SPARSITY IN HIGH DIMENSIONS

I have also started working on  high-dimensional prediction and estimation problems,usually referred to as the large p, small n paradigm, p being the dimension of the model and n the sample size. With the advent of modern scientific technology like microarrays and fMRI machines such high dimensional data have become quite common and pose a challenge to the conventional machine learning/statistical inference techniques. In high dimensional scenarios it is desirable to obtain sparse solutions. A sparse solution generally helps in better interpretation of the model and more importantly leads to better generalization on unseen data. I developed two different techniques to achieve sparsity in high dimensional scenarios--one is via a mixture prior and another via a mixture loss function. Both these methods are developed in the empirical Bayesian framework which combines both frequentist and Bayesian ideas. I have been doing this line of research in collaboration with Dr. Linda Zhao at the department of statistics at University of Pennsylvania.  

PUBLICATIONS

Empirical bayesian thresholding for sparse signals using mixture loss functions Vikas C. Raykar, and Linda H. Zhao To appear in Statistica Sinica [preprint] 

Nonparametric prior for adaptive sparsity Vikas C. Raykar and Linda H. Zhao, Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics (AISTATS) 2010, JMLR: W&CP 9, pp.629-636, Chia Laguna, Sardinia, Italy, May 13-15, 2010 [abstract] [paper] [slides] [bib]

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