Related papers: On the robustness of kernel-based pairwise learnin…

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…

Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semiparametric efficiency theory for more…

We propose a framework for determining whether the causal dependence of an outcome $Y$ on a covariate $X$ changes at a given time point, given confounders $\boldsymbol{Z}$. For instance, in financial markets, the effect of a market…

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…

We consider kernel based learning methods for regression and analyze what happens to the risk minimizer when new variables, statistically independent of input and target variables, are added to the set of input variables; this problem…

The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…

Regularized pairwise ranking with Gaussian kernels is one of the cutting-edge learning algorithms. Despite a wide range of applications, a rigorous theoretical demonstration still lacks to support the performance of such ranking estimators.…

The robust detection of statistical dependencies between the components of a complex system is a key step in gaining a network-based understanding of the system. Because of their simplicity and low computation cost, pairwise statistics are…

We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…

The literature on provable robustness in machine learning has primarily focused on static prediction problems, such as image classification, in which input samples are assumed to be independent and model performance is measured as an…

Despite the ubiquity of kernel-based clustering, surprisingly few statistical guarantees exist beyond settings that consider strong structural assumptions on the data generation process. In this work, we take a step towards bridging this…

Pairwise learning or dyadic prediction concerns the prediction of properties for pairs of objects. It can be seen as an umbrella covering various machine learning problems such as matrix completion, collaborative filtering, multi-task…

The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are…

A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to…

In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables $X$ and $Y$ taking values in general topological spaces. These nonparametric measures -- defined…

In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…

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…

Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine…