Wordle is a daily word puzzle that’s taken the internet by storm: if you want to get some assistance to solve the viral online game, even in hard mode and with any (also future) word lists, read on! There’s a new five-letter word every day that you get ... [Read more...]

With COVID-19 after the vaccination is before the vaccination. Now that most people in the developed countries have been vaccinated the question arises of how much boost is in the booster shot. We are here to help you understand the real power (or lack thereof) of the booster, so read ... [Read more...]

The following puzzle is a well-known meme in social networks. It is said to have been invented by young Einstein and back in the days I was ambitious enough to solve it by hand (you should try too!). Yet, even simpler is to use Constraint Programming (CP). An excellent choice ... [Read more...]

Over one billion dollars have been spent in the US to split up big schools into smaller ones because small schools regularly show up in rankings as top performers. In this post, I will show you why that money was wasted because of a widespread (but not so well known) ... [Read more...]

One of the most fiercely fought debates in quantitative finance is whether the stock market (or financial markets in general) is (are) efficient, i.e. whether you can find patterns in them that can be profitably used. If you want to learn about an ingenious method (that is already present ... [Read more...]

What is the “opposite” of sampling without replacement? In a classical urn model sampling without replacement means that you don’t replace the ball that you have drawn. Therefore the probability of drawing that colour becomes smaller. How about the opposite, i.e. that the probability becomes bigger? Then you ... [Read more...]

The Bundesliga is Germany’s primary football league. It is one of the most important football leagues in the world, broadcast on television in over 200 countries. If you want to get your hands on a tool to forecast the result of any game (and perform some more statistical analyses), read ... [Read more...]

In view of the current dramatic events in Afghanistan many wonder why the extensive international efforts to bring some stability to the country have failed so miserably. In this post, we will present and analytically examine a fascinating theory that seems to be able to explain political (in-)stability almost ... [Read more...]

Over the course of the last two and a half years, I have written over one hundred posts for my blog “Learning Machines” on the topics of data science, i.e. statistics, artificial intelligence, machine learning, and deep learning. I use many of those in my university classes and in ... [Read more...]

Everybody is talking about big data but the real skill lies in the art of inferring useful information from only a handful of values! If you want to learn how to determine the range of the typical value of a dataset (i.e. the median) with just five values and ... [Read more...]

In this post, we will first give some intuition for and then demonstrate what is often called the most beautiful formula in mathematics, Euler’s identity, in R – first numerically with base R and then also symbolically, so read on! Euler’s identity (also known as Euler’s equation) is ... [Read more...]

One of the big sensations of the UEFA Euro 2020 is that Switzerland kicked out world champion France. We take this as an opportunity to share with you a simple statistical model to predict football (soccer) results with R, so read on! Football is a highly stochastic game, which is one ... [Read more...]

This time we want to solve the following simple task with R: Take the numbers 1 to 100, square them, and add all the even numbers while subtracting the odd ones! If you want to see how to do that in at least seven different ways in R, read on! There are ... [Read more...]

More and more decisions by banks on who gets a loan are being made by artificial intelligence. The terms being used are credit scoring and credit decisioning. They base their decisions on models whether the customer will pay back the loan or will default, i.e. determine their creditworthiness. If ... [Read more...]

Not many people understand the financial alchemy of modern financial investment vehicles, like hedge funds, that often use sophisticated trading strategies. But everybody understands the meaning of rising and falling markets. Why not simply translate one into the other? If you want to get your hands on a simple R ... [Read more...]

Public-key cryptography is one of the foundations of our modern digital life. Normally it is quite hard to understand but with our literally colourful explanation it is a walk in the park. At the end we also give the nerd version, so read on! One problem with cryptography is that ... [Read more...]

A short one for today: in this post we will learn how to easily create truth tables with R and will contribute our code to the growing repository of Rosetta code. I hope that you will learn a few tricks along the way, so read on! We have covered bits ... [Read more...]

I sometimes joke that as an Aries I don’t believe in zodiac signs. But could there still be some pattern, e.g. in the sense that people born in spring are more prone to success than those born during the winter months? In this post, we will provide a ... [Read more...]

This is our 101’st blog post here on Learning Machines and we have prepared something very special for you! Oftentimes the different concepts of data science, namely artificial intelligence (AI), machine learning (ML), and deep learning (DL) are confused… so we asked the most advanced AI in the world, OpenAI ... [Read more...]

My father-in-law used to write down the numbers drawn on the lottery to find patterns, especially whether some numbers were “due” because they hadn’t been drawn for a long time. He is not alone! And don’t they have a point? Shouldn’t the numbers balance after some time? ... [Read more...]