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On risk bounds in isotonic and other shape restricted regression problems

- S. Chatterjee, Adityanand Guntuboyina, B. Sen
- Mathematics
- 15 November 2013

We consider the problem of estimating an unknown $\theta\in {\mathbb{R}}^n$ from noisy observations under the constraint that $\theta$ belongs to certain convex polyhedral cones in ${\mathbb{R}}^n$.… Expand

101 12- PDF

Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues

- Nihar B. Shah, Sivaraman Balakrishnan, Adityanand Guntuboyina, M. Wainwright
- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 19 October 2015

TLDR

100 11- PDF

Global risk bounds and adaptation in univariate convex regression

- Adityanand Guntuboyina, B. Sen
- Mathematics
- 7 May 2013

We consider the problem of nonparametric estimation of a convex regression function $$\phi _0$$ϕ0. We study the risk of the least squares estimator (LSE) under the natural squared error loss. We show… Expand

67 10- PDF

On matrix estimation under monotonicity constraints

- S. Chatterjee, Adityanand Guntuboyina, B. Sen
- Mathematics
- 10 June 2015

We consider the problem of estimating an unknown $n_1 \times n_2$ matrix $\mathbf{\theta^*}$ from noisy observations under the constraint that $\mathbf{\theta}^*$ is nondecreasing in both rows and… Expand

47 8- PDF

Covering Numbers for Convex Functions

- Adityanand Guntuboyina, B. Sen
- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 31 March 2012

TLDR

52 7- PDF

Adaptive Risk Bounds in Univariate Total Variation Denoising and Trend Filtering

- Adityanand Guntuboyina, Donovan Lieu, S. Chatterjee, B. Sen
- Mathematics
- 16 February 2017

We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given positive integer $r$, the $r$-th order trend filtering estimator is defined as the minimizer… Expand

37 6- PDF

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

- B. Fang, Adityanand Guntuboyina, B. Sen
- Mathematics
- 4 March 2019

We consider the problem of nonparametric regression when the covariate is $d$-dimensional, where $d \geq 1$. In this paper we introduce and study two nonparametric least squares estimators (LSEs) in… Expand

15 6- PDF

Lower Bounds for the Minimax Risk Using $f$-Divergences, and Applications

- Adityanand Guntuboyina
- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 30 January 2010

TLDR

70 5- PDF

Spatial Adaptation in Trend Filtering

- Adityanand Guntuboyina, Donovan Lieu, S. Chatterjee, B. Sen
- Mathematics
- 20 February 2017

15 4

Concentration of the spectral measure of large Wishart matrices with dependent entries

- Adityanand Guntuboyina, H. Leeb
- Mathematics
- 15 October 2008

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but… Expand

20 4- PDF

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