From bits to information : learning meets compressive sensing

A quantization approach to supervised learning, compressive sensing, and phase retrieval is presented in this thesis. We introduce a set of common techniques that allow us, in those three settings, to represent high dimensional data using the order statistics of linear and non linear measurements. We introduce new algorithms for signals classification in the multiclass and the multimodal settings, as well as algorithms for signals representation and recovery from quantized linear and quadratic measurements. We analyze the statistical consistency of our algorithms and prove their robustness to different sources of perturbation, as well as their computational efficiency. We present and analyze applications of our theoretical results in realistic setups, such as computer vision classification tasks, Audio-Visual Automatic Speech Recognition, lossy image compression and retrieval via locality sensitive hashing, locally linear estimation in large scale learning and Fourier sampling for phase retrieval - of particular interest in X-ray crystallography and super-resolution diffraction imaging applications. Our analysis of quantization based algorithms highlights interesting tradeoffs between memory complexity, sample complexity, and time complexity in algorithms design.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Mroueh, Youssef

Advisor dc:contributor.advisor

• Tomaso Poggio and Lorenzo Rosasco.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/97809

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/97809