A while ago, I heard an episode of Freakonomics Radio which discussed games and strategies for playing them. It stuck to pretty simple games, so there were no excursions into game theory or such, but the part about Hangman caught my interest. Discussions in that part largely amounted to the use of conditional probability – since you know something about the word you’re trying to guess, you might be able to come up with a better strategy than blind guessing or just guessing based on the frequency of letters in the English language.

Code for this was written in Python.

Partial regression plots – also called added variable plots, among other things – are a type of diagnostic plot for multivariate linear regression models. More specifically, they attempt to show the effect of adding a new variable to an existing model by controlling for the effect of the predictors already in use. They’re useful for spotting points with high influence or leverage, as well as seeing the partial correlation between the response and the new predictor.

This post is meant as a short tutorial on how to set up PySpark to access a MySQL database and run a quick machine learning algorithm with it. Both PySpark and MySQL are locally installed onto a computer running Kubuntu 20.04 in this example, so this can be done without any external resources.

There are plenty of methods to choose from for classification problems, all with their own strengths and weaknesses. This post will try to compare three of the more basic ones: linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and logistic regression.

Benford’s law is the tendency for small digits to be more common than large ones when looking at the first non-zero digits in a large, heterogenous collection of numbers. These frequencies range from about 30% for a leading 1 down to about 4.6% for a leading 9, as opposed to the constant 11.1% you would get if they all appeared at the same rate.

Since I recently wrote about unpacking the pages from a dump of the English Wikipedia, I thought would see if Benford’s law manifested in the text of Wikipedia, as it seems like it fits the idea of a “large, heterogenous collection of numbers” quite well.

The notebook containing the full code is here.

The t-test is a common, reliable way to check for differences between two samples. When dealing with multivariate data, one can simply run t-tests on each variable and see if there are differences. This could lead to scenarios where individual t-tests suggest that there is no difference, although looking at all variables jointly will show a difference. When a multivariate test is preferred, the obvious choice is the Hotelling’s \(T^2\) test.

Hotelling’s test has the same overall flexibility that the t-test does, in that it can also work on paired data, or even a single dataset, though this example will only cover the two-sample case.

If you want a large amount of text data, it’s hard to beat the dump of the English Wikipedia. Even when compressed, the text-only dumps will take up close to 20 gigabytes, and it’ll expand by a factor of 5 to 10 when uncompressed. Effectively handling all of this data can be done on a personal machine, though, due to a combination of two factors – the fact that you can access the data without decompressing it, thanks to the properties of BZ2 files, and the fact that it’s stored as XML data.

I’m going to focus purely on accessing the contents of the pages contained in the September 1, 2020 dump, not any of the multitude of supporting files that come with each dump, including – and especially – the complete page edit histories for each page, which are nearly a terabyte even while compressed. More complete information is on Wikipedia itself, with this page being a good starting point.

When trying to look at examples of LSTMs in Keras, I’ve found a lot that focus on using them to predict stock prices in the future. Most are pretty bare-bones though, consisting of little more than a basic LSTM network and a quick plot of the prediction. Though I think the utility of these models is a little questionable, it brought a question into my head: how accurate are the predictions made by a model trained on one stock if it’s predicting on another stock?

The full code can be found here.

Convolutional networks are most prominently used for image analysis or on data with multiple spatial dimensions. Of course, since the inputs to the CNNs are all just numbers, you can feed in other data that has some a relationship encoded into the dimensions of the array. This post involves feeding data for historical returns from exchange traded funds (ETFs) into a CNN, and using it to try to predict the direction of the Dow Jones Industrial Average (DJIA) some time in the future. I’ll be using Keras to code the neural network. The Jupyter notebook used to develop this code is here.

As with all posts of this nature, this shouldn’t be taken as advice on what to do with your money.

I recently had to go through some matrix operations in R and then write up the results in LaTeX. Formatting the R output to get it into a form for LaTeX isn’t particularly hard, but it’s tedious and it has a regular structure, so it seemed like it would be easy to code it up. So I decided to try it for R, Python, and Julia.