2 code implementations • 23 Nov 2021 • Dohyeong Ki, Billy Fang, Adityanand Guntuboyina

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

no code implementations • 7 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.

no code implementations • 3 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).

no code implementations • 21 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 $k \geq 1$.

no code implementations • 4 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.

1 code implementation • 18 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.

Methodology

no code implementations • 6 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.

no code implementations • 17 Sep 2017 • Adityanand Guntuboyina, Bodhisattva Sen

We consider the problem of nonparametric regression under shape constraints.

no code implementations • 19 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.

no code implementations • 15 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

no code implementations • 2 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.

Cannot find the paper you are looking for? You can
Submit a new open access paper.

Contact us on:
hello@paperswithcode.com
.
Papers With Code is a free resource with all data licensed under CC-BY-SA.