Related papers: Nystr\"om $M$-Hilbert-Schmidt Independence Criteri…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

Kernel-based multivariate statistical process control (K-MSPC) extends classical monitoring to nonlinear industrial processes. Its performance depends critically on kernel parameters such as lengthscales and variance terms. In current…

Machine learning methods are used to discover complex nonlinear relationships in biological and medical data. However, sophisticated learning models are computationally unfeasible for data with millions of features. Here we introduce the…

Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensionality. However, the theoretical foundations of this success remain poorly understood. We follow…

We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nystr\"om approach to kernel k-means. We analyze the statistical properties of the proposed method and show…

Reasoning based on causality, instead of association has been considered as a key ingredient towards real machine intelligence. However, it is a challenging task to infer causal relationship/structure among variables. In recent years, an…

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…

Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…

Time series forecasting relies on predicting future values from historical data, yet most state-of-the-art approaches-including transformer and multilayer perceptron-based models-optimize using Mean Squared Error (MSE), which has two…

Identification of joint dependence among more than two random vectors plays an important role in many statistical applications, where the data may contain sensitive or confidential information. In this paper, we consider the the…

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…

We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space…

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…

We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate $X$ from the response $Y$, given the projection of…

We consider the problem of conditional independence (CI) testing and adopt a kernel-based approach. Kernel-based CI tests embed variables in reproducing kernel Hilbert spaces, regress their embeddings on the conditioning variables, and test…

The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…

Many relations of scientific interest are nonlinear, and even in linear systems distributions are often non-Gaussian, for example in fMRI BOLD data. A class of search procedures for causal relations in high dimensional data relies on sample…

Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning…

Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with…