## Sticky Post – Read this first. Categories and Links in Mathemafrica

The navigability of Mathemafrica isn't ideal, so I have created this post which might guide you to what you are looking for. Here are a number of different categories of post which you might like to take a look at: First year mathematics notes and resources (particularly for the University [...]

## Covid-19 tests: probabilities

Bayes' Theorem is applied to medical tests, to calculate the probability of being infected with a virus, given a positive or negative test result. What drives the uncertainty is false negative results, or false positive results. In this article, I give a practical outline as to how one can interpret [...]

## A challenging limit

This post comes mostly from the youtube video by BlackPenRedPen found here: https://www.youtube.com/watch?v=89d5f8WUf1Y&t=3s This in turn comes from Brilliant.com - details and links can be found in the original video In this post we will have a look at a complicated-looking limit that has an interesting solution. Here it is: $latex [...]

## Parrondos Paradox

Introduction In this post we will have a look at Parrondos paradox. In a paper* entitled "Information Entropy and Parrondo's Discrete-Time Ratchet"** the authors demonstrate a situation where, by switching between 2 losing strategies, we can create a winning strategy. Setup The setup to this paradox is as follows: We [...]

## Basic Reverse Image Search Using an Autoencoder

Introduction In this post we are going to create a simple reverse image search on the MNIST handwritten image dataset. That is to say, given any image, we want to return images that look most similar to it. To do this, we will use an autoencoder, trained using Tensorflow 2. [...]

## A simple introduction to causal inference

Introduction Causal inference is a branch of Statistics that is increasing in popularity. This is because it allows us to answer questions in a more direct way than do other methods. Usually, we can make inference about association or correlation between a variable and an outcome of interest, but [...]

## Inverse Reinforcement Learning: Guided Cost Learning and Links to Generative Adversarial Networks

Recap In the first post we introduced inverse reinforcement learning, then we stated some result on the characterisation of admissible reward functions (i.e reward functions that solve the inverse reinforcement learning problem), then on the second post we saw a way in which we proceed with solving problems, more or [...]

## Maximum Entropy Inverse Reinforcement Learning: Algorithms and Computation

In the previous post we introduced inverse reinforcement learning. We defined the problem that is associated with this field, which is that of reconstructing a reward function given a set of demonstrations, and we saw what the ability to do this implies. In addition to this, we also saw came [...]

## Inverse Reinforcement Learning: The general basics

Standard Reinforcement Learning The very basic ideas in Reinforcement Learning are usually defined in the context of Markov Decision Processes. For everything that follows, unless stated otherwise, assume that the structures are finite. A Markov Decision Process (MDP) is a tuple $latex (S,A, P, \gamma, R)$ where the following is [...]

## Correlation vs Mutual Information

This post is based on a (very small) part of the (dense and technical) paper Fooled by Correlation by N.N. Taleb, found at (1) Notes on the main ideas in this post are available from Universidad de Cantabria, found at (2) The aims of this post are to 1) introduce mutual [...]

## The Res-Net-NODE Narrative

Humble Beginnings: Ordinary Differential Equations The story begins with differential equations. Consider $latex f$ such that $latex f:[0,T]\times \mathbb{R}^n\to \mathbb{R}^n$ is a continuous function. We can construct a rather simple differential equation given this in the following way. We let $latex \begin{cases} {y'(t)}=f(t,y(t))\\ y(0)=y_0\in \mathbb{R}^n \end{cases} $ A solution to [...]