Posts

Introduction In indoor sport climbing different routes to the top of the wall are put up by different route setters who are also given the task of awarding each climb a ‘grade’.

Introduction I recently wanted to port some python code to c++ (latency reasons) and I quickly realised it was not going to be a trivial port. It required some template metaprogramming trickery and in the process I found myself writing my first c++ concept 1.

Count data is commonly modelled using a generalised linear model with a Poisson likelihood, and this approach extends trivially to cases with multiple count data random variables, $Z_i\in {\mathbb{Z}}^{0+},i=1\dots N$ which are indepedent of one another, $Z_i\perp Z_j,\mathrm{\forall }i,j$ because the likelihoods factor out nicely.

This is an example from chapter 5 (‘Basis Expansions and Regularisation’) of the excellent Elements of Statistical Learning book 1. It’s section 5.2.3 - ‘Phoneme Recognition’. The dataset 2 contains 1717 examples of periodogram data for different test subjects saying the letter combinations such as “ao” and “aa”.

Introduction I play a bit of chess and enjoy solving chess problems, so when someone showed me this problem writen by the chess grandmaster Ben Finegold 1 I first had a go at solving it (manually) and then wondered if I could phrase it as a mixed integer programming (MIP) problem.

pytest is a very useful tool for writing and running python tests. I’ve used it extensively over the past 10 or so years and I really like it. In my opinion there are some less good features about it such as the slightly less-than-transparent importing of things from conftest but in general it’s an excellent package.

Introduction Time series data is very common. The obvious way such data arises is when measurements of a quantity (quantities) are taken repeatedly over time, leading to scalar (vector) timeseries. But another interesting example comes when working with event-driven software architectures.

Introduction In my last post about quantile regression post 1 I touched briefly about least absolute derivation (LAD) regression in order to motivate the pinball loss functioin, but LAD regression is interesting in it’s own right.

Introduction Given some covariates, $X$, and a dependent variable, $y$, ordinary least squares regression (OLS) provides a value for the expectated value $\mathbb{E}[Y|X]$ but this is not always sufficient. Often we want to know more about the full conditional distribution, $y|x$.

Introduction Mixed integer linear programmes (MIP) are applicable to an amazingly wide range of problems but I’d never considered that you could use them to discover how, given some sort of flow data going into, and out of a set of nodes, MIP could be used to desribe how a series of nodes are interconnected.

Introduction This is a follow up to part 1 1 in which we went through the theory required for the Expectation-Maximisation alogorithm and applied it to fit a gaussian mixture model.

When given the task of estimating the density of some simple dataset with a unique mode we can choose a family of distributions (e.g. Normal, t-distribution, etc.) and use Maximum Likelihood Estimation to find the parameters which best describe our data.