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Poster
QUIC & DIRTY: A Quadratic Approximation Approach for Dirty Statistical Models
Cho-Jui Hsieh · Inderjit S Dhillon · Pradeep Ravikumar · Stephen Becker · Peder A Olsen

Thu Dec 11 11:00 AM -- 03:00 PM (PST) @ Level 2, room 210D #None

In this paper, we develop a family of algorithms for optimizing "superposition-structured” or “dirty” statistical estimators for high-dimensional problems involving the minimization of the sum of a smooth loss function with a hybrid regularization. Most of the current approaches are first-order methods, including proximal gradient or Alternating Direction Method of Multipliers (ADMM). We propose a new family of second-order methods where we approximate the loss function using quadratic approximation. The superposition structured regularizer then leads to a subproblem that can be efficiently solved by alternating minimization. We propose a general active subspace selection approach to speed up the solver by utilizing the low-dimensional structure given by the regularizers, and provide convergence guarantees for our algorithm. Empirically, we show that our approach is more than 10 times faster than state-of-the-art first-order approaches for the latent variable graphical model selection problems and multi-task learning problems when there is more than one regularizer. For these problems, our approach appears to be the first algorithm that can extend active subspace ideas to multiple regularizers.

Author Information

Cho-Jui Hsieh (UCLA)
Inderjit S Dhillon (UT Austin & Amazon)
Pradeep Ravikumar (Carnegie Mellon University)
Stephen Becker (University of Colorado)
Peder A Olsen (IBM)

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