Weapons of Math Destruction – A Data Scientist’s Guide to Disarmament

I’ve had this book on pre-order since spring and it finally arrived on Friday. I subsequently devoured it over the weekend.

Long awaited Weapons of Math Destruction by Cathy O'Neil

The book lays out a clear and compelling case for how data-driven algorithms can become — in contrast to their promise of amoral objectivism — efficient means for reproducing and even exacerbating social inequalities and injustices. From predictive policing and recidivism risk models to targeted marketing for predatory loans and for-profit universities, O’Neil explains how to recognize WMDs by 3 distinct features:

  1. The model is either hidden, or opaque to the individuals affected by its calculations, restricting any possibility of seeking recourse against – or understanding of – its results or conclusions.
  2. The model works against the subject’s interest (eg. it is unfair).
  3. The model scales, giving it the opportunity to negatively affect a very large segment of the population.

The taxonomy provides a simple framework for identifying WMDs in the wild. However, importantly for data scientists and other data practitioners, it forms a checklist (or rather an anti-checklist) to keep in mind when developing models that will be deployed into the real world. As data scientists, many of us are strongly incentivized to achieve feature 3, and doing so only makes it increasingly important to be constantly questioning the degree to which our models could fall victim to features 2 and 1.

Feature 2, as O’Neil lays out, can occur despite the best intentions of a model’s creators. This can (and does!) happen in two ways: First, when a modeler seeks to create an objective system for rating individuals (say, for acceptance to a prestigious university, or for a payday loan), the data used to build the model is already encoded with the socially constructed biases of the conditions under which it was generated. Even when attempting to exclude potentially bias-laden factors such as race or gender, this information seeps into the model nonetheless via correlations to seemingly benign variables such as zip codes or the makeup of a subject’s social connections.

Second, when the outcome of the model results in the reinforcement of the unjust conditions from which it was created, a negative feedback loop is created. Such a negative feedback loop is particularly present and pernicious in the use of recidivism risk models to guide sentencing decisions. An individual may be labeled as high risk due not to qualities of the individual himself, but his circumstances of living in a poor, high crime neighborhood. Being incarcerated based on the results of this model renders him more likely to end up back in that neighborhood, subject to continued poverty and disproportionate policing. Thus the model has set up the conditions to fulfill its own prediction.

As machine learning algorithms become more and more accurate at a variety of tasks, their inner workings become harder and harder to understand. The trend will make it increasingly difficult to avoid feature 1 of the WMD taxonomy. Current advanced techniques like deep learning are creating models that are remarkably performant, yet not fully understood by the researchers creating them, much less the individuals affected by their results. In light of this, we need to think carefully as data scientists about how to communicate these models with as much transparency as possible. How to do so remains an open question. But the internal ‘black box’ nature of these algorithms does not obviate our responsibility to disclose exactly what input data went into a given model, what assumptions were made of that data, and on what criteria the model was trained.

Overall, WMD provides an incredibly important framework for thinking about the consequences of uncritically applying data and algorithms to people’s lives. For those of us, like O’Neil herself, who make our living using mathematics to create data-driven algorithms, taking to heart the lessons contained in Weapons Of Math Destruction will be our best defense against unwittingly creating the bomb ourselves.

Introduction to Machine Learning Talk

There was an amazing turnout at last night’s DataPhilly meetup (~200 people!). I was completely delighted by the turnout and people’s engagement level. Here are the slides of the talk I gave to set up the evening with a high-level introduction to machine learning.


Speaking at DataPhilly February 2016

The next DataPhilly meetup will feature a medley of machine-learning talks, including an Intro to ML from yours truly. Check out the speakers list and be sure to RSVP. Hope to see you there!

Thursday, February 18, 2016

6:00 PM to 9:00 PM


  • Corey Chivers
  • Randy Olson
  • Austin Rochford

Corey Chivers (Penn Medicine)

Abstract: Corey will present a brief introduction to machine learning. In his talk he will demystify what is often seen as a dark art. Corey will describe how we “teach” machines to learn patterns from examples by breaking the process into its easy-to-understand component parts. By using examples from fields as diverse as biology, health-care, astrophysics, and NBA basketball, Corey will show how data (both big and small) is used to teach machines to predict the future so we can make better decisions.

Bio: Corey Chivers is a Senior Data Scientist at Penn Medicine where he is building machine learning systems to improve patient outcomes by providing real-time predictive applications that empower clinicians to identify at risk individuals. When he’s not pouring over data, he’s likely to be found cycling around his adoptive city of Philadelphia or blogging about all things probability and data at bayesianbiologist.com.

Randy Olson (University of Pennsylvania Institute for Biomedical Informatics):

Automating data science through tree-based pipeline optimization

Abstract: Over the past decade, data science and machine learning has grown from a mysterious art form to a staple tool across a variety of fields in business, academia, and government. In this talk, I’m going to introduce the concept of tree-based pipeline optimization for automating one of the most tedious parts of machine learning — pipeline design. All of the work presented in this talk is based on the open source Tree-based Pipeline Optimization Tool (TPOT), which is available on GitHub at https://github.com/rhiever/tpot.

Bio: Randy Olson is an artificial intelligence researcher at the University of Pennsylvania Institute for Biomedical Informatics, where he develops state-of-the-art machine learning algorithms to solve biomedical problems. He regularly writes about his latest adventures in data science at RandalOlson.com/blog, and tweets about the latest data science news at http://twitter.com/randal_olson.

Austin Rochford (Monetate):

Abstract: Bayesian optimization is a technique for finding the extrema of functions which are expensive, difficult, or time-consuming to evaluate. It has many applications to optimizing the hyperparameters of machine learning models, optimizing the inputs to real-world experiments and processes, etc. This talk will introduce the Gaussian process approach to Bayesian optimization, with sample code in Python.

Bio: Austin Rochford is a Data Scientist at Monetate. He is a former mathematician who is interested in Bayesian nonparametrics, multilevel models, probabilistic programming, and efficient Bayesian computation.

Categorizing NIPS papers using LDA topic modeling

The Annual Conference on Neural Information Processing Systems (NIPS) has recently listed this year’s accepted papers. There are 403 paper titles listed, which made for great morning coffee reading, trying to pick out the ones that most interest me.

Being a machine learning conference, it’s only reasonable that we apply a little machine learning to this (decidedly _small_) data.

Building off of the great example code in a post by Jordan Barber on Latent Dirichlet Allocation (LDA) with Python, I scraped the paper titles and built an LDA topic model with 5 topics. All of the code to reproduce this post is available on github. Here are the top 10 most probable words from each of the derived topics:

0 1 2 3 4
0 learning learning optimization learning via
1 models inference networks bayesian models
2 neural sparse time sample inference
3 high models stochastic analysis networks
4 stochastic non model data deep
5 dimensional optimization convex inference learning
6 networks algorithms monte spectral fast
7 graphs multi carlo networks variational
8 optimal linear neural bandits neural
9 sampling convergence information methods convolutional

Normally, we might try to attach some kind of label to each topic using our beefy human brains and subject matter expertise, but I didn’t bother with this — nothing too obvious stuck out at me. If you think that you have appropriate names for them feel free to let me know. Given that we are only working with the titles (no abstracts or full paper text), I think that there aren’t obvious human-interpretable topics jumping out. But let’s not let that stop us from proceeding.

We can also represent the inferred topics with the much maligned, but handy-dandy wordcloud visualization:

Topic: 0
Topic: 1
Topic: 2
Topic: 3
Topic: 4

Since we are modeling the paper title generating process as a probability distribution of topics, each of which is a probability distribution of words, we can use this generating process to suggest keywords for each title. These keywords may or may not show up in the title itself. Here are some from the first 10 titles:


Double or Nothing: Multiplicative Incentive Mechanisms for Crowdsourcing
Generated Keywords: [u'iteration', u'inference', u'theory']


Learning with Symmetric Label Noise: The Importance of Being Unhinged
Generated Keywords: [u'uncertainty', u'randomized', u'neural']


Algorithmic Stability and Uniform Generalization
Generated Keywords: [u'spatial', u'robust', u'dimensional']


Adaptive Low-Complexity Sequential Inference for Dirichlet Process Mixture Models
Generated Keywords: [u'rates', u'fast', u'based']


Covariance-Controlled Adaptive Langevin Thermostat for Large-Scale Bayesian Sampling
Generated Keywords: [u'monte', u'neural', u'stochastic']


Robust Portfolio Optimization
Generated Keywords: [u'learning', u'online', u'matrix']


Logarithmic Time Online Multiclass prediction
Generated Keywords: [u'complexity', u'problems', u'stein']


Planar Ultrametric Rounding for Image Segmentation
Generated Keywords: [u'deep', u'graphs', u'neural']


Expressing an Image Stream with a Sequence of Natural Sentences
Generated Keywords: [u'latent', u'process', u'stochastic']


Parallel Correlation Clustering on Big Graphs
Generated Keywords: [u'robust', u'learning', u'learning']

Entropy and the most “interdisciplinary” paper title

While some titles are strongly associated with a single topic, others seem to be generated from more even distributions over topics than others. Paper titles with more equal representation over topics could be considered to be, in some way, more interdisciplinary, or at least, intertopicular (yes, I just made that word up). To find these papers, we’ll find which paper titles have the highest information entropy in their inferred topic distribution.

Here are the top 10 along with their associated entropies:

1.22769364291 Where are they looking?
1.1794725784 Bayesian dark knowledge
1.11261338284 Stochastic Variational Information Maximisation
1.06836891546 Variational inference with copula augmentation
1.06224431711 Adaptive Stochastic Optimization: From Sets to Paths
1.04994413148 The Population Posterior and Bayesian Inference on Streams
1.01801236048 Revenue Optimization against Strategic Buyers
1.01652797194 Fast Convergence of Regularized Learning in Games
0.993789478925 Communication Complexity of Distributed Convex Learning and Optimization
0.990764728084 Local Expectation Gradients for Doubly Stochastic Variational Inference

So it looks like by this method, the ‘Where are they looking’ has the highest entropy as a result of topic uncertainty, more than any real multi-topic content.


auto·di·dact n.
A self-taught person.
From Greek autodidaktosself-taught : auto-auto- + didaktostaught;


sim·u·late v.
To create a representation or model of (a physical system or particular situation, for example).
From Latin simulre, simult-, from similislike;

(If you can get past the mixing of Latin and Greek roots)

sim·u·di·dactic adj.
To learn by creating a representation or model of a physical system or particular situation. Particularly, using in silico computation to understand complex systems and phenomena.


This concept has been floating around in my head for a little while. I’ve written before on how I believe that simulation can be used to improve one’s understanding of just about anything, but have never had a nice shorthand for this process.

Simudidactic inquiry is the process of understanding aspects of the world by abstracting them into a computational model, then conducting experiments in this model world by changing the underlying properties and parameters. In this way, one can ask questions like:

  1. What type of observations might we make if x were true?
  2. If my model of the process is accurate, can I recapture the underlying parameters given the type of observations I can make in the real world? How often will I be wrong?
  3. Will I be able to distinguish between competing models given the observations I can make in the real world?

In addition to being able to ask these types of questions, the simudidact solidifies their understanding of the model by actually building it.

So go on, get simudidactic and learn via simulation!


Calculating AUC the hard way

The Area Under the Receiver Operator Curve is a commonly used metric of model performance in machine learning and many other binary classification/prediction problems. The idea is to generate a threshold independent measure of how well a model is able to distinguish between two possible outcomes. Threshold independent here just means that for any model which makes continuous predictions about binary outcomes, the conversion of the continuous predictions to binary requires making the choice of an arbitrary threshold above which will be a prediction of 1, below which will be 0.

AUC gets around this threshold problem by integrating across all possible thresholds. Typically, it is calculated by plotting the rate of false positives against false negatives across the range of possible thresholds (this is the Receiver Operator Curve)  and then integrating (calculating the area under the curve). The result is typically something like this:


I’ve implemented this algorithm in an R script (https://gist.github.com/cjbayesian/6921118) which I use quite frequently. Whenever I am tasked with explaining the meaning of the AUC value however, I will usually just say that you want it to be 1 and that 0.5 is no better than random. This usually suffices, but if my interlocutor is of the particularly curious sort they will tend to want more. At which point I will offer the interpretation that the AUC gives you the probability that a randomly selected positive case (1) will be ranked higher in your predictions than a randomly selected negative case (0).

Which got me thinking – if this is true, why bother with all this false positive, false negative, ROC business in the first place? Why not just use Monte Carlo to estimate this probability directly?

So, of course, I did just that and by golly it works.


# Simulate some binary outcomes #
n <- 100
x <- runif(n,-3,3)
p <- 1/(1+exp(-x))
y <- bs(p)

# Using my overly verbose code at https://gist.github.com/cjbayesian/6921118

## The hard way (but with fewer lines of code) ##
N <- 10000000
r_pos_p <- sample(p[y==1],N,replace=TRUE)
r_neg_p <- sample(p[y==0],N,replace=TRUE)

# Monte Carlo probability of a randomly drawn 1 having a higher score than
# a randomly drawn 0 (AUC by definition):

rAUC <- mean(r_pos_p > r_neg_p)

By randomly sampling positive and negative cases to see how often the positives have larger predicted probability than the negatives, the AUC can be calculated without the ROC or thresholds or anything. Now, before you object that this is necessarily an approximation, I’ll stop you right there – it is.  And it is more computationally expensive too. The real value for me in this method is for my understanding of the meaning of AUC. I hope that it has helped yours too!

From Whale Calls to Dark Matter: Competitive Data Science with R and Python

Back in June I gave a fun talk at Montreal Python on some of my dabbling in the competitive data science scene. The good people at Savior-fair Linux recorded the talk and have edited it all together into a pretty slick video. If you can spare twenty-minutes or so, have a look.

If you want the slides, head on over to my speakerdeck page.