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We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…
The Na\"ive Mean Field (NMF) approximation is widely employed in modern Machine Learning due to the huge computational gains it bestows on the statistician. Despite its popularity in practice, theoretical guarantees for high-dimensional…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
We consider the problem of inference for projection parameters in linear regression with increasing dimensions. This problem has been studied under a variety of assumptions in the literature. The classical asymptotic normality result for…
We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…
A variety of interesting parameters may depend on high dimensional regressions. Machine learning can be used to estimate such parameters. However estimators based on machine learners can be severely biased by regularization and/or model…
The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of…
Kernel ridge regression (KRR) is a popular class of machine learning models that has become an important tool for understanding deep learning. Much of the focus thus far has been on studying the proportional asymptotic regime, $n \asymp d$,…
We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…
We derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method. We develop a novel…
We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimation error under the Dudley distance between the latent joint distribution and the data joint distribution with appropriately specified architecture of the neural…
This paper introduces a local linear smoother for regression surfaces on the simplex. The estimator solves a least-squares regression problem weighted by a locally adaptive Dirichlet kernel, ensuring good boundary properties. Asymptotic…
We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…
Inspired by logistic regression, we introduce a regression model for data tuples consisting of a binary response and a set of covariates residing in a metric space without vector structures. Based on the proposed model we also develop a…
In this paper, we provide a precise characterization of generalization properties of high dimensional kernel ridge regression across the under- and over-parameterized regimes, depending on whether the number of training data n exceeds the…
The nonparametric estimation of integrated diffusion processes has been extensively studied, with most existing research focusing on pointwise convergence. This paper is the first to establish uniform convergence rates for the…
Nonstationary high-dimensional time series are increasingly encountered in biomedical research as measurement technologies advance. Owing to the homeostatic nature of physiological systems, such datasets are often located on, or can be well…
We present a non-asymptotic lower bound on the eigenspectrum of the design matrix generated by any linear bandit algorithm with sub-linear regret when the action set has well-behaved curvature. Specifically, we show that the minimum…
In this paper, we prove the long neck principle, band width estimates, and width inequalities of the geodesic collar neighborhoods of the boundary in the setting of general initial data sets for the Einstein equations, subject to certain…