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!
The book covers the basic foundations up to advanced theory and algorithms. I copied the table of contents below. It’s kind of math heavy, but well explained with visual examples and pseudo-code.
Moreover, the book contains multiple exercises for you to internalize the knowledge and skills.
As an added bonus, the professors teach a number of machine learning courses, the lecture slides and materials of which you can also access for free via the book’s website.
Machine learning is one of the fastest growing areas of computer science, with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way. The book provides a theoretical account of the fundamentals underlying machine learning and the mathematical derivations that transform these principles into practical algorithms. Following a presentation of the basics, the book covers a wide array of central topics unaddressed by previous textbooks. These include a discussion of the computational complexity of learning and the concepts of convexity and stability; important algorithmic paradigms including stochastic gradient descent, neural networks, and structured output learning; and emerging theoretical concepts such as the PAC-Bayes approach and compression-based bounds. Designed for advanced undergraduates or beginning graduates, the text makes the fundamentals and algorithms of machine learning accessible to students and non-expert readers in statistics, computer science, mathematics and engineering.
# You can get the official version from CRAN:
## Or 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.
Despite the pandemic, 2020 has been a great year for me.
Professionally, I grew into my role as data science product owner. And next to this, I got more and more freelance side gigs. Mostly teaching, but also some consultancy projects. Unfortunately, all my start-up ideas failed miserably again this year, yet I’ll keep trying : )
Personally, 2020 was also generous to us. We have a family expansion coming in 2021! (Un)Fortunately, the whole quarantaine situation provided a lot of time to make our house baby-ready!
A year in numbers
2020 was also a great year for our blog.
Here are some statistics. We reached 300 followers, on the last day of the year! Who could have imagined that?!
This tremendous growth of the website is despite me posting a lot less frequently this year.
After a friend’s advice, I started posting less, but more regularly.
Can you spot the pattern in my 2020 posting behavior?
Compare that to my erratic 2019 posting:
Now my readers have got something to look forward to every Tuesday!
Yet, is Tuesday really the best day for me to post my stuff?
You seem to prefer visiting my blog on Wednesdays.
Let me know what you think in the comments!
I am looking forward to what 2021 has in store for my blogging. I guess a baby will result in even less posts… But we’ll just focus on quality over quantity!
I hope I can keep up with the exponential growth:
Best new articles in 2020
There are many ways in which you could define the quality of an article.
For me, the most obvious would be to look at some view-based metric. Something like the number of views, or the number of unique visitors.
Yet, some articles have been online longer than others. So maybe we should focus on the average views per day. Still these you can expect to be increase as articles have been in existance longer.
In my opinion, how an article attract viewers over time tells an interesting story. For instance, how stable are the daily viewer numbers? Are they rising? This is often indicative that external websites link to my article. Which implies it holds valuable information to a specific readership. In turn, this suggests that the article is likely to continue attracting viewers in the future.
Here is an abstract visualization. Every line represents and article. Every line/article starts in the lower left corner. On the x-axis you see the number of days since posting. So lines slowly move right, the longer they have been on my website. On the y-axis you see the total viewers it attracted.
You can see three types of blog articles: (1) articles that attract 90% of their views within the first month, (2) articles that generate a steady flow of visitors, (3) articles that never attract (m)any readers.
Here’s a different way of visualizing those same articles: by their average daily visitors (x) and the standard deviation in daily visitors (y).
Basically, I hope to write articles that get many daily visitors (high x). Yet, I also hope that my articles have either have stable (or preferably increasing) visitor numbers. This would mean that they either score low on y, or that y increases over time.
By these measures, my best articles of 2020 are, in my opinion:
Coming from a social sciences background, I learned to use R-squared as a way to assess model performance and goodness of fit for regression models.
Yet, in my current day job, I nearly never use the metric any more. I tend to focus on predictive power, with metrics such as MAE, MSE, or RMSE. These make much more sense to me when comparing models and their business value, and are easier to explain to stakeholders as an added bonus.