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2013 NeurIPS NeurIPS 2013

Dirty Statistical Models

Abstract

We provide a unified framework for the high-dimensional analysis of “superposition-structured” or “dirty” statistical models: where the model parameters are a “superposition” of structurally constrained parameters. We allow for any number and types of structures, and any statistical model. We consider the general class of $M$-estimators that minimize the sum of any loss function, and an instance of what we call a “hybrid” regularization, that is the infimal convolution of weighted regularization functions, one for each structural component. We provide corollaries showcasing our unified framework for varied statistical models such as linear regression, multiple regression and principal component analysis, over varied superposition structures.

🌉 Interdisciplinary Bridge - Artificial Intelligence and Mathematics & Optimization

📈 Trend Setter - Regularization

🐣 Hot Topic Early Bird - linear regression

Authors

Eunho Yang, Pradeep K Ravikumar

Topics

Machine Learning > Core Methods > Regression Machine Learning > Optimization & Theory > Optimization Machine Learning > Optimization & Theory > Statistical Learning Mathematics & Optimization > Mathematics > Statistics Mathematics & Optimization > Optimization > Continuous Optimization Machine Learning > Core Methods > Feature Selection Machine Learning > Learning Types > Multi-Task Learning Machine Learning > Core Methods > Feature Learning Mathematics & Optimization > Optimization > Sparse Optimization Machine Learning > Optimization & Theory > Sparse Optimization Machine Learning > Core Methods > Structured Prediction Machine Learning > Learning Types > Regularization Machine Learning > Learning Types > Sparse Learning Deep Learning > Optimization & Theory > Regularization

Keywords

statistical learning regularization convex optimization principal component analysis feature selection sparse estimation high-dimensional statistics multi-task feature learning high-dimensional analysis linear regression sparse optimization m-estimators superposition structure sparse model hybrid regularization

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