Tag: modelling

Is R-squared Useless?

Is R-squared Useless?

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.

I recently wrote about the predictive power score as an alternative to correlation analysis.

Are there similar alternatives that render R-squared useless? And why?

Here’s an interesting blog explaining the standpoints of Cosma Shalizi of Carnegie Mellon University:

  • R-squared does not measure goodness of fit.
  • R-squared does not measure predictive error.
  • R-squared does not allow you to compare models using transformed responses.
  • R-squared does not measure how one variable explains another.

I have never found a situation where R-squared helped at all.

Professor Cosma Shalizi (according to Clay Ford)

How 457 data scientists failed to predict life outcomes

How 457 data scientists failed to predict life outcomes

This blog highlights a recent PNAS paper in which 457 data scientists and academic scholars were challenged use machine learning to predict life outcomes using a rich dataset.

Yet, I can not summarize the result better than this tweet by the author of the paper:

Over 750 scientific papers have used the Fragile Families dataset.

The dataset is famous for its richness of cohort (survey) data on the included families’ lives and their childrens’ upbringings. It includes a whopping 12.942 variables!!

Some of these variables reflect interesting life outcomes of the included families.

For instance, the childrens’ grade point averages (GPA) and grit, but also whether the family was ever evicted or experienced hardship, or whether their primary caregiver had received job training or was laid off at work.

You can read more about the exact data contents in the paper’s appendix.

A visual representation of the data
via pnas.org/content/pnas/117/15/8398/F1.medium.gif

Now Matthew and his co-authors shared this enormous dataset with over 160 teams consisting of 457 academics researchers and data scientists alike. Each of them well versed in statistics and predictive modelling.

These data scientists were challenged with this task: by all means possible, make the most predictive model for the six life outcomes (i.e., GPA, conviction, etc).

The scientists could use all the Fragile Families data, and any algorithm they liked, and their final model and its predictions would be compared against the actual life outcomes in a holdout sample.

According to the paper, many of these teams used machine-learning methods that are not typically used in social science research and that explicitly seek to maximize predictive accuracy.

Now, here’s the summary again:

If hundreds of [data] scientists created predictive algorithms with high-quality data, how well would the best predict life outcomes?

Not very well.


Even the best among the 160 teams’ predictions showed disappointing resemblance of the actual life outcomes. None of the trained models/algorithms achieved an R-squared of over 0.25.

Via twitter.com/msalganik/status/1263886779603705856/photo/1

Here’s that same plot again, but from the original publication and with more detail:

Via pnas.org/content/117/15/8398

Wondering what these best R-squared of around 0.20 look like? Here’s the disappointg reality of plot C enlarged: the actual TRUE GPA’s on the x-axis, plotted against the best team’s predicted GPA’s on the y-axis.

Via twitter.com/msalganik/status/1263886781449191424/photo/1

Sure, there’s some relationship, with higher actual scores getting higher (average) predictions. But it ain’t much.

Moreover, there’s very little variation in the predictions. They all clump together between the range of about 2.1 and 3.8… that’s not really setting apart the geniuses from the less bright!

Matthew sums up the implications quite nicely in one of his tweets:

For policymakers deploying predictive algorithms in high-stakes decisions, our result is a reminder of a basic fact: one should not assume that algorithms predict well. That must be demonstrated with transparent, empirical evidence.


According to Matthew this “collective failure of 160 teams” is hard to ignore. And it failure highlights the understanding vs. predicting paradox: these data have been used to generate knowledge on how the world works in over 750 papers, yet few checked to see whether these same data and the scientific models would be useful to predict the life outcomes we’re trying to understand.

I was super excited to read this paper and I love the approach. It is actually quite closely linked to a series of papers I have been working on with Brian Spisak and Brian Doornenbal on trying to predict which people will emerge as organizational leaders. (hint: we could not really, at least not based on their personality)

Apparently, others were as excited as I am about this paper, as Filiz Garip already published a commentary paper on this research piece. Unfortunately, it’s behind a paywall so I haven’t read it yet.

Moreover, if you want to learn more about the approaches the 160 data science teams took in modelling these life outcomes, here are twelve papers in which some teams share their attempts.

Very curious to hear what you think of the paper and its implications. You can access it here, and I’d love to read your comments below.

Predictive Power Score: Finding predictive patterns in your dataset

Predictive Power Score: Finding predictive patterns in your dataset

Last week, I shared this Medium blog on PPS — or Predictive Power Score — on my LinkedIn and got so many enthousiastic responses, that I had to share it with here too.

Basically, the predictive power score is a normalized metric (values range from 0 to 1) that shows you to what extent you can use a variable X (say age) to predict a variable Y (say weight in kgs).

A PPS high score of, for instance, 0.85, would show that weight can be predicted pretty good using age.

A low PPS score, of say 0.10, would imply that weight is hard to predict using age.

The PPS acts a bit like a correlation coefficient we’re used too, but it is also different in many ways that are useful to data scientists:

  1. PPS also detects and summarizes non-linear relationships
  2. PPS is assymetric, so that it models Y ~ X, but not necessarily X ~ Y
  3. PPS can summarize predictive value of / among categorical variables and nominal data

However, you may argue that the PPS is harder to interpret than the common correlation coefficent:

  1. PPS can reflect quite complex and very different patterns
  2. Therefore, PPS are hard to compare: a 0.5 may reflect a linear relationship but also many other relationships
  3. PPS are highly dependent on the used algorithm: you can use any algorithm from OLS to CART to full-blown NN or XGBoost. Your algorithm hihgly depends the patterns you’ll detect and thus your scores
  4. PPS are highly dependent on the the evaluation metric (RMSE, MAE, etc).

Here’s an example picture from the original blog, showing a case in which PSS shows the relevant predictive value of Y ~ X, whereas a correlation coefficient would show no relationship whatsoever:


Here’s two more pictures from the original blog showing the differences with a standard correlation matrix on the Titanic data:

I highly suggest you read the original blog for more details and information, and that you check out the associated Python package ppscore:

Installing the package:

pip install ppscore

Calculating the PPS for a given pandas dataframe:

import ppscore as pps
pps.score(df, "feature_column", "target_column")

You can also calculate the whole PPS matrix:


There’s no R package yet, but it should not be hard to implement this general logic.

Florian Wetschoreck — the author — already noted that there may be several use cases where he’d think PPS may add value:

Find patterns in the data [red: data exploration]: The PPS finds every relationship that the correlation finds — and more. Thus, you can use the PPS matrix as an alternative to the correlation matrix to detect and understand linear or nonlinear patterns in your data. This is possible across data types using a single score that always ranges from 0 to 1.

Feature selection: In addition to your usual feature selection mechanism, you can use the predictive power score to find good predictors for your target column. Also, you can eliminate features that just add random noise. Those features sometimes still score high in feature importance metrics. In addition, you can eliminate features that can be predicted by other features because they don’t add new information. Besides, you can identify pairs of mutually predictive features in the PPS matrix — this includes strongly correlated features but will also detect non-linear relationships.

Detect information leakage: Use the PPS matrix to detect information leakage between variables — even if the information leakage is mediated via other variables.

Data Normalization: Find entity structures in the data via interpreting the PPS matrix as a directed graph. This might be surprising when the data contains latent structures that were previously unknown. For example: the TicketID in the Titanic dataset is often an indicator for a family.

ML Model Degradation, and why work only just starts when you reach production

ML Model Degradation, and why work only just starts when you reach production

The assumption that a Machine Learning (ML) project is done when a trained model is put into production is quite faulty. Neverthless, according to Alexandre Gonfalonieri — artificial intelligence (AI) strategist at Philips — this assumption is among the most common mistakes of companies taking their AI products to market.

Actually, in the real world, we see pretty much the opposite of this assumption. People like Alexandre therefore strongly recommend companies keep their best data scientists and engineers on a ML project, especially after it reaches production!


If you’ve ever productionized a model and really started using it, you know that, over time, your model will start performing worse.

In order to maintain the original accuracy of a ML model which is interacting with real world customers or processes, you will need to continuously monitor and/or tweak it!

In the best case, algorithms are retrained with each new data delivery. This offers a maintenance burden that is not fully automatable. According to Alexandre, tending to machine learning models demands the close scrutiny, critical thinking, and manual effort that only highly trained data scientists can provide.

This means that there’s a higher marginal cost to operating ML products compared to traditional software. Whereas the whole reason we are implementing these products is often to decrease (the) costs (of human labor)!

What causes this?

Your models’ accuracy will often be at its best when it just leaves the training grounds.

Building a model on relevant and available data and coming up with accurate predictions is a great start. However, for how long do you expect those data — that age by the day — continue to provide accurate predictions?

Chances are that each day, the model’s latent performance will go down.

This phenomenon is called concept drift, and is heavily studied in academia but less often considered in business settings. Concept drift means that the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways.

In simpler terms, your model is no longer modelling the outcome that it used to model. This causes problems because the predictions become less accurate as time passes.

Particularly, models of human behavior seem to suffer from this pitfall.

The key is that, unlike a simple calculator, your ML model interacts with the real world. And the data it generates and that reaches it is going to change over time. A key part of any ML project should be predicting how your data is going to change over time.

Read more about concept drift here.


How do we know when our models fail?

You need to create a monitoring strategy before reaching production!

According to Alexandre, as soon as you feel confident with your project after the proof-of-concept stage, you should start planning a strategy for keeping your models up to date.

How often will you check in?

On the whole model, or just some features?

What features?

In general, sensible model surveillance combined with a well thought out schedule of model checks is crucial to keeping a production model accurate. Prioritizing checks on the key variables and setting up warnings for when a change has taken place will ensure that you are never caught by a surprise by a change to the environment that robs your model of its efficacy.

Alexandre via

Your strategy will strongly differ based on your model and your business context.

Moreover, there are many different types of concept drift that can affect your models, so it should be a key element to think of the right strategy for you specific case!

Image result for concept drift
Different types of model drift (via)

Let’s solve it!

Once you observe degraded model performance, you will need to redesign your model (pipeline).

One solution is referred to as manual learning. Here, we provide the newly gathered data to our model and re-train and re-deploy it just like the first time we build the model. If you think this sounds time-consuming, you are right. Moreover, the tricky part is not refreshing and retraining a model, but rather thinking of new features that might deal with the concept drift.

A second solution could be to weight your data. Some algorithms allow for this very easily. For others you will need to custom build it in yourself. One recommended weighting schema is to use the inversely proportional age of the data. This way, more attention will be paid to the most recent data (higher weight) and less attention to the oldest of data (smaller weight) in your training set. In this sense, if there is drift, your model will pick it up and correct accordingly.

According to Alexandre and many others, the third and best solution is to build your productionized system in such a way that you continuously evaluate and retrain your models. The benefit of such a continuous learning system is that it can be automated to a large extent, thus reducing (the human labor) maintance costs.

Although Alexandre doesn’t expand on how to do these, he does formulate the three steps below:

Via the original blog

In my personal experience, if you have your model retrained (automatically) every now and then, using a smart weighting schema, and keep monitoring the changes in the parameters and for several “unit-test” cases, you will come a long way.

If you’re feeling more adventureous, you could improve on matters by having your model perform some exploration (at random or rule-wise) of potential new relationships in your data (see for instance multi-armed bandits). This will definitely take you a long way!

Solving concept drift (via)

A Visual Introduction to Hierarchical Models, by Michael Freeman

Hierarchical models I have covered before on this blog. These models are super relevant in practice. For instance, in HR, employee data is always nested within teams which are in turn nested within organizational units. Also in my current field of insurances, claims are always nested within policies, which can in turn be nested within product categories. Data is hierachical, and we need to take that into account when we model it.

Hierarchical models do just that. Interested in how they do this? Have a look at this amazing browser application made in React.js!


This project was built by Michael Freeman, a faculty member at the University of Washington Information School.

All code for this project is on GitHub, including the script to create the data and run regressions (done inR). Feel free to issue a pull request for improvements, and if you like it, share it on Twitter. Layout inspired by Tony Chu.

About this project
Artificial Stupidity – by Vincent Warmerdam @PyData 2019 London

Artificial Stupidity – by Vincent Warmerdam @PyData 2019 London

PyData is famous for it’s great talks on machine learning topics. This 2019 London edition, Vincent Warmerdam again managed to give a super inspiring presentation. This year he covers what he dubs Artificial Stupidity™. You should definitely watch the talk, which includes some great visual aids, but here are my main takeaways:

Vincent speaks of Artificial Stupidity, of machine learning gone HorriblyWrong™ — an example of which below — for which Vincent elaborates on three potential fixes:

Image result for paypal but still learning got scammed
Example of a model that goes HorriblyWrong™, according to Vincent’s talk.

1. Predict Less, but Carefully

Vincent argues you shouldn’t extrapolate your predictions outside of your observed sampling space. Even better: “Not predicting given uncertainty is a great idea.” As an alternative, we could for instance design a fallback mechanism, by including an outlier detection model as the first step of your machine learning model pipeline and only predict for non-outliers.

I definately recommend you watch this specific section of Vincent’s talk because he gives some very visual and intuitive explanations of how extrapolation may go HorriblyWrong™.

Be careful! One thing we should maybe start talking about to our bosses: Algorithms merely automate, approximate, and interpolate. It’s the extrapolation that is actually kind of dangerous.

Vincent Warmerdam @ Pydata 2019 London

Basically, we can choose to not make automated decisions sometimes.

2. Constrain thy Features

What we feed to our models really matters. […] You should probably do something to the data going into your model if you want your model to have any sort of fairness garantuees.

Vincent Warmerdam @ Pydata 2019 London

Often, simply removing biased features from your data does not reduce bias to the extent we may have hoped. Fortunately, Vincent demonstrates how to remove biased information from your variables by applying some cool math tricks.

Unfortunately, doing so will often result in a lesser predictive accuracy. Unsurprisingly though, as you are not closely fitting the biased data any more. What makes matters more problematic, Vincent rightfully mentions, is that corporate incentives often not really align here. It might feel that you need to pick: it’s either more accuracy or it’s more fairness.

However, there’s a nice solution that builds on point 1. We can now take the highly accurate model and the highly fair model, make predictions with both, and when these predictions differ, that’s a very good proxy where you potentially don’t want to make a prediction. Hence, there may be observations/samples where we are comfortable in making a fair prediction, whereas in most other situations we may say “right, this prediction seems unfair, we need a fallback mechanism, a human being should look at this and we should not automate this decision”.

Vincent does not that this is only one trick to constrain your model for fairness, and that fairness may often only be fair in the eyes of the beholder. Moreover, in order to correct for these biases and unfairness, you need to know about these unfair biases. Although outside of the scope of this specific topic, Vincent proposes this introduces new ethical issues:

Basically, we can choose to put our models on a controlled diet.

3. Constrain thy Model

Vincent argues that we should include constraints (based on domain knowledge, or common sense) into our models. In his presentation, he names a few. For instance, monotonicity, which implies that the relationship between X and Y should always be either entirely non-increasing, or entirely non-decreasing. Incorporating the previously discussed fairness principles would be a second example, and there are many more.

If we every come up with a model where more smoking leads to better health, that’s bad. I have enough domain knowledge to say that that should never happen. So maybe I should just make a system where I can say “look this one column with relationship to Y should always be strictly negative”.

Vincent Warmerdam @ Pydata 2019 London

Basically, we can integrate domain knowledge or preferences into our models.

Conclusion: Watch the talk!