2017/02/10 by Tung Duy Luu, Luu, Tung Duy, Jalal Fadili +3
Computer Science · Mathematics · #62G07 #62G20 #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic Gradient Optimization Techniques
paper · doi:10.48550/arxiv.1702.03166
openalex publication_date 2017/02/10 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
In this paper,we consider a high-dimensional statistical estimation problem in which the the number of parameters is comparable or larger than the sample size. We present a unified analysis of the performance guarantees of exponential weighted aggregation and penalized estimators with a general class of data losses and priors which encourage objects which conform to some notion of simplicity/complexity. More precisely, we show that these two estimators satisfy sharp oracle inequalities for prediction ensuring their good theoretical performances. We also highlight the differences between them. When the noise is random, we provide oracle inequalities in probability using concentration inequalities. These results are then applied to several instances including the Lasso, the group Lasso, their analysis-type counterparts, the ℓ_∞ and the nuclear norm penalties. All our estimators can be efficiently implemented using proximal splitting algorithms.