Related papers: Sequential Kernel Embedding for Mediated and Time-…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…

In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…

We study the problem of estimating the effect function for a continuous treatment, which maps each treatment value to a population-averaged outcome. A central challenge in this setting is confounding: treatment assignment often depends on…

We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…

A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…

Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…

We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…

Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which…

Kernel conditional mean embeddings (CMEs) offer a powerful framework for representing conditional distribution, but they often face scalability and expressiveness challenges. In this work, we propose a new method that effectively combines…

Time series are an interesting frontier for kernel-based methods, for the simple reason that there is no kernel designed to represent them and their unique characteristics in full generality. Existing sequential kernels ignore the time…

We propose a nonparametric bivariate time-varying coefficient model for longitudinal measurements with the occurrence of a terminal event that is subject to right censoring. The time-varying coefficients capture the longitudinal…

An essential goal of program evaluation and scientific research is the investigation of causal mechanisms. Over the past several decades, causal mediation analysis has been used in medical and social sciences to decompose the treatment…

We consider the problem of estimating a dose-response curve. Continuous treatments arise often in practice, e.g. in the form of time spent on an operation, distance traveled to a location or dosage of a drug. Letting $A$ denote a continuous…

Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

Kernel methods have been extensively utilized in machine learning for classification and prediction tasks due to their ability to capture complex non-linear data patterns. However, single kernel approaches are inherently limited, as they…

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…