Related papers: Kernel-based Partial Permutation Test for Detectin…
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…
Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work,…
Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be…
In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…
Functional data often arise as sequential temporal observations over a continuous state-space. A set of functional data with a possible change in its structure may lead to a wrong conclusion if it is not taken in to account. So, sometimes,…
In this article we investigate the effects of conformal transformations on kernel functions used in Support Vector Machines. Our focus lies in the task of text document categorization, which involves assigning each document to a particular…
We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve…
This paper proposes a Kolmogorov-Smirnov type statistic and a Cram\'er-von Mises type statistic to test linearity in semi-functional partially linear regression models. Our test statistics are based on a residual marked empirical process…
Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative.…
Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…
There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have…
Gaussian process regression (GPR) model is a popular nonparametric regression model. In GPR, features of the regression function such as varying degrees of smoothness and periodicities are modeled through combining various covarinace…
We propose a permutation-based method for testing a large collection of hypotheses simultaneously. Our method provides lower bounds for the number of true discoveries in any selected subset of hypotheses. These bounds are simultaneously…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…