Subgradient and Sampling Algorithms for `l_1` Regression

Ken Clarkson

Bell Labs

`l_1` Regression: Points and Lines

sum= 0 rms= 0

`l_1` Regression: Matrices and Vectors

Who cares?

l_1 green, l_2 red sum= 0 rms= 0

Previous Results

New Results

Overview of Algorithms

Elementary Column Operations

Conditioning `A`

Conditioning `A`, Motivation

Conditioning `A`, in more detail

Overview of Algorithms, again


Subgradient Descent Method

Subgradient Method: Stepsize

Subgradients Animation

sum= 0 rms= 0

How good is the subgradient?

Subgradient Method: Using conditioning

Using the Subgradient

Sampling Algorithm: Preprocessing

Sampling and Solving

Sampling Algorithm: Why it works

Bernstein Bounds

Coresets (motivation)

Coresets: uses