Date of Award

Spring 5-29-2024

Document Type

Thesis (Undergraduate)

Department

Computer Science

First Advisor

Amit Chakrabarti

Abstract

In this work, we wish to investigate the following situation: suppose we are in an underconstrained linear system where observations are constant but predictors are streaming in. That is, the number of predictors—and therefore the dimensionality of our solution—is changing. How hard is it for a streaming algorithm to maintain the ”size” or norm of the solution if we are constrained in space? More informally, can we keep track of the norm of the solution as new data is streaming in without naively memorizing all data and computing the solution directly? We first show a lower bound that any streaming algorithm which returns the minimum l0 norm must use at least linear space. We then follow this up with a streaming algorithm that can return the minimum l2 norm in sublinear space when the system is highly underconstrained.

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