Day 12, Thursday, Mar 8, 2018

Fitting a linear model to data, cont'd

Pointwise errors ei = αxi + β − yi

Some freedom in defining overall error E in terms of pointwise errors {ei}

We found a formula the line that minimizes the choice E = ni = 1e2i

argmin(α, β) ∈ ℝ2 E

Quiz 6

Examples of minimizer of E = ni = 1|ei|

How to find best (α, β) for other choices?

Brute force?

Random choices of (α, β)

Grid of points (α, β) (harder!)

Advanced numpy

Numpy broadcasting




Setting the seed in numpy.random

Reproducibility of random results with numpy.random.seed()

My conjecture: a line containing 2 of the data points is in argmin E when we choose E = ni = 1|ei|. (If true, this narrows down the possibilities to a finite set.)

Color maps


More efficient finding of minimizer?

Stagger downhill?

Project 3

A comparative study of several definitions of badness of fit of a linear function to data {(xi, yi) ∈ ℝ2 : i ∈ {1, 2, ..., n}}

Looking for best-fit line according to several definitions of error for a variety of data sets (large/small, regular/irregular), and your own personal value judgments based on the examples you present.