal structure learning for point processes require empirical tests of local independence. Existing tests require strong model assumptions, e.g. that the true data generating model is a Hawkes process with no latent…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…
Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and…
We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert…