Related papers: Kernel Methods for Causal Functions: Dose, Heterog…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and commonly used in nonparametric…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
General predictive models do not provide a measure of confidence in predictions without Bayesian assumptions. A way to circumvent potential restrictions is to use conformal methods for constructing non-parametric confidence regions, that…
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…
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…
This paper derives limit properties of nonparametric kernel regression estimators without requiring existence of density for regressors in $\mathbb{R}^{q}.$ In functional regression limit properties are established for multivariate…
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with…
Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article…
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…
Learning causal relationships is a fundamental problem in science. Anchor regression has been developed to address this problem for a large class of causal graphical models, though the relationships between the variables are assumed to be…
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…
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…
Marginal structural models have been widely used in causal inference to estimate mean outcomes under either a static or a prespecified set of treatment decision rules. This approach requires imposing a working model for the mean outcome…
Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits…
We propose a new estimation method for heterogeneous causal effects which utilizes a regression discontinuity (RD) design for multiple datasets with different thresholds. The standard RD design is frequently used in applied researches, but…
We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, this problem is reformulated as an unsupervised learning task…
We develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures…
In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…
The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset…