SafeGram: visualising drug safety

Update: an RMarkdown notebook explaining the whole process is available here.

Visualising vaccine safety is hard. Doing so from passive (or, as we say it in Britain, ‘spontaneous’!) pharmacovigilance (PhV) sources is even harder. Unlike in active or trial pharmacovigilance, where you are essentially dividing the number of incidents by the person-time or the number of patients in the cohort overall, in passive PhV, only incidents are reported. This makes it quite difficult to figure out their prevalence overall, but fortunately, we have some metrics we can use to better understand the issues with a particular medication or vaccine. The proportional reporting ratio ($PRR$) is a metric that can operate entirely on spontaneous reporting, and reflect how frequent a particular symptom is for a particular treatment versus all other treatments.

Defining $PRR$$PRR$

For convenience’s sake, I will use the subscript $*$ operator to mean a row or column sum of a matrix, so that

$N_{i,*} = \displaystyle \sum_{j=1}^{n} N_{i,j}$

and

$N_{*,j} = \displaystyle \sum_{i=1}^{m} N_{i,j}$

and furthermore, I will use the exclusion operator $* \neg$ to mean all entities except the right hand value. So e.g.

$N_{i, * \neg k} = \displaystyle \sum_{j=1, j \neq k}^m N_{i,j}$

Conventionally, the PRR is often defined to with reference to a 2×2 contingency table that cross-tabulates treatments ($m$ axis) with adverse effects ($n$ axis):

($i$)
($\neg i$)
TOTAL
Treatment of interest
($j$)
$a = D_{i,j}$ $b = D_{i, * \neg j}$ $a + b = D_{i, *} = \displaystyle \sum_{j = 1}^{n} D_{i, j}$
All other treatments
($\neg j$)
$c = D_{* \neg i, j}$ $d = D_{* \neg i, * \neg j}$ $c + d = D_{* \neg i, *} = \displaystyle \sum_{k=1, k \neq i}^{m} \sum_{l = 1}^{n} D_{k, l}$

With reference to the contingency table, the $PRR$ is usually defined as

$\frac{a / (a+b)}{c / (c+d)} = \frac{a}{a + b} \cdot \frac{c + d}{c}$

However, let’s formally define it over any matrix $D$.

Definition 1. $PRR$. Let $D$ be an $m \times n$ matrix that represents the frequency with which each of the $m$ adverse effects occur for each of the $n$ drugs, so that $D_{i,j}$ ($i \in m$, $j \in n$) represents the number of times the adverse effect $j$ has occurred with the treatment $i$.

For convenience’s sake, let $D_{*,j}$ denote $\sum_{i=1}^{m} D_{i,j}$, let $D_{i,*}$ denote $\sum_{j=1}^{n} D_{i,j}$, and let $D_{*,*}$ denote $\sum_{i=1}^{m} \sum_{j=1}^{n} D_{i,j}$. Furthermore, let $D_{* \neg i, j}$ denote $\sum_{k \neq i}^{m} D_{k,j}$ and $D_{i, * \neg j}$ denote $\sum_{k \neq j}^{n} D_{i, k}$.

Then, $PRR$ can be calculated for each combination $D_{i,j}$ by the following formula:

$PRR_{i,j} = \frac{D_{i,j} / D_{i,*}}{D_{* \neg i, j} / D_{* \neg i, *}} = \frac{D_{i,j}}{D_{i,*}} \cdot \frac{D_{*\neg i, *}}{D_{*\neg i, j}}$

Expanding this, we get

$PRR_{i,j} = \frac{D_{i,j}}{\displaystyle\sum_{q=1}^n D_{i,q}} \cdot \frac{\displaystyle\sum_{r=1, r\ne i}^{m} \displaystyle\sum_{s=1}^{n} D_{r,s}}{\displaystyle\sum_{t=1, t\ne i}^{m} D_{t,j}}$

Which looks and sounds awfully convoluted until we start to think of it as a relatively simple query operation: calculate the sum of each row, then calculate the quotient of the ADR of interest associated with the treatment of interest divided by all uses of the treatment of interest on one hand and the ADR of interest associated with all other drugs ($j \mid \neg i$ or $c$) divided by all ADRs associated with all treatments other than the treatment of interest. Easy peasy!

Beyond $PRR$$PRR$

However, the PRR only tells part of the story. It does show whether a particular symptom is disproportionately often reported – but does it show whether that particular symptom is frequent at all? Evans (1998) suggested using a combination of an $N$-minimum, a $PRR$ value and a chi-square value to identify a signal.[1] In order to represent the overall safety profile of a drug, it’s important to show not only the $PRR$ but also the overall incidence of each risk. The design of the SafeGram is to show exactly that, for every known occurred side effect. To show a better estimate, instead of plotting indiviual points (there are several hundreds, or even thousands, of different side effects), the kernel density is plotted.

The reason why SafeGrams are so intuitive is because they convey two important facts at once. First, the PRR cut-off (set to 3.00 in this case) conclusively excludes statistically insignificant increases of risk.[2] Of course, anything above that is not necessarily dangerous or proof of a safety signal. Rather, it allows the clinician to reason about the side effect profile of the particular medication.

• The meningococcal vaccine (left upper corner) had several side effects that occurred frequently (hence the tall, ‘flame-like’ appearance). However, these were largely side effects that were shared among other vaccines (hence the low PRR). This is the epitome of a safe vaccine, with few surprises likely.
• The injectable polio vaccine (IPV) has a similar profile, although the wide disseminated ‘margin’ (blue) indicates that ht has a wider range of side effects compared to the meningococcal vaccine, even though virtually all of these were side effects shared among other vaccines to the same extent.
• The oral polio vaccine (OPV, left bottom corner) shows a flattened pattern typical for vaccines that have a number of ‘peculiar’ side effects. While the disproportionately frequently reported instances are relatively infrequent, the ‘tail-like’ appearance of the OPV SafeGram is a cause for concern. The difference between meningococcal and IPV on one hand and OPV on the other is explained largely by the fact that OPV was a ‘live’ vaccine, and in small susceptible groups (hence the low numbers), they could provoke adverse effects.
• The smallpox vaccine, another live vaccine, was known to have a range of adverse effects, with a significant part of the population (about 20%) having at least one contraindication. The large area covered indicates that there is a rather astonishing diversity of side effects, and many of these – about half of the orange kernel – lies above the significance boundary of 3.00. The large area covered by the kernel density estimate and the reach into the right upper corner indicates a very probable safety signal worth examining.

Interpretation

A SafeGram for each vaccine shows the two-dimensional density distribution of two things – the frequency and the proportional reporting rate of each vaccine (or drug or device or whatever it is applied to). When considering the safety of a particular product, the most important question is whether a particular adverse effect is serious – a product with a low chance of an irreversible severe side effect is riskier than one with a high probability of a relatively harmless side effect, such as localized soreness after injection. But the relative severity of a side effect is hard to quantify, and a better proxy for that is to assume that in general, most severe side effects will be unique to a particular vaccine. So for instance while injection site reactions and mild pyrexia following inoculation are common to all vaccines and hence the relative reporting rates are relatively low, reflecting roughly the number of inoculations administered, serious adverse effects tend to be more particular to the vaccine (e.g. the association of influenza vaccines with Guillain-Barré syndrome in certain years means that GBS has an elevated PRR, despite the low number of occurrences, for the flu vaccines). Discarding vaccines with a very low number of administered cases, the SafeGram remains robust to differences between the number of vaccines administered. Fig. 1 above shows a number of typical patterns. In general, anything to the left of the vertical significance line can be safely ignored, as they are generally effects shared between most other vaccines in general and exhibit no specific risk signal for the particular vaccine. On the other hand, occurrences to the right of the vertical significance line may – but don’t necessarily do – indicate a safety signal. Of particular concern are right upper quadrant signals – these are frequent and at the same time peculiar to a particular vaccine, suggesting that it is not part of the typical post-inoculation syndrome (fever, fatigue, malaise) arising from immune activation but rather a specific issue created by the antigen or the adjuvant. In rare cases, there is a lower right corner ‘stripe’, such as for the OPV, where a wide range of unique but relatively infrequent effects are produced. These, too, might indicate the need for closer scrutiny. It is crucial to note that merely having a density of signals in the statistically significant range does not automatically mean that there is a PhV concern, but rather that such a concern cannot be excluded. Setting the PRR significance limit is somewhat arbitrary, but Evans et al. (2001) have found a PRR of 2, more than 3 cases over a two year period and a chi-square statistic of 4 or above to be suggestive of a safety signal. Following this lead, the original SafeGram code looks at a PRR of 3.0 and above, and disregards cases with an overall frequency of $3Y$, where $Y$ denotes the number of years considered.

Limitations

The SafeGram inherently tries to make the best out of imperfect data. Acknowledging that passive reporting data is subject to imperfections, some caveats need to be kept in mind.

• The algorithm assigns equal weight to every ‘symptom’ reported. VAERS uses an unfiltered version of MedDRA, a coding system for regulatory activities, and this includes a shocking array of codes that do not suggest any pathology. For instance, the VAERS implementation of MedDRA contains 530 codes for normal non-pathological states (e.g. “abdomen scan normal”), and almost 18,000 (!) events involve at least one of these ‘everything is fine!’ markers. This may be clinically useful because they may assist in differential diagnosis and excluding other causes of symptoms, but since they’re not treated separately from actually pathological symptoms, they corrupt the data to a minor but not insignificant extent. The only solution is manual filtering, and with tens of thousands of MedDRA codes, one would not necessarily be inclined to do so. The consequence is that some symptoms aren’t symptoms at all – they’re the exact opposite. This is not a problem for the $PRR$ because it compares a symptom among those taking a particular medication against the same symptom among those who are not.
• A lot of VAERS reports are, of course, low quality reports, and there is no way for the SafeGram to differentiate. This is a persistent problem with all passive reporting systems.
• The SafeGram gives an overall picture of a particular drug’s or vaccine’s safety. It does not differentiate between the relative severity of a particular symptom.
• As usual, correlation does not equal causation. As such, none of this proves the actual risk or danger of a vaccine, but rather the correlation or, in other words, potential safety signals that are worth examining.

SafeGrams are a great way to show the safety of vaccines, and to identify which vaccines have frequently occurring and significantly distinct (high-$PRR$) AEFIs that may be potential signals. It is important to note that for most common vaccines, including controversial ones like HPV, the centre of the density kernel estimate are below the margin of the $PRR$ signal limit. The SafeGram is a useful and visually appealing proof of the safety of vaccines that can get actionable intelligence out of VAERS passive reporting evidence that is often disregarded as useless.

References   [ + ]

 1 ↑ Evans, S. J. W. et al. (1998). Proportional reporting ratios: the uses of epidemiological methods for signal generation. Pharmacoepidemiol Drug Saf, 7(Suppl 2), 102. 2 ↑ According to Evans et al., the correct figure for PRR exclusion is 2.00, but they also use N-restriction and a minimum chi-square of 4.0.

Ebola! Graph databases! Contact tracing! Bad puns!

Thanks to the awesome folks at Neo4j Budapest and GraphAware, I will be talking tonight about Ebola, contact tracing, how graph databases help us understand epidemics and maybe prevent them someday. Now, if flying to Budapest on short notice might not work for you, you can listen to a livestream of the whole event here! It starts today, 13 February, at 1830 CET, 1730 GMT or 1230 Eastern Time, and I sincerely hope you will listen to it, live or later from the recording, also accessible here.

Are you looking for a data science sensei?

Maybe you’re a junior data scientist, maybe you’re a software developer who wants to go into data science, or perhaps you’ve dabbled in data for years in Excel but are ready to take the next step.

If so, this post is all about you, and an opportunity I offer every year.

You see, life has been very good to me in terms of training as a data scientist. I have been spoiled, really – I had the chance to learn from some of the best data scientists, work with some exceptional epidemiologists, experience some unusual challenges and face many of the day-to-day hurdles of working in data analytics. I’ve had the fortune to see this profession in all its contexts, from small enterprises to multi-million dollar FTSE100 companies, from well-run agile start-ups to large and sometimes pretty slow dinosaurs, from government through the private sector to NGOs: I’ve seen it all. I’ve done some great things. And I’ve made some superbly dumb mistakes.

And so, at the start of every year, I have opened applications for young, start-of-career data scientists looking for their Mr. Miyagi. Don’t worry: no car waxing involved. I will be choosing a single promising young data scientist and pass on as much as I can of my so-called wisdom. At the end, your skills will shine like Mr. Miyagi’s 1947 Ford Deluxe Convertible. There’s no catch, no hidden trap, no fees or charges involved (except the one mentioned below).

Eligibility criteria

To be eligible, you must be:

• 18 or above if you are taking a gap year or not attending a university/college.
• You do not have to have a formal degree in data science or a relevant subject, but you must have completed it if you do. In other words: if you’re in your 3rd year of an English Lit degree, you’re welcome to apply, but if you’re in the middle of your CS degree, you have to wait until you’re finished – sorry. The same goes if you intend to go straight on to a data science-related postgrad within the year.
• Have a solid basis in mathematics: decent statistics, combinatorics, linear algebra and some high school calculus are the very minimum.
• You must be familiar with Python (3.5 and above), and either familiar with the scientific Python stack (SciPy, NumPy, Pandas, matplotlib) or willing to pick up a lot on the go.
• Be willing to put in the work: we’ll be convening about once every week to ten days by Skype for an hour, and you’ll probably be doing 6-10 hours’ worth of reading and work for the rest of the week. Please be realistic if you can sustain this.
• If, as recommended, you are working on an AWS EC2 instance, be aware this might cost money and make sure you can cover the costs. In practice, these are negligible.
• You must understand that this is a physically and intellectually strenuous endeavor, and it is your responsibility to know whether you’re physically and mentally up for the job. However, no physical or mental disabilities are regarded as automatically excluding you of consideration.
• You must not live in, reside in or be a citizen of any of the countries listed in CFR Title 22 Part 126, §126.1(d)(1) and (2).
• You must not have been convicted of a felony anywhere. This includes ‘spent’ UK criminal convictions.

Preferred applicants

When assessing applications, the following groups are given preference:

• Persons with mental or physical disabilities whose disability precludes them from finding conventional employment – please outline this situation on the application form.
• Honourably discharged (or equivalent) veterans of NATO forces and the IDF – please include member 4 copy of DD-214, Wehrdienstzeitbescheinigung or equivalent document that lists type of discharge.

What we’ll be up to

Over the 42 weeks to follow, you will be undergoing a rigorous and structured semi-self-directed training process. This will take your background, interests and future ambitions into account, but at the core, you will:

• master Python’s data processing stack,
• learn how to visualize data in Python,
• work with networks and graph databases, including Neo4j,
• acquire the correct way of presenting results in data science to stakeholders,
• delve into cutting-edge methods of machine learning, such as deep learning using keras,
• work on problems in computer vision and get familiar with the Python bindings of OpenCV,
• scrape data from social networks, and
• learn convenient ways of representing, summarizing and distributing our results.

The programme is divided into three ‘terms’ of 14 weeks each, which each consist of 9 weeks of directed study, 4 weeks of self-directed project work and one week of R&R.

What you’ll be getting out of this

In the past years, mentees have noted the unusual breadth of knowledge they have acquired about data science, as well as the diversity of practical topics and the realistic question settings, with an emphasis on practical applications of data science such as presenting data products. I hope that this year, too, I’ll be able to convey the same important topics. Every year is a little different as I try to adjust the course to meet the individual participant’s needs.

The programme is not, of course, accredited by any accreditation body, but a certificate of completion will be issued to any participant who wishes so.

Application process

Simply fill in the form below and send it off by 14 January 2018. The top contenders will be contacted by e-mail or telephone for a brief conversation thereafter. Finally, a lucky winner will be picked by the 21st January 2018. Easy peasy!

FAQ

Q: What does ‘semi-self-directed’ mean? Is there a fixed curriculum?

A: No. There are some basic topics (see list above) that I think are quite likely to come up, but ultimately, this is about making you the data scientist you want to be. For this reason, we’ll begin by planning out where you want to improve – kinda like a PT gives you a training plan before you start out at their gym. We will then adjust as needed. This is not an exam prep, it’s a learning experience, and for that reason, we can focus on delving deeper and getting the fundaments right over other cramming in a particular curriculum.

Q: Can I bring your own data?

A: Sure. In general, we’ll be using standard data sets, because they’re well-known and high-quality data. But if you have a dataset you collected or are otherwise entitled to use that would do equally well, there’s no reason why we couldn’t use it! Note that you must have the right to use and share the data set, meaning it’s unlikely you’re able to use data sets from your day job.

Q: Will this give me an employment advantage?

A: I don’t quite know – it’s impossible to predict. The field of data science degrees is something of a Wild West still, and while some reputable degrees have emerged, others are dubious. Employers still don’t know what to go by. However, you will most definitely be better prepared for an employment interview in data science!

Q: Why are you so keen on presenting data the right way?

A: Because as data scientists, we’re expected to not merely understand the data and draw the right conclusions, but also to convey them to stakeholders at various levels, from plant management to C-suite, in a way that gets the right message across at the first go.

Q: You’re a computational epidemiologist. Can I apply even if my work doesn’t really involve healthcare?

A: Sure. The principles are the same, and we’re largely focusing on generic topics. You might be exposed to bits and pieces of epidemiology, but I can guarantee it won’t hurt.

Q: Why do you only take on one mentee?

A: To begin with, my life is pretty busy – I have a demanding job, a family and – shock horror! – I even need to sleep every once in a while. More importantly, I want to devote my undivided attention to a worthy candidate.

Q: How come I’ve never heard of this before?

A: Until now, I’ve largely gotten mentees by word of mouth. I am concerned that this is keeping some talented people out and limiting the pool of people we should have in. That’s why this year, I have tried to make this process much more transparent.

No.

No.

Q: I have more questions.

A: You can ask them here.

How I predicted Trump’s victory

Introit

“Can you, just once, explain it in intelligible words?”, my wife asked.

We’ve been talking for about an hour about American politics, and I made a valiant effort at trying to explain to her how my predictive model for the election worked, what it took into account and what it did… but twenty minutes in, I was torn between either using terms like stochastic gradient descent and confusing her, or having to start to build everything up from high school times tables onwards.

Now, my wife is no dunce. She is one of the most intelligent people I’ve ever had the honour to encounter, and I’ve spent years moving around academia and industry and science. She’s not only a wonderful artist and a passionate supporter of the arts, she’s also endowed with that clear, incisive intelligence that can whittle down the smooth, impure rock of a nascent theory into the Koh-I-Noor clarity of her theoretical work.

Yet, the fact is, we’ve become a very specialised industry. We, who are in the business of predicting the future, now do so with models that are barely intelligible to outsiders, and some even barely intelligible to those who do not share a subfield with you (I’m looking at you, my fellow topological analytics theorists!). Quite frankly, then: the world is run by algorithms that at best a fraction of us understand.

So when asked to write an account of how I predicted Trump’s victory, I’ve tried to write an account for a ‘popular audience’. [1] That means there’s more I want to get across than the way I built some model that for once turned out to be right. I also want to give you an insight into a world that’s generally pretty well hidden behind a wall made of obscure theory, social anxiety and plenty of confusing language. The latter, in and of itself, takes some time and patience to whittle down. People have asked me repeatedly what this support vector machine I was talking about all the time looked like, and were disappointed to hear it was not an actual machine with cranks and levers, just an algorithm. And the joke is not really on them, it’s largely on us. And so is the duty to make ourselves intelligible.

Prelude

I don’t think there’s been a Presidential election as controversial as Trump’s in recent history. Certainly I cannot remember any recent President having aroused the same sort of fervent reactions from supporters and opponents alike. As a quintessentially apolitical person, that struck me as the kind of odd that attracts data scientists like flies. And so, about a year ago, amidst moving stacks of boxes into my new office, I thought about modelling the outcome of the US elections.

It was a big gamble, and it was a game for a David with his sling. Here I was, with a limited (at best) understanding of the American political system, not much access to private polls the way major media and their court political scientists have, and generally having to rely on my own means to do it. I had no illusions about the chances.

After the first debate, I tweeted this:

Also, as so many asked: post debate indicators included, only 1 of over 200 ensemble models predict a HRC win. Most are strongly Trump win.

– Chris (@DoodlingData), September 28, 2016

To recall, this was a month and a half ago, and chances for Trump looked dim. He was assailed from a dozen sides. He was embroiled in what looked at the time as the largest mass accusation of sexual misconduct ever levelled against a candidate. He had, as many right and left were keen on pointing out, “no ground game”, polling unanimously went against him and I was fairly sure dinner on 10 November at our home will include crow.

But then, I had precious little to lose. I was never part of the political pundits’ cocoon, nor did I ever have a wish to be so. There’s only so much you can offer a man in consideration of a complete commonsensectomy. I do, however, enjoy playing with numbers – even if it’s a Hail Mary pass of predicting a turbulent, crazy election.

I’m not alone with that – these days, the average voter is assailed by a plethora of opinions, quantifications, pontifications and other -fications about the vote. It’s difficult to make sense of most of it. Some speak of their models downright with the same reverence one might once have invoked the name of the Pythiae of the Delphic Oracle. Others brashly assert that ‘math says’ one or other party has ‘already won’ the elections, a month ahead. And I would entirely forgive anyone who were to think that we are, all in all, a bunch of charlatans with slightly more high-tech dowsing rods and flashier crystal balls.

Like every data scientist, I’ve been asked a few times what I ‘really’ do. Do I wear a lab coat? I work in a ‘lab’, after all, so many deduced I would be some sort of experimental scientist. Or am I the Moneyball dude? Or Nate Silver?

Thankfully, neither of those is true. I hate working in the traditional experimental science lab setting (it’s too crowded and loud for my tastes), I don’t wear a lab coat (except as a joke at the expense of one of my long-term harassers), I don’t know anything about baseball statistics and, thanks be to God, I am not Nate Silver.

I am, however, in the business of predicting the future. Which sounds very much like theorising about spaceships and hoverboards, but is in fact quite a bit narrower. You see, I’m a data scientist specialising in several fields of working with data, one of which is ‘predictive analytics’ (PA). PA emerged from combinatorics (glorified dice throwing), statistics (lies, damned lies and ~) and some other parts of math (linear algebra, topology, etc.) and altogether aims to look at the past and find features that might help predicting the future. Over the last few years, this field has experienced an absolute explosion, thanks to a concept called machine learning (ML).

ML is another of those notions that evokes more passionate fear than understanding. In fact, when I explained to a kindly old lady with an abundance of curiosity that I worked in machine learning, she asked me what kind of machines I was teaching, and what I was teaching them – and whether I had taught children before. The reality is, we don’t sit around and read Moby Dick to our computers. Nor is ML some magic step towards artificial intelligence, like Cortana ingesting the entire Forerunner archives in Halo. No, machine learning is actually quite simple: it’s the art and science of creating applications that, at least when they work well, perform better each time than the time before.

It is high art and hard science. Most of modern ML is unintelligible without very solid mathematical foundations, and yet knowledge has never really been able to substitute for experience and a flair for constructing, applying and chaining mathematical methods to the point of accomplishing the best, most accurate result.

Wait, I haven’t talked about results yet! In machine learning, we have two kinds of ‘result’. We have processes we call ‘supervised learning’, where we give the computer a pattern and expect it to keep applying it. For instance, we give it a set (known in this context as the training set) of heart rhythm (ECG) tracings, and tell it which ones are fine and which ones are pathological. We then expect the computer to accurately label any heart rhythm we give to it.

There is also another realm of machine learning, called ‘unsupervised learning’. In unsupervised learning, we let the computer find the similarities and connections it wants to. One example would be giving the computer the same set of heart traces. It would then return what we call a ‘clustering’ – a group of heartbeats on one hand that are fine, and the pathological heartbeats on the other. We are somewhat less concerned with this type of machine learning. Electoral prediction is pretty much a straightforward supervised learning task, although there are interesting addenda that one can indeed do by leveraging certain unsupervised techniques. For instance, groups of people designated by certain characteristics might vote together, and a supervised model might be ‘told’ that a given number of people have to vote ‘as a block’.

These results are what we call ‘models’.

On models

Ever since Nate Silver allegedly predicted the Obama win, there has been a bit of a mystery-and-no-science-theatre around models, and how they work. Quite simply, a model is a function, like any other. You feed it source variables, it spits out a target variable. Like your washing machine:

$f(C_d, W, E_{el}, P_w) = (C_c)$

That is, put in dirty clothes ($C_d$), water ($W$), electricity ($E_{el}$) and washing powder ($P_w$), get clean clothes ($C_c$) as a result. Simple, no?

The only reason why a model is a little different is that it is, or is supposed to be, based on the relationship between some real entities on each side of the equality, so that if we know what’s on the left side (generally easy-to-measure things), we can get what’s on the right side. And normally, models were developed in some way by reference to data where we do have both sides of the equation. An example for this is the tool known as Henssge’s nomogram, which is a tool called a nomogram, a visual representation of certain physical relationships. That particular model was developed from hundreds, if not thousands, of measurements of (get your retching bag ready), butthole temperature measurements of dead bodies where the time of death actually was known. As I’m certain you know, when you die, you slowly assume room temperature. There are a million factors that influence this, and to calculate the time since death could certainly break a supercomputer. And it would be accurate, but not much more accurate than Henssge’s method. Turns out, a gentleman called Claus Henssge discovered, that three and a half factors are pretty much enough to estimate the time since death with reasonable accuracy: the ambient temperature, the aforementioned butthole temperature, the decedent’s body weight, and a corrective factor to take account for the decedent’s state of nakedness. Those factors altogether give you 95% or so accuracy – which is pretty good.

The Henssge nomogram illustrates two features of every model:

1. They’re all based on past or known data.
2. They’re all, to an extent, simplifications.

Now, traditionally, a model used to be built by people who reasoned deductively, then did some inductive stuff such as testing to assuage the more scientifically obsessed. And so it was with the Henssge nomogram, where data was collected, but everyone had a pretty decent hunch that time of death will correlate best with body weight and the difference between ambient and core (= rectal) temperature. That’s because heat transfer from a body to its environment generally depends on the temperature differential and the area of the surface of exchange:

$Q = hA(T_a - T_b)$

where $Q$ is heat transferred per unit time, h is the heat transfer coefficient, A is the area of the object and $T_a - T_b$ is the temperature difference. So from that, it then follows that $T_a$ and $T_b$ can be measured, $h$ is relatively constant for humans (most humans are composed of the same substance) and $A$ can be relatively well extrapolated from body weight.[2]

The entire story of modelling can be understood to focus on one thing, and do it really well: based on a data set (the training set), it creates a model that seeks to describe the essence of the relationship between the variables involved in the training set. The simplest suich relationships are linear: for instance, if the training set consists of {number of hamburgers ordered; amount paid}, the model will be a straight line – for every increase on the hamburger axis, there will be the same increase on the amount paid axis. Some models are more complex – when they can no longer be described as a combination of straight lines, they’re called ‘nonlinear’. And eventually, they get way too complex to be adequately plotted. That is often the consequence of the training dataset consisting not merely of two fields (number of hamburgers and the target variable, i.e. price), but a whole list of other fields. These fields are called elements of the feature vector, and when there’s a lot of them, we speak of a high-dimensional dataset. The idea of a ‘higher dimension’ might sound mysterious, but true to fashion, mathematicians can make it sound boring. In data science, we regularly throw around data sets of several hundred or thousand dimensions or even more – so many, in fact, that there are whole techniques intended to reduce this number to something more manageable.

But just how do we get our models?

Building our model

In principle, you can sit down, think about a process and create a model based on some abstract simplifications and some other relationships you are aware of. That’s how the Henssge model was born – you need no experimental data to figure out that heat loss will depend on the radiating area, the temperature difference to ‘radiate away’ and the time the body has been left to assume room temperature: these things more or less follow from an understanding of how physics happens to work. You can then use data to verify or disprove your model, and if all goes well, you will get a result in the end.

There is another way of building models, however. You can feed a computer a lot of data, and have it come up with whatever representation gives the best result. This is known as machine learning, and is generally a bigger field than I could even cursorily survey here. It comes in two flavours – unsupervised ML, in which we let the computer loose on some data and hope it turns out ok, and supervised ML, in which we give the computer a very clear indication of what approrpiate outputs are for given input values. We’re going to be concerned with the latter. The general idea of supervised ML is as follows.

1. Give the algorithm a lot of value pairs from both sides of the function – that is, show the algorithm what comes out given a particular input. The inputs, and sometimes even the outputs, may be high-dimensional – in fact, in the field I deal with normally, known as time series analytics, thousands of dimensions of data are pretty frequently encountered. This data set is known as the training set.
2. Look at what the algorithm came up with. Start feeding it some more data to which you know the ‘correct’ output, so to speak, data which you haven’t used as part of the training set. Examine how well your model is doing predicting the test set.
3. Tweak model parameters until you get closer to higher accuracy. Often, an algorithm called gradient descent is used, which is basically a fancy way of saying ‘look at whether changing a model parameter in a particular direction by $\mu$ makes the model perform better, and if so, keep doing it until it doesn’t’. $\mu$ is known as the ‘learning rate’, and determines on one hand how fast the model will get to a best possible approximation of the result (how fast the modell will converge), and on the other, how close it will be to the true best settings. Finding a good learning rate is more a dark art than science, but something people eventually get better at with practice.

In this case, I was using a modelling approach called a backpropagation neural network. An artificial neural network (ANN) is basically a bunch of nodes, known as neurons, connected to each other. Each node runs a function on the input value and spits it out to its output. An ANN has these neurons arranged in layers, and generally nodes feed in one direction (‘forward’), i.e. from one layer to the next, and never among nodes in the same layer.

Neurons are connected by ‘synapses’ that are basically weighted connections (weighting simply means multiplying each input to a neuron by a value that emphasises its significance, so that these values all add up to 1). The weights are the ‘secret sauce’ to this entire algorithm. For instance, you may have an ANN set to recognise handwritten digits. The layers would get increasingly complex. So one node may respond to whether the digit has a straight vertical line. The output node for the digit 1 would weight the output from this node quite strongly, while the output node for 8 would weight it very weakly. Now, it’s possible to pick the functions and determine the weights manually, but there’s something better – an algorithm called backpropagation that, basically, keeps adjusting weights using gradient descent (as described above) to reach an optimal weighting, i.e. one that’s most likely to return accurate values.

My main premise for creating the models was threefold.

1. No polling. None at all. The explanation for that is twofold. First, I am not a political scientist. I don’t understand polls as well as I ought to, and I don’t trust things I don’t understand completely (and neither should you!). Most of all, though, I worry that polls are easy to influence. I witnessed the 1994 Hungarian elections, where the incumbent right-wing party won all polls and exit-poll surveys by a mile… right up until eventually the post-communists won the actual elections. How far that was a stolen election is a different question: what matters is that ever since, I have no faith at all in polling, and that hasn’t gotten better lately. Especially in the current elections, a stigma has developed around voting Trump – people have been beaten up, verbally assaulted and professionally ostracised for it. Clearly asking them politely will not give you the truth.
2. No prejudice for or against particular indicators. The models were generated from a vast pool of indicators, and, to put it quite simply, a machine was created that looked for correlations between electoral results and various input indicators. I’m pretty sure many, even perhaps most, of those correlations were spurious. At the same time, spurious correlations don’t hurt a predictive model if you’re not intending to use the model for anything other than prediction.
3. Assumed ergodicity. Ergodicity, quite simply, means that the average of an indicator over time is the same as the average of an indicator over space. To give you an example:[3] assume you’re interested in the ‘average price’ of shoes. You may either spend a day visiting every shoe store and calculate the average of their prices (average over space), or you may swing past the window of the shoe store on your way to work and look at the prices every day for a year or so. If the price of shoes is ergodic, then the two averages will be the same. I thus made a pretty big and almost certainly false assumption, namely that the effect of certain indicators on individual Senate and House races is the same as on the Presidency. As said, while this is almost certainly false, it did make the model a little more accurate and it was the best model I could use for things for which I do not have a long history of measurements, such as Twitter prevalence.

One added twist was the use of cohort models. I did not want to pick one model to stake all on – I wanted to generate groups (cohorts) of 200 models each, wherein each would be somewhat differently tuned. Importantly, I did not want to create a ‘superteam’ of the best 200 models generated in different runs. Rather, I wanted to select the group of 200 models that is most likely to give a correct overall prediction, i.e. in which the actual outcome would most likely be the outcome predicted by the majority of the models. This allows for picking models where we know they will, ultimately, act together as an effective ensemble, and models will ‘balance out’ each other.

A supercohort of 1,000 cohorts of 200 models each was trained on electoral data since 1900. Because of the ergodicity assumption (as detailed above), the models included non-Presidential elections, but anything ‘learned’ from such elections was penalised. This is a decent compromise if we consider the need for ergodicity. For example, I have looked at the (normalised fraction[4] of the) two candidates’ media appearances and their volume of bought advertising, but mass media hasn’t always been around for the last 116 years in its current form. So I looked at the effect that this had on smaller elections. All variables weighted to ‘decay’ depending on their age.

Tuning of model hyperparameters and deep architecture was attempted in two ways. I initially began with a classical genetic algorithm for tuning hyperparameters and architecture, aware that this was less efficient than gradient descent based algorithms but more likely to give you a diversity of hyperparameters and far more suited to multi-objective systems. Compared with gradient descent algorithms, genetic algorithms took longer but performed better. This was an acceptable tradeoff to me, so I eventually adapted a multi-objective genetic algorithm implementation, drawing on the Python DEAP package and some (ok, a LOT of) custom code. Curiously (or maybe not – I recently learned this was a ‘well known’ finding –  apparently not as well known after all!), the best models came out of ‘split training’: genetically optimised convolutional layers, genetically optimised structure but non-convolutional layers are trained using backpropagation.

Another twist was the use of ‘time contingent parameters’. That’s a fancy word of saying data that’s not available ab initio. An example for that would be post-debate changes of web search volumes for certain keywords associated with each candidate. Trivially, that information is not in existence until a week or so post-debate. These models were trained to ‘variants’. So if a particular model had information missing, it defaulted to an equally weighted model without the nodes that would have required that information. Much as this was a hacky solution, it was acceptable to me as I knew that by late October, every model would have complete information.

I wrote a custom mdoel runner in Python with an easy-as-heck output interface – I was not concerned with creating pretty, I was concerned with creating good. The runner first pulled all data it required once again, diffed it against the previous version, reran feature extractors where there was a change, then ran the models over the feature vectors. Outputs went into CSV files and simple outputs that looked like this (welcome to 1983):

CVoncsefalvay @ orinoco ~/Developer/mfarm/election2016 \$ mrun –all

< lots of miscellaneous debug outputs go here >

[13:01:06.465 02 Nov 2016 +0000] OK DONE.
[13:01:06.590 02 Nov 2016 +0000] R 167; D 32; DNC 1
[13:01:06.630 02 Nov 2016 +0000] Output written to outputs/021301NOV2016.mconfdef.csv

That’s basically saying that (after spending the best part of a day scoring through all the models) 167 models were predicting a Republican victory, 32 a Democratic victory and one model crashed, did not converge somewhere or otherwise broke. The CSV output file would then give further data about each submodel, such as predicted turnout, predictions of the electoral college and popular vote, etc. The model was run with a tolerance of 1%, i.e. up to two models can break and the model would still be acceptable. Any more than that, and a rerun would be initiated automatically. One cool thing: this was my first application using the Twilio API to send me messages keeping me up to date on the model. Yes, I know, the 1990s called, they want SMS messaging back.

By the end of the week, the first models have phoned back. I was surprised: was Trump really that far ahead? The polls have slammed him, he seemed hopeless, he’s not exactly anyone’s idea of the next George Washington and he ran against more money, more media and more political capital. I had to spend the best part of a weekend confirming the models, going over them line by line, doing tests and cross-validation, until I was willing to trust my models somewhat.

But part of our story in science is to believe evidence with the same fervour we disbelieve assertions without it. And so, after being unable to find the much expected error in my code and the models, I concluded they must be right.

Living with the models

The unique exhilaration, but also the most unnerving feature, of creating these models was how different they are from my day-to-day fare. When I write predictive models, the approach is, and remains, quintessentially iterative. We build models, we try them, and iteratively improve on them. It is dangerous to fall in love with one’s own models – today’s hero is in all likelihood destined for tomorrow’s dungheap, with another, better model taking its place – until that model, too, is discarded for a better approach, and so on. We do this because of the understanding that reality is a harsh taskmaster, and it always has some surprises in store for us. This is not to say that data scientists build and sell half-assed, flawed products – quite the opposite: we give you the best possible insight we can with the information we’ve got. But how reality pans out will give us more new information, and we can work with that to move another step closer to the elusive truth of predicting the future. And one day, maybe, we’ll get there. But every day, if we play the game well, we get closer.

Predicting a one-time event is different. You don’t get pointers as to whether you are on the right track or not. There are no subtle indications of whether the model is going to work or not. I have rarely had a problem sticking by a model I built that I knew was correct, because I knew every day that new information would either confirm or improve my model – and after all, turning out the best possible model is the important part, not getting it in one shot, right? It was unnerving to have a model built on fairly experimental techniques, with the world predicting a Clinton win with a shocking unanimity. There were extremely few who predicted a Trump win, and we all were at risk of being labelled either partisans for Trump (a rather hilarious accusation when levelled at me!) or just plain crackpots. So I pledged not to discuss the technical details of my models unless and until the elections confirmed they were right.

So it came to pass that it was me, the almost apolitical one, rather than my extremely clever and politically very passionate wife, who stayed up until the early hours of the morning, watching the results pour in. With CNN, Fox and Twitter over three screens, refreshing all the time, I watched as Trump surged ahead early and maintained a steady win.

My model was right.

Coda

It’s the 16th of November today. It’s been almost a week since the elections, and America is slowly coming to terms with the unexpected. It is a long process, it is a traumatic process, and the polling and ‘quantitative social science’ professions are, to an extent, responsible for this. There was all kinds of sloppiness, multiplication of received wisdom, ‘models’ that in fact were thin confirmations of the author’s prejudices in mathematical terms, and a great deal of stupidity. That does sound harsh, but there’s no better way really to describe articles that, weeks before the election, state without a shade of doubt that we needed to ‘move on’, for Clinton had already won. I wonder if Mr Frischling had a good family recipe for crow? And on the note of election night menu, he may exchange tips with Dr Sam Wang, whom Wired declared 2016’s election data hero in an incredibly complimentary puff piece, apparently quite more on the basis that the author, Jeff Nesbit, hoped Wang was right rather than any indications for analytical superiority.

The fact is, the polling profession failed America and has no real reason to continue to exist. The only thing it has done is make campaigns more expensive and add to the pay-to-play of American politics. I don’t really see myself crying salt tears at the polling profession’s funeral.

The jury is still out on the ‘quantitative social sciences’, but it’s not looking good. The ideological homogeneity in social science faculties worldwide, but especially in America, has contributed to the kind of disaster that happens when people live in a bubble. As scientists, we should never forget to sanity check our conclusions against our experiences, and intentionally cultivate the most diverse circle of friends we can to get as many little slivers of the human experience as we can. When one’s entire milieu consists of pro-Clinton academics, it’s hard to even entertain doubt about who is going to win – the availability heuristic is a strong and formidable adversary, and the only way to beat it is by recruiting a wide array of familiar people, faces, notions, ideas and experiences to rely on.

As I write this, I have an inch-thick pile of papers next to me: calculations, printouts, images, drafts of a longer academic paper that explains the technical side of all this in detail. Over the last few days, I’ve fielded my share of calls from the media – which was somewhat flattering, but this is not my field. I’m just an amateur who might have gotten very lucky – or maybe not.

Time will tell.

In a few months, I will once again be sharing a conference room with my academic brethren. We will discuss, theorize, ideate and exchange views; a long, vivid conversation written for a 500-voice chorus, with all the beauty and passion and dizzying heights and tumbling downs of Tallis’s Spem in Alium. The election has featured prominently in those conversations last time, and no doubt that will be the case again. Many are, at least from an academic perspective, energised by what happened. Science is the only game where you actually want to lose from time to time. You want to be proven wrong, you want to see you don’t know anything, you want to be miles off, because that means there is still something else to discover, still some secrets this Creation conceals from our sight with sleights of hand and blurry mirrors. And so, perhaps the real winners are not those few, those merry few, who got it right this time. The real winners are those who, led by their curiosity about their failure to predict this election, find new solutions, new answers and, often enough, new puzzles.

That’s not a consolation prize. That’s how science works.

And while it’s cool to have predicted the election results more or less correctly, the real adventure is not the destination. The real adventure is the journey, and I hope that I have been able to grant you a little insight into this adventure some of us are on every hour of every day.

References   [ + ]

 1 ↑ There is an academic paper with a lot more details forthcoming on the matter – incidentally, because republication is generally not permitted, it will contain many visualisations I was not able or allowed to put into this blog post. So just for that, it may be worth reading once it’s out. I will post a link to it here. 2 ↑ The reasoning here is roughly as follows. Assume the body is a sphere. All bodies are assumed of being made of the same material, which is also assumed to be homogenous. The volume of a sphere $V = \frac{4}{3} \pi r^3$$V = \frac{4}{3} \pi r^3$, and its weight is that multiplied by its density $\rho$$\rho$. Thus the radius of a sphere of a matter of known density $\rho$$\rho$ can be calculated as $r = \sqrt[3]{\frac{3}{4} \frac{M}{\pi \rho}}$$r = \sqrt[3]{\frac{3}{4} \frac{M}{\pi \rho}}$. From this, the surface area can be calculated ($A = 4 \pi r^2$$A = 4 \pi r^2$). Thus, body weight is a decent stand-in for surface area. 3 ↑ I am indebted to Nassim Nicholas Taleb for this example. 4 ↑ Divide the smaller by the larger value, normalise to 1.

The Fear Factor

Update: Adam has a great response, much from his own (rather different yet nonetheless fascinating and infinitely important) perspective, that should be a valuable read to anyone who found this post even mildly interesting.

As I was perusing Twitter, I bumped into this sponsored tweet by Shell, promoting Sensabot, a ruggedised remote ops robot designed for operations in dangerous environments by Carnegie Mellon’s NREC and now apparently adapted/adopted by Shell:

That sounds great… unfortunately, it strikes me, it misunderstands a couple of things – namely,

1. fear, and the function it has in the human mind (not just the psyche – fear is a primarily neural response, secondarily perhaps cognitive and far behind it is any psychological aspect thereof), and
2. what a robot ought to do/know.

Now, this might just be a marketing puff, though it probably is in its own way true – I have yet to see robots with a specific system catering for fear. It is also hardly just Shell and NREC I’m singling out here – the points are much more generic and have more to do with that robots do and what they therefore ought to understand about being human.

When I was a child, I once managed to piss off my grandfather enough to have him lock me in the shed. The shed smelled of chicken feed, something that turns my guts upside down to this day. Now, the shed was pretty ok, all things considered, albeit dark and damp. However, I shared it with what at my youthful estimation must have been several hundred of small insects, spiders, centipedes and other creepy-crawlies.

I love nature. I just hate the things it sometimes produces. Safe to say if it does not have a brain and does creepy-crawly stuff, I will in all likelihood be creeped out by it.

So there I was, locked in with what I now know were more along the lines of a few thousands of these critters. I screamed like a banshee, until my grandmother took pity on me and released me.

Years and years later, memories of this crawled their way back into my mind at the most inopportune times. It was an uncharacteristically cool midsummer day, in the ageless and timeless beauty that you only get at NSC Bisley, the capital of UK target rifle shooting. Looking through the high-resolution scope of my rifle at Stickledown, the long distance (1,000+ yd) match rifle range, I was immersed in doing calculations of wind and gust patterns and adjustments and projectile drop in my head, trying to look out for any sign of crosswind at what is rightly known as one of the most treacherous ranges in the world of long distance target rifle shooting. That was when I suddenly felt that familiar crawl of a spider up my right leg. Had it not been for the fact that freaking out like a lunatic at a firing range while holding a stupidly overpowered sniper rifle in the middle of a few dozen other shooters on edge at what is to many of them a career match is generally shunned upon, I would probably have screamed. Instead, I unloaded, kicked the spider off me and tried to settle down, but by that time, it was all lost. My heart, pickled in adrenalin, pounded and pounded and I got some stupidly bad shots away before I conceded. And that’s how great my first Imperial Meeting went, back in 2006.

I was so bothered by this episode, I applied my usual method to it – reading every single book ever written on the subject of fear and anxiety responses (years later, when I would once again have to face scary memories from my past, much of that reading would prove helpful in retaining a modicum of sanity). I read tomes of evolutionary biology, a field so unfamiliar to me I had to ask a fellow student to give me the Cliff’s Notes of it. I read a fantastic book, The Gift of Fear by Gavin de Becker, in which he explains the importance of fear signals in avoiding violence. I read copiously on the physiology of fear responses, of the need for the inotropy and chronotropy[1] of adrenaline, and the reason why battle cries and battle shouts are a universal feature of human civilisations.

And eventually, I came to realise that while fear probably lost me any stab I had at the Halford, the much coveted 1,100yd/1,200yd trophy that year (if we’re being honest here, any such chances were… fairly slim at best), it was a crucial part of getting my species, and quite probably the individual self, to that point. Of course, because this is not a Hollywood blockbuster about facing one’s fears and winning, I never went back to Bisley after this event and I would in fact never again shoot in a public competition. I would, however, spend plenty of time on the more fortunate end of a rifle, and never have another problem with it – even in inhospitable climates with various nasty creepy-crawlies.

Now, there’s a reason I’m giving a little personal vignette here – and that is to understand that we’re more familiar with the adverse effects of fear than we are with its ‘gift’, to use de Becker’s term. We, as a society, are in the mindset I was as I walked down the firing point and tried to figure out how the hell I am going to explain all this to my coach without becoming the club joke. Fear is bad. Fear is so bad, if you get too much of it, many opt for taking medication or seeking professional help (and that’s perfectly right so!). “Freedom from fear”, one of FDR’s often-quoted four freedoms, has put fear on the level of starvation, religious persecution and oppression of free expression. Fear is a big deal.

And justly so. Fear is, well, not nice. It puts people ‘on edge’, which is just fine, but is a prioritisation mechanism – it puts efficiency and survival ahead of communication and courtesy, and leads you to be perceived as unpleasant. Fear, especially long-term levels of heightened stress response (known sometimes the ‘biological embedding of anxiety’) can have utterly deleterious effects on long-term health[2] and there seems now ample evidence that the damage is on a genetic level[3], i.e. capable of being passed on. The harm of fear thus becomes intergenerational.

At the same time, fear is necessary for humans, and it does not take much to think of a scenario when your entire ancestral line could have been wiped out if it had not been for your slightly anxious great-great-great^n-ancestor so pathologically afraid of floods that he insisted on dwelling on a hill or so fearful of sabre-tooth tigers that he always carried a sharp object that might just be credited for his survival. In fact, Marks and Nesse (1994) argue that eliminating fear would be by no means exclusively positive – and perhaps even the existence of a pathological state of low fear they term ‘hypophobic disorder’.[4] Certainly the lack of fear response, such as that induced by ablation of metabotropic glutamate receptor subtype 7[5] or interneuronal ablation by inhibition of the Dlx1 gene[6] in the experimental setting or witnessed in the context of pervasive neurodevelopmental disorders both in models[7] and in vivo,[8] has significant evolutionary drawbacks – it is not hard to see how behaviour without fear in a world of danger can quickly lead to reduced life expectancies.

And so we get to the Sensabot, our ‘fearless’ robot. What benefits does his fearlessness yield us? None, I submit, for the reasons below.

Fear is a diverse phenomenon. Cutting it out is neurosurgery with a hatchet.

Fear is a single word (albeit one replete with synonyms) for a number of states of mind that connect somewhere in the human reactions they evoke via the amygdala and thence the limbic system, quite prominently the hypothalamic fight/flight response.[9] It bundles together your fear of spiders (a genuine phobia), your fear of nuclear war (a longer-term anxiety), your fear of wasting your life (an even less acute, more existential perception) and so on. Cutting it all out is doing neurosurgery with a hatchet. A not very sharp one, either.

To put it in the context of the robot: of course, a robot who is not worried about spiders, doesn’t hyperventilate and sweat when handling dangerous substances and doesn’t freeze at the sight of a few zombies emerging from the neighbouring compartment (a risk I doubt Shell needs to envisage at this point, of course!) lacks maladaptive manifestations of fear. These intersect somewhere in the shared fact that they’re either disproportionate to the risk (spiders) or unproductive in the situation (handling dangerous substances and freezing at the sight of a zombie).

But what about other aspects of fear? Fear is a natural way to warn us of existential danger. The Sensabot relies on the human operator to have at least some degree of that, but more autonomous bots will not be able to. Nor do operators act the same when they’re in the cockpit than when they’re piloting an unmanned vehicle.[10] Of course, Sensabots can be replaced far easier than humans, but that’s irrelevant here, both axiomatically and practically (the collateral damage of e.g. an explosion caused by an incorrect action might well be an actual human in the area). Nor does the bot have the neurophysiological advantages that fear – specifically, the cardiac effects of faster movement, better cognitive capabilities and so on. Fear is a reserve, and machines don’t have that reserve.

Fear prioritises.

Fear is best represented as a vector, having both magnitude and direction (example: “I’m very afraid (magnitude) of spiders (direction)”). Different magnitudes help prioritising for immediacy and apprehended risk (likelihood times expected loss). Of course, it is not possible to simply bestow this upon a computer, and there are other methods of prioritising risk, but the great benefit of fear is that it distills signals down into a simple and fast calculation that is remarkably rarely wrong. It does so by considering a current signal in the context of all signals, the signal space of all possible signals, as well as learned patterns and the wider context in which the entire process is taking place. The decision whether to be afraid of something is, actually, quite complex.

This prioritisation is often lampooned when it appears to go wrong, typically when people are afraid of certain rare risks than more frequent ones. Typically, such caricatures of the way human fears work get several things wrong – they reduce the situation to mere probability when in reality, the likelihood of loss, the manner of loss, its impact on others, its impact on your wider community at large and so on are taken into account. That’s why more people fear terrorist attacks than car accidents, even though the latter are much more frequent. Context is everything, and if we learn only one thing from fear, let it be that the evaluation of risks takes place in a very wide context, and with its holistic nature – involving the limbic system, the median prefrontal cortex (mPFC) for memory, somewhat affected by the person’s state of arousal and HPA axis function, mediated by sensory perceptions mixed with our interpretations thereof –, fear is a highly multifactorial response that can be promoted, mediated or inhibited by a number of factors on the way. There is now a degree of awareness in literature that learned and innate fears are differentiated in their propagation pathways (specifically, the involvement of the prelimbic mPFC),[11] indicating again that fear is a single response to different processes reacting to different stimuli. This underlines how fear, rather than simply getting one’s brain pickled in adrenaline, is a complex phenomenon. From an evolutionary perspective, this complexity calls for an explanation – the holistic nature of fear comes, of course, at the expense of the time it takes to trigger release of adrenaline and fight/flight responses. That explanation is, of course, that fear has to accomplish more objectives than merely recoiling, reliably and every time, from a trigger: it has to weigh whether a response is going to put us in more danger, it has to weigh our resources against plans of escape, it has to consider the entire context of a situation, including the past (via the memory activity of the prelimbic mPFC).

Humans are afraid. Their robot co-workers need to understand this.

He’s entirely right – if robots and humans work together, robots need to have what is sometimes referred to as the ‘theory of mind’ – an internal concept of an external mind – in order to anticipate and understand their workmates. And humans, well, humans experience fear. There’s no way to getting around that. An interesting consideration here would be a fear related adaptation of Baron-Cohen’s Sally-Anne test,[13] which I will call the Sally-Zombie test. Anne is, in this case, replaced by a rotting carcass reanimated by dark forces. A robot ought to be able to reason about Sally’s reaction to this. Merely predicting a response is unlikely – even in the absence of in-depth knowledge of Sally’s decisions in the past, it will be hard to predict whether she will freeze, run or reach for the nearest object to decapitate her once-friend-turned-zombie with. The robot, thus, ought to understand multiple things here:

• The human emotional context: humans and their fear of their body being taken over, a fear rooted in the human appreciation for autonomy and capacity.
• The human cultural context: zombie movies are a staple of Western culture and at least to Western observers, zombies are unequivocally scary (more advanced models would need to consider cultural differences, e.g. the response Sally would have, had she grown up with a culture, such as Haitian Voodoo or Palo Malombe, where zombies occupy a more complex albeit still fear-inducing position).
• The human personal context: what are Sally’s experiences with zombies? With similar stressors? With the concept of losing a friend to an abomination?
• The human physiological context: given Sally’s state, what is she most likely to experience when her body goes through the motions of fear/panic and the corresponding neural level reactions?

The fact is that the qualia of fear is a uniquely human perception.[14] No machine, however intricate, will ever have the qualia of fear. Whether it needs the qualia, however, in order to do its job is debatable. At the same time, its sheer richness and multifactorial nature, as well as extent of its manifestations, make fear unsuitable to a mere scripted response level of understanding. While some basic features can be easily responded to without having an understanding of fear (“If Joe is around tons of highly explosive material, Joe will have a heart rate exceeding his basal heart rate by approximately 10-25% and experience palmar hydrosis”), most cannot. And that means that robots, to be effective, have to develop something in between the unattainable qualia and the insufficient scripted understanding.

It’s important to understand that this is not merely for robots to understand how their human companions will think, but also to allow the latter to understand how their robot coworker would perceive a situation. A coworker who lacks, say, an ordinary human level of fear might not only endanger his companions, his actions are also likely to be unintelligible to them: why is Steve running towards the madly out-of-control spinning saw blades without any protective equipment?! Fear is so fundamental to being human that it is part of the unwritten set of shared presumptions that help us understand and anticipate each other. This is a system into which robots will, someday soon, integrate themselves.

Conclusion

Do we want robots to be afraid? Some applications, such as the recent proliferation of humanoid, emotionally expressive robots for therapeutic, educational,[15] or general usage purposes[16] certainly rely on at least an understanding of where the display of the physiological-communicative responses to stimuli is appropriate. But that’s not where the story ought to end. In fact, robots that need to have more than trivial ability to reason on their own, especially if they need to do so in a human context. There is much that robots can do better than humans – they don’t feel pain, remorse, regret, doubt, boredom or fatigue. To inject into what one might perceive as almost perfect creatures the maladaptive aspects, too, of human responses to perceived dangers sounds counterintuitive. At the same time, on the large (evolutionary) scale as well as the individual long-term scale, fear is a gift. It is a gift we as humans must consider to pass on to our creations.

References   [ + ]

 1 ↑ That’s ‘making your heart beat stronger’ and ‘making your heart beat faster’ in human language, respectively. 2 ↑ Miller, Gregory E., Edith Chen, and Karen J. Parker. “Psychological stress in childhood and susceptibility to the chronic diseases of aging: moving toward a model of behavioral and biological mechanisms.” Psychological Bulletin 137.6 (2011): 959. 3 ↑ Sasaki, Aya, Wilfred C. de Vega, and Patrick O. McGowan. “Biological embedding in mental health: An epigenomic perspective 1.” Biochemistry and Cell Biology 91.1 (2013): 14-21. 4 ↑ Nesse, Randolph M. “Fear and fitness: An evolutionary analysis of anxiety disorders.” Ethology and sociobiology 15.5 (1994): 247-261. 5 ↑ Masugi, Miwako, et al. “Metabotropic glutamate receptor subtype 7 ablation causes deficit in fear response and conditioned taste aversion.” The Journal of Neuroscience 19.3 (1999): 955-963. 6 ↑ Mao, Rong, et al. “Reduced conditioned fear response in mice that lack Dlx1 and show subtype-specific loss of interneurons.” Journal of Neurodevelopmental Disorders 1.3 (2009): 224. 7 ↑ Markram, Kamila, et al. “Abnormal fear conditioning and amygdala processing in an animal model of autism.” Neuropsychopharmacology 33.4 (2008): 901-912. 8 ↑ Consider DSM-IV 299.0, at Associated Features and Disorders, para.1 9 ↑ Said at risk of massive oversimplification. It is WAY more complex than that, of course, and the mPFC as well as other parts of the brain play a significant role. There is an increasing understanding that some of our most fundamental emotions like fear are as close as one gets to global in the brain! 10 ↑ As this song attests. 11 ↑ Corcoran, Kevin A., and Gregory J. Quirk. “Activity in prelimbic cortex is necessary for the expression of learned, but not innate, fears.” The Journal of neuroscience 27.4 (2007): 840-844. 12 ↑ Adam (Elkus 13 ↑ Baron-Cohen, Simon, Alan M. Leslie, and Uta Frith. “Does the autistic child have a “theory of mind”?.” Cognition 21.1 (1985): 37-46. 14 ↑ Buck, Ross. “What is this thing called subjective experience? Reflections on the neuropsychology of qualia.” Neuropsychology 7.4 (1993): 490. 15 ↑ Movellan, Javier, et al. “Sociable robot improves toddler vocabulary skills.” Proceedings of the 4th ACM/IEEE international conference on Human robot interaction. ACM, 2009. 16 ↑ Consider in this field Hashimoto, Takuya, et al. “Development of the face robot SAYA for rich facial expressions.” 2006 SICE-ICASE International Joint Conference. IEEE, 2006. and Itoh, Kazuko, et al. “Various emotional expressions with emotion expression humanoid robot WE-4RII.” Robotics and Automation, 2004. TExCRA’04. First IEEE Technical Exhibition Based Conference on. IEEE, 2004.

The one study you shouldn’t write

I might have my own set of ideological prejudices,[1] while at the same time I am more sure than I am about any of these I am certain about this: show me proof that contradicts my most cherished beliefs, and I will read it, evaluate it critically and if correct, learn from it. This, incidentally, is how I ended up believing in God and casting away the atheism of my early teens, but that’s a lateral point.

As such, I’m in support of every kind of inquiry that does not, in its process, harm humans (I am, you may be shocked to learn, far more supportive of torturing raw data than people). There’s one exception. There is that one study for every sociologist, every data scientist, every statistician, every psychologist, everyone – that one study that you should never write: the study that proves how your ideological opponents are morons, psychotics and/or terminally flawed human beings.[2]

Virginia Commonwealth University scholar Brad Verhulst, Pete Hatemi (now at Penn State, my sources tell me) and poor old Lindon Eaves, who of all of the aforementioned should really know better than to darken his reputation with this sort of nonsense, have just learned this lesson at what I believe will be a minuscule cost to their careers compared to the consequence this error ought to cost any researcher in any field.

In 2012, the trio published an article in the American Journal of Political Science, titled Correlation not causation: the relationship between personality traits and political ideologies. Its conclusion was, erm, ground-breaking for anyone who knows conservatives from more than the caricatures they have been reduced to in the media:

First, in line with our expectations, higher P scores correlate with more conservative military attitudes and more socially conservative beliefs for both females and males. For males, the relationship between P and military attitudes (r = 0.388) is larger than the relationship between P and social attitudes (r = 0.292). Alternatively, for females, social attitudes correlate more highly with P (r = 0.383) than military attitudes (r = 0.302).

Further, we find a negative relationship between Neuroticism and economic conservatism ($r_{females}$ = −0.242, $$r_{males}$$ = −0.239). People higher in Neuroticism tend to be more economically liberal.

(P, in the above, being the score in Eysenck’s psychoticism inventory.)

The most damning words in the above were among the very first. I am not sure what’s worst here: that actual educated people believe psychoticism correlates to military attitudes (because the military is known for courting psychotics, am I right? No? NO?!), or that they think it helps any case to disclose what is a blatant bias quite openly. In my lawyering years, if the prosecution expert had stated that the fingerprints on the murder weapon “matched those of that dirty crook over there, as I expected”, I’d have torn him to shreds, and so would any good lawyer. And that’s not because we’re born and raised bloodhounds but because we prefer people not to have biases in what they are supposed to opine on in a dispassionate, clear, clinical manner.

And this story confirms why that matters.

Four years after the paper came into print (why so late?), an erratum had to be  published (that, by the way, is still not replicated on a lot of sites that republished the piece). It so turns out that the gentlemen writing the study have ‘misread’ their numbers. Like, real bad.

The authors regret that there is an error in the published version of “Correlation not Causation: The Relationship between Personality Traits and Political Ideologies” American Journal of Political Science 56 (1), 34–51. The interpretation of the coding of the political attitude items in the descriptive and preliminary analyses portion of the manuscript was exactly reversed. Thus, where we indicated that higher scores in Table 1 (page 40) reflect a more conservative response, they actually reflect a more liberal response. Specifically, in the original manuscript, the descriptive analyses report that those higher in Eysenck’s psychoticism are more conservative, but they are actually more liberal; and where the original manuscript reports those higher in neuroticism and social desirability are more liberal, they are, in fact, more conservative. We highlight the specific errors and corrections by page number below:

It also magically turns out that the military is not full of psychotics.[3] Whodda thunk.

…Ρ is substantially correlated with liberal military and social attitudes, while Social Desirability is related to conservative social attitudes, and Neuroticism is related to conservative economic attitudes.

“No shit, Sherlock,” as they say.

The authors’ explanation is that the dog ate their homework. Ok, only a little bit better: the responses were “miscoded”, i.e. it’s all the poor grad student sods’ fault. Their academic highnesses remain faultless:

The potential for an error in our article initially was pointed out by Steven G. Ludeke and Stig H. R. Rasmussen in their manuscript, “(Mis)understanding the relationship between personality and sociopolitical attitudes.” We found the source of the error only after an investigation going back to the original copies of the data. The data for the current paper and an earlier paper (Verhulst, Hatemi and Martin (2010) “The nature of the relationship between personality traits and political attitudes.” Personality and Individual Differences 49:306–316) were collected through two independent studies by Lindon Eaves in the U.S. and Nichols Martin in Australia. Data collection began in the 1980’s and finished in the 1990’s. The questionnaires were designed in collaboration with one of the goals being to be compare and combine the data for specific analyses. The data were combined into a single data set in the 2000’s to achieve this goal. Data are extracted on a project-by-project basis, and we found that during the extraction for the personality and attitudes project, the specific codebook used for the project was developed in error.

As a working data scientist and statistician, I’m not buying this. This study has, for all its faults, intricate statistical methods. It’s well done from a technical standpoint. It uses Cholesky decomposition and displays a relatively sophisticated statistical approach, even if it’s at times bordering on the bizarre. The causal analysis is an absolute mess, and I have no idea where the authors have gotten the idea that a correlation over 0.2 is “large enough for further consideration”. That’s not a scientifically accepted idea. A correlation is significant or not significant. There is no weird middle way of “give us more money, let’s look into it more”. The point remains, however, that the authors, while practising a good deal of cargo cult science, have managed to oversee an epic blunder like this. How could that have happened?

Well, really, how could it have happened? I trust this should be explained by the words I’ve pointed out before. The authors had what is called “cognitive contamination” in the field of criminal forensic science. The authors had an idea about conservatives and liberals and what they are like. These ideas were caricaturesque to the extreme. They were blind as a bat, blinded by their own ideological biases.

And there goes my point. There are, sometimes, articles that you shouldn’t write.

Let me give you an analogy. My religion has some pretty clear rules about what married people are, and aren’t, allowed to do. Now, what my religion also happens to say is that it’s easier not to mess up these things if you do not engage in temptation. If you are a drug addict, you should not hang out with coke heads. If you are a recovering alcoholic, you would not exactly benefit from hanging out with your friends on a drunken revelry. If you’ve got political convictions, you are more prone to say stupid things when you find a result that confirms your ideas. The term for this is ‘confirmation bias’, the reality is that it’s the simple human proneness to see what we want to see.

Do you remember how as a child, you used to play the game of seeing shapes in clouds? Puppies, cows, elephants and horses? The human brain works on the basis of a Gestalt principle of reification, allowing us to reconstruct known things from its parts. It’s essential to the way our brain works. But it’s also making us see the things we want to see, not what we’re actually seeing.

And that’s why you should never write that one article. The one where you explain why the other side is dumb, evil or has psychotic and/or neurotic traits.

References   [ + ]

 1 ↑ Largely, they presume outlandish stuff like ‘human life is exceptional and always worth defending’ or ‘death does not cure illnesses’, you get my drift. 2 ↑ For starters, I maintain we all are at the very least the latter, quite probably the middle one at least a portion of the time and, frankly, the first one more often than we would believe ourselves. 3 ↑ Yes, I know a high Eysenck P score does not mean a person is ‘psychotic’ and Eysenck’s test is a personality trait test, not a test to diagnose a psychotic disorder.