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 [...]

By | January 17th, 2018|0 Comments

CRL Task 3: Counterfactual Decision Making

In the previous blog post we discussed some theory of how to select optimal and possibly optimal interventions in a causal framework. For those interested in the decision science, this blog post may be more inspiring. This next task involves applying counterfactual quantities to boost learning performance. This is clearly [...]

By | July 10th, 2021|2 Comments

CRL Task 2: Interventions – When and Where?

In the previous blog post we discussed the gorey details of generalised policy learning - the first task of CRL. We went into some very detailed mathematical description of dynamic treatment regimes and generalised modes of learning for data processing agents. The next task is a bit more conceptual and [...]

By | July 6th, 2021|3 Comments

CRL Task 1: Generalised Policy Learning

In the previous blog post we developed some ideas and theory needed to discuss a causal approach to reinforcement learning. We formalised notions of multi-armed bandits (MABs), Markov Decision Processes (MDPs), and some causal notions. In this blog post we'll finally get to developing some causal reinforcement learning ideas. The [...]

By | July 1st, 2021|3 Comments

Preliminaries for CRL

In the previous blog post we discussed and motivated the need for a causal approach to reinforcement learning. We argued that reinforcement learning naturally falls on the interventional rung of the ladder of causation. In this blog post we'll develop some ideas necessary for understanding the material covered in this [...]

By | April 6th, 2021|5 Comments

Causal Reinforcement Learning: A Primer

As part of any honours degree at the University of Cape Town, one is obliged to write a thesis 'droning' on about some topic. Luckily for me, applied mathematics can pertain to pretty much anything of interest. Lo and behold, my thesis on merging causality and reinforcement learning. This was [...]

By | February 3rd, 2021|4 Comments

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 [...]

By | January 1st, 2021|0 Comments

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 [...]

By | November 29th, 2020|0 Comments

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 [...]

By | November 11th, 2020|0 Comments

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. [...]

By | October 21st, 2020|0 Comments

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 [...]

By | August 20th, 2020|0 Comments
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