2017/05/30 by Qilong Gu, Arindam Banerjee, Gu, Qilong +1
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1705.10886
openalex publication_date 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models which allow sum of any number of component parameters, and each component structure can be characterized by any norm. We present a simple estimator for such models, give a geometric condition under which the components can be accurately estimated, characterize sample complexity of the estimator, and give high probability non-asymptotic bounds on the componentwise estimation error. We use tools from empirical processes and generic chaining for the statistical analysis, and our results, which substantially generalize prior work on superposition models, are in terms of Gaussian widths of suitable sets.