Algorithms for Sparsity-Constrained Optimization [Paperback]

This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a greedy algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.

This thesis presents a wholly new technique in the structural analysis of data that uses a greedy algorithm to derive optimal sparse solutions, enabling faster and more accurate results in formerly problematic areas of machine learning and signal processing.

Introduction.- Preliminaries.- Sparsity-Constrained Optimization.- Background.- 1-bit Compressed Sensing.- Estimation Under Model-Based Sparsity.- Projected Gradient Descent for `p-constrained Least Squares.- Conclusion and Future Work.- Appendix A Proofs of Chapter 3.- Appendix B Proofs of Chapter 4.- Appendix C Proofs of Chapter 5.- Appendix D Proofs of Chapter 6.

Dr. Bahmani completed his thesis at Carnegie Mellon University and is currently employed by the Georgia Institute of Technology.This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a greedy algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.

Nominated by Carnegie Mellon University as an outstanding Ph.D. thesis

Provides an new direction of research into problems of extracting structure from data

Advances the science of structure discovery through sparsity

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