A few months ago, I wrote about the Predictive Power Score (PPS): a handy metric to quickly explore and quantify the relationships in a dataset.

As a social scientist, I was taught to use a correlation matrix to describe the relationships in a dataset. Yet, in my opinion, the PPS provides three handy advantages:

PPS works for any type of data, also nominal/categorical variables

PPS quantifies non-linear relationships between variables

PPS acknowledges the asymmetry of those relationships

# You can get the development version from GitHub:
# install.packages('devtools')
devtools::install_github('https://github.com/paulvanderlaken/ppsr')

Usage

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

Visualizing 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.

Exploring mtcars

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.

Exploring trees

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.

Conclusion

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.

Enjoy the R package, or the Python module for that matter, and let me know if you see any improvements!

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?!

Statistic

2019

2020

delta

Views

107.828

150.599

40%

Visitors

70.870

100.539

42%

Followers

159

300

89%

Posts

96

72

-25%

Comments

40

59

48%

per post

0,42

0,82

97%

Likes

116

86

-26%

per post

1,21

1,19

-1%

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:

For the first time, my blog roll & archives were the most visited page of my website this year! A whopping 13k views!!

With regard to the most visited pages of this year, not much has changed since 2019. We see some golden oldies and I once again conclude that my viewership remains mostly R-based:

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.

A flowchart is a picture of the separate steps of a process in sequential order. It it super useful to organize and interpret business processes, IT systems, or computer algorithms.

I draw flowcharts and process diagrams all the time in my daily work as a data scientist!

Drawing out the business process is often a first step in any project, in order to really understand the underlying business workflow and problems. I feel doing so greatly facilitates opportunity finding.

Moreover, when designing a machine learning or data science architecture — with data coming from different sources, being manipulated using different workflows, and ending up in models feeding multiple business processes — drawing the whole she-bang out really helps me personally to keep overview.

There are licensed software programs such as Microsoft Visio that allow you to create flowcharts. But there are also numerous free applications that can help you draw up a flow chart.

I’ve recently transitioned to VS Code for all my Python programming, so I really welcome this cool feature. It integrates all the flow chart functionality of draw.io right there in your IDE. Incredible!

Here’s a demo:

Here’s another demo, but with a light theme, showing how easy it is to export your diagrams to a shareable png file.

Moreover, due to VS Code’s amazing “LiveShare” feature, you can even collaborate with colleagues and build a flow chart together, simulatenously:

Now there are many more features to this plugin. You can write and change the JavaScript code behind the objects to tailor it completely to your theme and tastes. Or if you prefer working with XML, you can just alter that code. Everything seems to work as a charm.

Want to consider artificial intelligence applications and implementations from an ethical standpoint? Here’s a high-level conceptual view you might like:

Kolja Verhage wrote a report The Implementation of Trustworthy/Ethical AI in the US and Canada in cooperation with the Netherlands Innovation Attaché Network. Based on numerous interviews with AI ethics experts, Kolja presents an overview of approaches and models on how to implement ethical AI.

For over 30 years there has been academic research on ethics and technology. Over the past five years, however, we’ve seen an acceleration in the impact of algorithms on society. This has led both companies and governments across the world to think about how to govern these algorithms and control their impact on society. The first step of this has been for companies and governments to present abstract high-level principles of what they consider “Ethical AI”.