Philosophy of using command line is that input and output files are files. Basic Commands: Correct grammar of command is: verb adverb object where adverb is the flag you add to a command e.g -h...
Why do we need Measure Theory
In this post I describe the motivation for why we need to use measure theory in probability. In the ideal case, for some arbitrary sample space $\Omega$ we would like to be able to define a func...
Kernel PCA
In traditional PCA, as shown in my PCA post, we look for a linear subspace to project the data vectors onto orthogonally to provide a low dimensional representation of the data. However, restricti...
PCA - Solution
In a previous post we introduce PCA, and two equivalent objective definitions. In this post we now give the exact solutions to PCA. We saw that the objective can be written as: [\begin{align} \un...
linux aliases
To creata a Linux terminal alias you add the alias to the .bashrc file in your home directory. These are the aliases I am currently using: # custom aliases alias gs='git status' alias pers='cd /...
pandoc md file to pdf
On linux to install pandoc: $ sudo apt install \ pandoc \ texlive-latex-base \ texlive-fonts-recommended \ texlive-extra-utils \ texlive-latex-extra \ texlive-xetex Then ...
PCA - Definitions
In this post I will describe Principal Component Analysis (PCA), and in particular sample PCA. I show that the common definition of PCA can be formulated as finding the “best” low rank approximatio...
Duality
Duality In this document I give the main results for duality in standard optimisation problems. Main references: Convex Optimisation by Boyd and Vandenberghe - Chapter 5 Slides on KKT condit...
Using Overleaf as a Remote Repository
It is possible to set up Overleaf as a remote repository such that you can use it as an interface for a local repository. Then whenever you make a change on Overleaf, and compile, you can run git p...