CMLDA

Repository for the course Computational Mathematics for Learning and Data Analysis.

Installation

These steps are for MacOS, with brew and python3 already installed.

Installing Julia

brew install julia

Installing JupyterLab and IJulia kernel

IJulia kernel

Inside the julia REPL:

using Pkg
Pkg.add("IJulia")

A simple notebook experience can be obtained by simply running noteboot(), which will install in a separate conda environment the needed python packages.

JupyterLab

A separate environment with virtualenv or virtualenvwrapper is recommended.

pip install jupyterlab

Running

To run simply start the notebook with jupyter lab , the julia kernel should be automatically detected.

Project 19 (Non-ML)

Project

In the folder Project there is our implementation for the project.

Project description:

(P) is the linear least squares problem

\min_{w} \lVert \hat{X}w-\hat{y} \rVert

where

\hat{X}= \begin{bmatrix} X^T \newline \lambda I_m \end{bmatrix},\ \ \hat{y} = \begin{bmatrix} y \newline 0 \end{bmatrix},

with X the (tall thin) matrix from the ML-cup dataset by prof. Micheli, \lambda > 0 and y is a random vector.

(A1) is an algorithm of the class of limited-memory quasi-Newton methods.

(A2) is thin QR factorization with Householder reflectors, in the variant where one does not form the matrix Q, but stores the Householder vectors u_k and uses them to perform (implicitly) products with Q and Q^T.

Report

In the folder Report there is the latex project for the report of the project.

Run to compile:

pdflatex  -file-line-error -shell-escape  --synctex=1 -interaction=nonstopmode main.tex
biber main
pdflatex  -file-line-error -shell-escape  --synctex=1 -interaction=nonstopmode main.tex