Search Results for author: Adityanand Guntuboyina

Found 11 papers, 2 papers with code


2 code implementations23 Nov 2021 Dohyeong Ki, Billy Fang, Adityanand Guntuboyina

MARS fits simple nonlinear and non-additive functions to regression data.


On Suboptimality of Least Squares with Application to Estimation of Convex Bodies

no code implementations7 Jun 2020 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.

Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators

no code implementations3 Jun 2020 Gil Kur, Fuchang Gao, Adityanand Guntuboyina, Bodhisattva Sen

The least squares estimator (LSE) is shown to be suboptimal in squared error loss in the usual nonparametric regression model with Gaussian errors for $d \geq 5$ for each of the following families of functions: (i) convex functions supported on a polytope (in fixed design), (ii) bounded convex functions supported on a polytope (in random design), and (iii) convex Lipschitz functions supported on any convex domain (in random design).


Max-Affine Regression: Provable, Tractable, and Near-Optimal Statistical Estimation

no code implementations21 Jun 2019 Avishek Ghosh, Ashwin Pananjady, Adityanand Guntuboyina, Kannan Ramchandran

Max-affine regression refers to a model where the unknown regression function is modeled as a maximum of $k$ unknown affine functions for a fixed $k \geq 1$.

regression Retrieval

Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation

no code implementations4 Mar 2019 Billy Fang, Adityanand Guntuboyina, Bodhisattva Sen

We show that the finite sample risk of these LSEs is always bounded from above by $n^{-2/3}$ modulo logarithmic factors depending on $d$; thus these nonparametric LSEs avoid the curse of dimensionality to some extent.

Denoising regression

Two-component Mixture Model in the Presence of Covariates

1 code implementation18 Oct 2018 Nabarun Deb, Sujayam Saha, Adityanand Guntuboyina, Bodhisattva Sen

We propose a tuning parameter-free nonparametric maximum likelihood approach, implementable via the EM algorithm, to estimate the unknown parameters.


On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoising

no code implementations6 Dec 2017 Sujayam Saha, Adityanand Guntuboyina

We study the Nonparametric Maximum Likelihood Estimator (NPMLE) for estimating Gaussian location mixture densities in $d$-dimensions from independent observations.

Clustering Denoising

Nonparametric Shape-restricted Regression

no code implementations17 Sep 2017 Adityanand Guntuboyina, Bodhisattva Sen

We consider the problem of nonparametric regression under shape constraints.


Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues

no code implementations19 Oct 2015 Nihar B. Shah, Sivaraman Balakrishnan, Adityanand Guntuboyina, Martin J. Wainwright

On the other hand, unlike in the BTL and Thurstone models, computing the minimax-optimal estimator in the stochastically transitive model is non-trivial, and we explore various computationally tractable alternatives.

Adaptive estimation of planar convex sets

no code implementations15 Aug 2015 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.

Statistics Theory Statistics Theory

Sharp Inequalities for $f$-divergences

no code implementations2 Feb 2013 Adityanand Guntuboyina, Sujayam Saha, Geoffrey Schiebinger

$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc.

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