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’. 1There 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. 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.2The 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 , and its weight is that multiplied by its density \rho . Thus the radius of a sphere of a matter of known density \rho can be calculated as r = \sqrt[3]{\frac{3}{4} \frac{M}{\pi \rho}} . From this, the surface area can be calculated (A = 4 \pi r^2 ). Thus, body weight is a decent stand-in for surface area.

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:3I am indebted to Nassim Nicholas Taleb for this example. 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 fraction4Divide the smaller by the larger value, normalise to 1. 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 , and its weight is that multiplied by its density \rho . Thus the radius of a sphere of a matter of known density \rho can be calculated as r = \sqrt[3]{\frac{3}{4} \frac{M}{\pi \rho}} . From this, the surface area can be calculated (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.
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