MathsToML

Perpetual Children

2024-12-22 00:00 | 2 minute read

Image by Vivek Kumar The Question A couple chooses to keep having children till they have an equal number of boys and girls. How many children will they have on average? In this article we will cover 2 ways to solve this problem. First using a random walk and proof by contradiction. The second is Optiver’s solution to this problem. Solution 1 Let $X_t$ denote the random variable for which child has been born at time $t$.

Some Questions in Probability I

2024-12-21 00:00 | 4 minute read

Image by Cameron Cress The Drunkard Suppose someone has had a heavy evening in the pub and upon leaving the pub they have somehow ended up by the side of a cliff. Since he has one a one too many drinks he can’t walk well and they now has 1/3 probability to walk off the edge of the cliff or 2/3 probability to take a step backwards. What is the probability that he will eventually fall off the edge of the cliff?

GAMs

2024-12-18 00:00 | 9 minute read

Image by Anh Vy. In this article we will cover Generalised Additive Models (GAMs). We’ll cover the base case by modelling a response variable with a univariate smooth function. We’ll then build on this by incorporating multiple exogenous variables to create additive models. After then, the GAM can be covered. For more details about this methods please read the book by Simon N. Wood about Generalised Additive Models. GAMs GAMS: GAMs are a form of generalised linear models with linear response variables that depend on unknown smooth functions of some exogenous variables. These forms of models were initially developed to blend the properties of Generalised Linear Models (GLMs) with additive models.

Docker

2024-11-01 00:00 | 8 minute read

Image by Will Turner In this article, we will cover what containerisation means and we look at Docker, a containerisation platform. Furthermore, we will cover the key commands and concepts needed to create your own containers in docker. What is Docker? Docker is an open-source software platform that assists the deployment of applications. It does this by creating standardized units called containers which are isolated environments containing the application code, runtime, libraries, and any dependencies. These containers are a type of virtual machine that has an OS but does not simulate the entire computer. It is like a sandboxed environment.

Martingale Theory

2024-11-01 00:00 | 10 minute read

Image by sq lim Today’s article will look at one of the more difficult areas in probability called martingale theory. We will cover the basic theory and look at 2 examples which use martingale theory (the drunk man and the ABRACADABRA problem). The Theory Before jumping into the problem, we have to cover some of the theory behind martingales. It is important to mention we will be skipping over many of the measure theory definitions and theorems. These will be covered at a later time. If you wish to read up more about this area of mathematics, I’d recommend reading the paper by T. Smith here. This paper was the basis for this article [1].

Non-Convex Optimisation Learning Rate Scheduling

2024-11-01 00:00 | 6 minute read

Image by Joshua Sukoff One of the most crucial hyperparameters in any machine learning (ML) model is the learning rate. A small learning rate often results in longer training times and can lead to overfitting. Conversely, a large learning rate may accelerate initial training but risks hindering the model’s convergence to the global minimum and can even cause divergence. Therefore, selecting the appropriate learning rate is a critical step in training any ML model.

The Ant Problem

2024-11-01 00:00 | 6 minute read

Image by mi_shots Today we’ll be looking at a classic problem in probability: “The Ant Problem”. The Question: An ant leaves its anthill in order to forage for food. It moves with the speed of 10cm per second, but it doesn’t know where to go, therefore every second it moves randomly 10cm directly north, south, east or west with equal probability. a) If the food is located on east-west lines 20cm to the north and 20cm to the south, as well as on north-south lines 20cm to the east and 20cm to the west from the anthill, how long will it take the ant to reach it on average?

Rest APIs

2024-10-30 00:00 | 7 minute read

Image by Ante Hamersmit What are APIs Before we just into the class of Rest APIs it is best to understand what is an API. An API is simply an acronym for application programming interface, a software intermediary that allows two applications to talk to each other. They are usually explained in terms of a client and a server. The application that sends a request is called the client and the application that sends the response is called the server.

ARMA & ARIMA

2024-10-05 00:00 | 10 minute read

Image by Elijah Grimm In this article we will cover the ARMA and ARIMA based statistical models, cover the maths behind these models, and look at the statistical test required prior and the post the model fitting. I’d recommend reading the previous article here before reading the remainder of this article. In that article we cover the basics of what is a time series and how we could model it. Definitions: Recall from our previous article that given a sequence of data points $\{ X_{t}, t \in \mathbb{Z} \}$, the sequence is strongly stationary or strictly stationary if

What is a Time Series & How can we Model it?

2024-10-05 00:00 | 9 minute read

Image by Oğuzhan Kıran This article will cover what is a time series, what does it mean for a time series to be stationary, and how could an autoregressive process or moving average process be used to model the time series. Before starting this article, I would like to mention the Cambridge notes from here form the foundation of this content. What is a Time Series? In short, time series is area of statistics which focuses on describing a set of data points which are collected on regular intervals by fitting low-dimensional models and making forecasts.