# Learning Heteroscedastic Models by Convex Programming under Group Sparsity

arXiv: https://arxiv.org/abs/1304.4549 · HTML: https://mlsanity.com/paper/1304.4549/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2013.

## Built on by (most cited first, 3 of 3)

- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Heteroscedasticity-aware residuals-based contextual stochastic optimization](https://mlsanity.com/paper/2101.03139/) (2021)
- [Variance function estimation in regression model via aggregation procedures](https://mlsanity.com/paper/2110.02715/) (2021)

## Abstract (arXiv)

Popular sparse estimation methods based on ℓ1-relaxation, such as the Lasso and the Dantzig selector, require the knowledge of the variance of the noise in order to properly tune the regularization parameter. This constitutes a major obstacle in applying these methods in several frameworks---such as time series, random fields, inverse problems---for which the noise is rarely homoscedastic and its level is hard to know in advance. In this paper, we propose a new approach to the joint estimation of the conditional mean and the conditional variance in a high-dimensional (auto-) regression setting. An attractive feature of the proposed estimator is that it is efficiently computable even for very large scale problems by solving a second-order cone program (SOCP). We present theoretical analysis and numerical results assessing the performance of the proposed procedure.