141 citations · 297 across the 30 of their papers we have counts for
28 papers · 1 filter
What Functions Does XGBoost Learn?
Dohyeong Ki, Adityanand Guntuboyina
This paper establishes a rigorous theoretical foundation for the function class implicitly learned by XGBoost, bridging the gap between its empirical success and our theoretical un…
Totally Concave Regression
Dohyeong Ki, Adityanand Guntuboyina
Shape constraints in nonparametric regression provide a powerful framework for estimating regression functions under realistic assumptions without tuning parameters. However, most…
Convergence rates for estimating multivariate scale mixtures of uniform densities
Arlene K. H. Kim, Gil Kur, Adityanand Guntuboyina
The Grenander estimator is a well-studied procedure for univariate nonparametric density estimation. It is usually defined as the Maximum Likelihood Estimator (MLE) over the class…
MARS via LASSO
Dohyeong Ki, Billy Fang, Adityanand Guntuboyina
Multivariate adaptive regression splines (MARS) is a popular method for nonparametric regression introduced by Friedman in 1991. MARS fits simple nonlinear and non-additive functio…
Multivariate, Heteroscedastic Empirical Bayes via Nonparametric Maximum Likelihood
Jake A. Soloff, Adityanand Guntuboyina, Bodhisattva Sen
Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametri…
Minimax bounds for estimating multivariate Gaussian location mixtures
Arlene K. H. Kim, Adityanand Guntuboyina
We prove minimax bounds for estimating Gaussian location mixtures on under the squared and the squared Hellinger loss functions. Under the squared loss,…
Covariance estimation with nonnegative partial correlations
Jake A. Soloff, Adityanand Guntuboyina, Michael I. Jordan
We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estima…
On Suboptimality of Least Squares with Application to Estimation of Convex Bodies
Gil Kur, Alexander Rakhlin, Adityanand Guntuboyina
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application,…
Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators
Gil Kur, Fuchang Gao, Adityanand Guntuboyina +1
Under the usual nonparametric regression model with Gaussian errors, Least Squares Estimators (LSEs) over natural subclasses of convex functions are shown to be suboptimal for esti…
Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation
Billy Fang, Adityanand Guntuboyina, Bodhisattva Sen
We consider the problem of nonparametric regression when the covariate is -dimensional, where . In this paper we introduce and study two nonparametric least squares es…
Distribution-free properties of isotonic regression
Jake A. Soloff, Adityanand Guntuboyina, Jim Pitman
It is well known that the isotonic least squares estimator is characterized as the derivative of the greatest convex minorant of a random walk. Provided the walk has exchangeable i…
Adaptation in multivariate log-concave density estimation
Oliver Y. Feng, Adityanand Guntuboyina, Arlene K. H. Kim +1
We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities. The first consists of densities with…
On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoising
Sujayam Saha, Adityanand Guntuboyina
We study the Nonparametric Maximum Likelihood Estimator (NPMLE) for estimating Gaussian location mixture densities in -dimensions from independent observations. Unlike usual lik…
Nonparametric Shape-restricted Regression
Adityanand Guntuboyina, Bodhisattva Sen
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regr…
On the risk of convex-constrained least squares estimators under misspecification
Billy Fang, Adityanand Guntuboyina
We consider the problem of estimating the mean of a noisy vector. When the mean lies in a convex constraint set, the least squares projection of the random vector onto the set is a…
The geometry of hypothesis testing over convex cones: Generalized likelihood tests and minimax radii
Yuting Wei, Martin J. Wainwright, Adityanand Guntuboyina
We consider a compound testing problem within the Gaussian sequence model in which the null and alternative are specified by a pair of closed, convex cones. Such cone testing probl…
A note on the approximate admissibility of regularized estimators in the Gaussian sequence model
Xi Chen, Adityanand Guntuboyina, Yuchen Zhang
We study the problem of estimating an unknown vector from an observation drawn according to the normal distribution with mean and identity covariance matrix under the k…
Adaptive Risk Bounds in Univariate Total Variation Denoising and Trend Filtering
Adityanand Guntuboyina, Donovan Lieu, Sabyasachi Chatterjee +1
We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given positive integer , the -th order trend filtering estimator is define…
Adaptation in log-concave density estimation
Arlene K. H. Kim, Adityanand Guntuboyina, Richard J. Samworth
The log-concave maximum likelihood estimator of a density on the real line based on a sample of size is known to attain the minimax optimal rate of convergence of …
Adaptive estimation of planar convex sets
Tony Cai, Adityanand Guntuboyina, Yuting Wei
In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estim…
On matrix estimation under monotonicity constraints
Sabyasachi Chatterjee, Adityanand Guntuboyina, Bodhisattva Sen
We consider the problem of estimating an unknown matrix from noisy observations under the constraint that is nondecreasing in both rows…
On Bayes Risk Lower Bounds
Xi Chen, Adityanand Guntuboyina, Yuchen Zhang
This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A low…
On risk bounds in isotonic and other shape restricted regression problems
Sabyasachi Chatterjee, Adityanand Guntuboyina, Bodhisattva Sen
We consider the problem of estimating an unknown from noisy observations under the constraint that belongs to certain convex polyhedral cones in ${\mathbb…
Global risk bounds and adaptation in univariate convex regression
Adityanand Guntuboyina, Bodhisattva Sen
We consider the problem of nonparametric estimation of a convex regression function . We study the risk of the least squares estimator (LSE) under the natural squared error lo…