2012/05/21 by Mladen Kolar, Kolar, Mladen, James Sharpnack +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #stat.ME #stat.ML
paper · pdf · doi:10.48550/arxiv.1205.4770
Appearing in Proceedings of the 29 th International Conference on Machine Learning, Edinburgh, Scotland, UK, 2012
arxiv created 2012/05/21 · openalex publication_date 2012/05/21 · arxiv updated 2012/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the high-dimensional heteroscedastic regression model, where the mean and the log variance are modeled as a linear combination of input variables. Existing literature on high-dimensional linear regres- sion models has largely ignored non-constant error variances, even though they commonly occur in a variety of applications ranging from biostatis- tics to finance. In this paper we study a class of non-convex penalized pseudolikelihood estimators for both the mean and variance parameters. We show that the Heteroscedastic Iterative Penalized Pseudolikelihood Optimizer (HIPPO) achieves the oracle property, that is, we prove that the rates of convergence are the same as if the true model was known. We demonstrate numerical properties of the procedure on a simulation study and real world data.