The power of randomized algorithms : from numerical linear algebra to biological systems

In this thesis we study simple, randomized algorithms from a dual perspective. The first part of the work considers how randomized methods can be used to accelerate the solution of core problems in numerical linear algebra. In particular, we give a randomized low-rank approximation algorithm for positive semidefinite matrices that runs in sublinear time, significantly improving upon what is possible with traditional deterministic methods. We also discuss lower bounds on low-rank approximation and spectral summarization problems that attempt to explain the importance of randomization and approximation in accelerating linear algebraic computation. The second part of the work considers how the theory of randomized algorithms can be used more generally as a tool to understand how complexity emerges from low-level stochastic behavior in biological systems. We study population density- estimation in ant colonies, which is a key primitive in social decision-making and task allocation. We define a basic computational model and show how agents in this model can estimate their density using a simple random-walk-based algorithm. We also consider simple randomized algorithms for computational primitives in spiking neural networks, focusing on fast winner-take-all networks.

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

2018

Author dc:creator

• Musco, Cameron N. (Cameron Nicholas)

Advisor dc:contributor.advisor

• Nancy A. Lynch.

• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written 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/1721.1/120424

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/120424