In 2016, Saul Pwanson designed a plain-text file format for crossword puzzle data, and then spent a couple of months building a micro-data-pipeline, scraping tens of thousands of crosswords from various sources.
After putting all these crosswords in a simple uniform format, Saul used some simple command line commands to check for common patterns and irregularities.
Surprisingly enough, after visualizing the results, Saul discovered egregious plagiarism by a major crossword editor that had gone on for years.
I thoroughly enjoyed watching this talk on Youtube.
Saul covers the file format, data pipeline, and the design choices that aided rapid exploration; the evidence for the scandal, from the initial anomalies to the final damning visualization; and what it’s like for a data project to get 15 minutes of fame.
I tried to localize the dataset online, but it seems Saul’s website has since gone offline. If you do happen to find it, please do share it in the comments!
# You can get the development version from GitHub:
The ppsr package has three main functions that compute PPS:
score() – which computes an x-y PPS
score_predictors() – which computes X-y PPS
score_matrix() – which computes X-Y PPS
Subsequently, there are two main functions that wrap around these computational functions to help you visualize your PPS using ggplot2:
visualize_predictors() – producing a barplot of all X-y PPS
visualize_matrix() – producing a heatmap of all X-Y PPS
Note that Species is a nominal/categorical variable, with three character/text options.
A correlation matrix would not be able to show us that the type of iris Species can be predicted extremely well by the petal length and width, and somewhat by the sepal length and width. Yet, particularly sepal width is not easily predicted by the type of species.
It takes about 10 seconds to run 121 decision trees with visualize_matrix(mtcars). Yet, the output is much more informative than the correlation matrix:
cyl can be much better predicted by mpg than the other way around
the classification of vs can be done well using nearly all variables as predictors, except for am
yet, it’s hard to predict anything based on the vs classification
a cars’ am can’t be predicted at all using these variables
The correlation matrix does provides insights that are not provided by the PPS matrix. Most importantly, the sign and strength of any linear relationship that may exist. For instance, we can deduce that mpg relates strongly negatively with cyl.
Yet, even though half of the matrix does not provide any additional information (due to the symmetry), I still find it hard to derive the most important relations and insights at a first glance.
Moreover, the rows and columns for vs and am are not very informative in this correlation matrix as it contains pearson correlations coefficients by default, whereas vs and am are binary variables. The same can be said for cyl, gear and carb, which contain ordinal categories / integer data, so you can discuss the value of these coefficients depicted here.
In R, there are many datasets built in via the datasets package. Let’s explore some using the ppsr::visualize_matrix() function.
datasets::trees has data on 31 trees’ girth, height and volume.
visualize_matrix(datasets::trees) shows that both girth and volume can be used to predict the other quite well, but not perfectly.
Let’s have a look at the correlation matrix.
The scores here seem quite higher in general. A near perfect correlation between volume and girth.
Is it near perfect though? Let’s have a look at the underlying data and fit a linear model to it.
You will still be pretty far off the real values when you use a linear model based on Girth to predict Volume. This is what the original PPS of 0.65 tried to convey.
Actually, I’ve run the math for this linaer model and the RMSE is still 4.11. Using just the mean Volume as a prediction of Volume will result in 16.17 RMSE. If we map these RMSE values on a linear scale from 0 to 1, we would get the PPS of our linear model, which is about 0.75.
So, actually, the linear model is a better predictor than the decision tree that is used as a default in the ppsr package. That was used to generate the PPS matrix above.
Yet, the linear model definitely does not provide a perfect prediction, even though the correlation may be near perfect.
In sum, I feel using the general idea behind PPS can be very useful for data exploration.
Particularly in more data science / machine learning type of projects. The PPS can provide a quick survey of which targets can be predicted using which features, potentially with more complex than just linear patterns.
Yet, the old-school correlation matrix also still provides unique and valuable insights that the PPS matrix does not. So I do not consider the PPS so much an alternative, as much as a complement in the toolkit of the data scientist & researcher.
Data types are one of those things that you don’t tend to care about until you get an error or some unexpected results. It is also one of the first things you should check once you load a new data into pandas for further analysis.
In this short tutorial, Chris shows how to the pandasdtypes map to the numpy and base Python data types.
Moreover, Chris demonstrates how to handle and convert data types so you can speed up your data analysis. Both using custom functions and anonymous lambda functions.
A very handy guide indeed, after which you will be able to read in your datasets into Python in the right format from the get-go!