Related papers: Nonparametric Instrumental Regression via Kernel M…

We investigate nonparametric estimation of sliced inverse regression (SIR) via the $k$-nearest neighbors approach with a kernel. An estimator of the covariance matrix of the conditional expectation of the explanatory random vector given the…

In this paper, we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish…

Semi-implicit variational inference (SIVI) extends traditional variational families with semi-implicit distributions defined in a hierarchical manner. Due to the intractable densities of semi-implicit distributions, classical SIVI often…

In this paper, we study the problem of early stopping for iterative learning algorithms in a reproducing kernel Hilbert space (RKHS) in the nonparametric regression framework. In particular, we work with the gradient descent and (iterative)…

We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function…

Several causal parameters in short panel data models are functionals of a nested nonparametric instrumental variable regression (nested NPIV). Recent examples include mediated, time varying, and long term treatment effects identified using…

Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel…

Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$…

Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…

The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…

This paper studies the challenging problem of estimating causal effects from observational data, in the presence of unobserved confounders. The two-stage least square (TSLS) method and its variants with a standard instrumental variable (IV)…

The endogeneity issue is fundamentally important as many empirical applications may suffer from the omission of explanatory variables, measurement error, or simultaneous causality. Recently, \cite{hllt17} propose a "Deep Instrumental…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…

Instrumental variable (IV) regression can be approached through its formulation in terms of conditional moment restrictions (CMR). Building on variants of the generalized method of moments, most CMR estimators are implicitly based on…

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…

Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…

We consider learning an unknown target function $f_*$ using kernel ridge regression (KRR) given i.i.d. data $(u_i,y_i)$, $i\leq n$, where $u_i \in U$ is a covariate vector and $y_i = f_* (u_i) +\varepsilon_i \in \mathbb{R}$. A recent string…

This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a…

This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function $h_0$ and its functionals. First, we derive sup-norm convergence rates…