Tuesday, November 6, 2018

Noise and collective behaviour

"You should never do anything random!", Michael Osborne told the room at large for the umpteenth time during my PhD. Mike, now an Associate Professor at Oxford, is still telling anyone who will listen about the evils of using random numbers in machine learning algorithms. He contends that for any algorithm that makes decisions at random, there is a better algorithm that makes those decisions according to some non-random criterion.
Having seen this debate sporadically erupt over a decade or so has burned the issue of random decision making deep into my psyche, where it has lurked until I recently had reason to think a bit more deeply about the use of random decision making in my own research area: modelling animal behaviour.

Many models of animal behaviour make use of random decisions, or 'noise'. For example, an animal may choose a new direction in which to move by averaging the current directions of the other individuals around itself, and then add some random error to that average to give its own new direction. But why should an animal do something random? Surely there is a 'best' action to be taken based on what the animal knows, and it should do this. Indeed, how would an animal do something random? It is remarkably difficult for humans to write down 'random' series of numbers without the aid of a random number generator, such as a coin or a dice. If you were asked to pick one of two options with a probability of 0.65, how would you do it? Why should an animal be any different?

Usually when we ascribe noise to animal or human decisions, what we are really doing is modelling that part of the decision that we either don't understand, or that we choose to ignore. For example, in a recent paper my coauthors and I looked at factors influencing neighbourhood choice in Stockholm. We modelled choices as being influenced by the characteristics of the moving household and the neighbourhoods they were choosing from, but ultimately being probabilistic - i.e. random. As we say in the paper, this is equivalent to assuming that the households are influenced by many other factors that we don't observe, and that they make the best choice given all this extra information. Because we don't see everything that influences the decision, it appears 'noisy' to us.

So far, so good. This is fundamentally no more controversial than treating a coin toss as random, even though we know that the coin is obeying deterministic physical rules. As long as we use a decent model for the stochasticity in these decisions, we can happily treat what are really deterministic decisions as being random, and still make solid inferences about what influenced them. But we can run into trouble when we forget that only we are playing this trick. This becomes a problem in the world of collective behaviour, where we want to understand how animals are influencing and being influenced by each other. Though we might treat individual animals' decisions as being partly random, we cannot guarantee that the animals themselves also do the same thing. Indeed, it is likely that the animals themselves have a better idea about what factors motivate and influence each other than we do. Where we might, in our ignorance, see a random action, another animal might well see a response to some cue that we haven't thought to look for.

To illustrate, lets imagine that you and I are trying to choose a restaurant. For the purposes of simplicity I will assume that we like very much the same things in a restaurant - we have the same tastes in food and ambience. We approach two seemingly similar-looking restaurants, A and B. I can smell that the food in restaurant A smells somewhat more appetising than in B. Nonetheless, I see you starting to walk in the direction of restaurant B. I know we can both smell that the food in A is better, so what should I make of your decision? If I assume your decision is partly random, I might just assume you made a mistake - A really is better, but you randomly picked B instead. I am then free to pick A. But if I assume you made the best choice with the information available, I must conclude that you have some private information that outweighs the information we share - maybe you earlier read an excellent review of restaurant B. Since our tastes are very similar, I should also conclude that if I had access to your private information as well, I would have made the same choice, since the choice is determined exactly by the information. So now I really ought to pick restaurant B as well.
This place looked great on the web...
[Kyle Moore, CC-SA 1.0]
Looking at collective decision making this way shows that how individuals should respond to each other depends on how much they ascribe the choices made by others to random chance, not how much we do. We therefore need to be careful not to assume that 'noise' in the behaviour of animals in groups is an intrinsic property of the decisions, but instead remember that it depends on choices we make in deciding what to measure, and what to care about. The animals themselves may make very different choices. The consequences of adopting this viewpoint are laid out in detail in my recent paper: Collective decision making by rational individuals. In short they are:

1. The order in which previous decisions have been made is crucial in determining what the next individual will do - the most recent decisions are the most important.

2. Because of the above, how animals appear to interact depends strongly on what we choose to measure. Social information isn't something we can measure in a model-free, neutral way.

3. Group behaviour should change predictably when we observe animals (or humans) in their natural habitat versus the laboratory. In general, social behaviour will probably be stronger in the lab.

None of this is to say that animals or humans always (or ever) do behave rationally. Rather, that they make decisions on the basis of reasons, not the roll of a dice. And their reaction to the choices made by others will be shaped by what they perceive those reasons to be in other individuals. Perhaps, to paraphrase Michael Osborne, we should never assume that other people or animals are doing anything random. Or at least we shouldn't assume that other people are assuming that.........

Thursday, November 1, 2018

Yet more reasons to fund diverse basic science

Research is an incremental, iterative process. New advances build on those that came before, and open up new lines of research to follow afterwards. But not all research leads anywhere. The office drawers of academics are full of manuscripts that never got published, or data from studies that never showed any results. Whole fields such as phrenology enjoy periods in the sun before fading away (if you know of any modern research that directly descends from phrenology, let me know in the comments).

In this respect, research is a lot like the Tree of Life, with each project or study being a species. Species may give rise to new species (new research questions), or they may go extinct, but the Tree of Research (hopefully) endures. 

Mathematicians have tools for understanding tree-generating processes such as these: birth-death models. These specify what types of tree are likely to be generated based on the rates of speciation and extinction for individual species.

Graham Budd and I recently published a study investigating the properties of these processes. Trees generating by birth-death processes are very vulnerable; a newly created tree with only a few species can easily stop growing if all of those species go extinct. On the flip side, trees that have already generated many species can be very robust and are hard to push towards extinction. A consequence of this is that trees that do survive a long time tend to have bursts of rapid diversification at the start. Looking more deeply into the trees that survive, we find that the surviving lineages (those species that have modern descendants) are always diversifying like crazy, speciating at twice the rate we would otherwise expect.

Trees that survive for a long time tend to diversify quickly when they are small (Budd & Mann 2018)

What does this have to do with research funding? Increasingly research funding is allocated on the basis of competitive grant applications. I have written before about the waste involved in this, but another consequence is that research diversity suffers. To get a grant in the UK for example, you must convince the funder and reviewers that you have a very good chance to make notable findings and have impact in academia, industry and elsewhere. This requirement, along with the notable and growing bias towards funding senior academics who have substantial previous funding, favours research that is predictable, which follows the researcher's previously demonstrated expertise and where preliminary results are already available. This in turn reduces the diversity of possible research avenues that might be explored. 

What is the result of reducing diversity? Our research suggests that if we depress the diversification of research we risk extinguishing the Tree of Research altogether. If we focus research efforts too narrowly we put too many eggs in too few baskets. The future success of those research areas is less predictable than we might like to think - few phrenologists thought that their expertise would one day be seen as quackery. If those bets don't pay off then scientific progress may slow down or stop altogether.

Lineages that give rise to long-term descendants are always diversifying quickly (red lines). Green lines diversify slowly and go extinct (Budd & Mann 2018)

But surely, you might reply, isn't it a good idea to check on the track record of scientists and look at their ideas before giving them lots of public money? No doubt there is some value in scrutiny, but given the competition for academic jobs I think we can safely say that most academics have already been scrutinised before they start asking for money. As stated above, I believe our ability to predict what will be a success is highly limited. Moreover, several studies have shown that we can't even agree on what is good or not anyway, reducing weeks or months of labour to a lottery. Just as importantly, as another of my recent papers, this time with Dirk Helbing, has shown, the way that we allocate rewards and resources based on past success can distort the things that people choose to research, and as a result reduce the collective wisdom of academia as a whole. Dirk and I showed that too much diversity in what people choose to research is greatly preferable to too little: as a collective we need the individuals who research seemingly mad questions with little chance of success. Unfortunately, the most natural ways to reward and fund academics based on their track record would seem to create far too little diversity of research.

Fig. 2.

Rewards influence diversity and collective wisdom. Too much diversity (orange line) is better than too little (black and blue lines). (Mann & Helbing 2017).
So what can be done? Dirk and I showed that collective intelligence can be optimised by retrospectively rewarding individuals who are proved right when the majority is wrong. This mirrors approaches in statistics for ensemble learning called Boosting, wherein we train models to predict data that other models were unable to predict accurately. So I would be in favour of targeting grants to those who have gone against prevailing opinion and been proved right. However, we also showed that if agents choose what to research at random this will create greater collective intelligence than many reward schemes. This would support funding many scientists with unconditional funding that supports research wherever their curiosity takes them. This would have the additional advantage of removing much of the deadweight cost of grant applications.


Monday, May 21, 2018

What crosswords can teach us about collective intelligence

Dear reader: it is only fair to give you advance warning that this post will be a thinly-veiled excuse for me to crow about winning the prize for the weekly Times Jumbo Cryptic Crossword...

...that being said, I have long meant to write a post about crosswords, and in particular what they can teach us about collective intelligence. So here we go:
Alexander wept, for there were no more worlds to conquer.
Most weeks I complete several crosswords in The Times (London not New York). I'm not an especially good crossword solver, and solving a typical crossword might take me anywhere from 30min to several hours depending on the difficulty. Clearly solving a cryptic crossword is a task that requires 'intelligence' to perform, though exactly how transferable that concept of intelligence is can be debated. You don't need to be a maths whizz or a language expert - most of it is about learning a few basic rules of cryptic clueing and fostering a reasonably open mind. In the case of The Times it also helps to absorb a lot of weirdly specific knowledge and jargon of the sort that a certain demographic of person possesses - picture an English man in his 50's-70's who went to private or grammar school and then Oxbridge, and who grew up on a diet of Enid Blyton books and cricket. For reasons that are completely inexplicable you also need to know that 'rhino' can be a synonym for 'money'. 

All of that is to say that I am not positing crosswords as a benchmark for general intelligence, but that they can be used as an example of a task that requires some type of intelligence to perform. In terms of crosswords, we can measure 'intelligence' firstly by how many clues one gets right, and among those who get all clues right, by the speed of completion.

What does this have to do with collective intelligence? Well, on many occasions I complete crosswords together with my friend Graham Budd [1]. As the saying goes, two heads are better than one, and when solving together we typically finish the crossword more quickly than on my own, despite us wasting time bemoaning the particularly excruciating clues and otherwise dwelling on our perceptions of ongoing societal collapse. As such, this is an example of collective intelligence - together we are able to solve a problem with greater intelligence than either of us alone.
An excruciating clue: Sunday Times Crytic 4619
So far this is not especially noteworthy. Of course we are faster together!  We can divide the labour. When one of us gets a clue we both get it. Even if we don't agree to split the clues, neither of us has the solve all the clues ourselves. However, what is surprising is that we often finish the crossword in less than half the time it would take me alone. That means that our 'intelligence' has more than doubled. 

Such a case is called superadditive; If I write the performance of some individuals as f(Individuals) then:

f(Me + Graham) > f(Me) + f(Graham)

Or in plain language, Graham and I are 'more than the sum of our parts'

Conversely, many cases of collective intelligence are subadditive, i.e.

f(Me + Graham) < f(Me) + f(Graham)

For instance, one of the most famous examples of collective wisdom comes from Francis Galton. Galton observed punters guessing the weight of a bull at a fair, and noted that the average of their guesses was uncannily accurate. We know that this is a consequence of the Law of Large Numbers, and thus we also know that the error in the average guess scales as 1/N, where N is the number of guessers. This is a subadditive relation. If we double the number of guessers we do not halve the error, but only reduce it by a factor of about 1.4. 

These illustrate two fundamentally different regimes of collective intelligence. The superadditive relationship is one we typically see when groups have evolved specifically to work together, such as a colony of insects or the cells in your brain. An termite colony is truly more intelligent than the sum of its parts: no single termite could build the large intricate nest that the colony inhabits, even if it were given a huge amount of time to try. Likewise, no single neuron in your brain could learn...almost anything. The interactions between individuals produce something far beyond what they can do alone. In these situations the group can grow very large, as the benefits of group living increase with each new member. 
Grand designs
On the flipside, subadditive collective intelligence is what we often see in groups of unrelated individuals, like the punters guessing the weight of Galton's bull. Other examples with similar properties are seen in the way that navigating birds pool their knowledge about how to fly home, or how groups of fish become better at avoiding predators. In each case the group is better than one individual, but there are diminishing benefits of adding more and more group members. In such situations the benefits of being in a group are naturally limited: for example, you might get better at finding or catching food, but then you have to share it with more other individuals. 

Humans are not like insect colonies - we do not live in groups of genetically identical individuals who specialise and collaborate for the common good. But the most interesting examples of human collective intelligence occur when, despite this, we still find superadditive scenarios, where we can become more than the sum of our parts. Some problems naturally lend themselves to this type of collective solution. A good example is mathematics, where someone may work on a problem for years until they meet just the right person with the right knowledge to solve a problem together. On a more humdrum level, consider Graham and I completing the crossword. Despite sharing some things in common, we also have a lot of different knowledge. This means that Graham will easily solve some of the clues I find most difficult and vice versa. And due to the nature of the puzzle, when Graham solves a clue he may make the one I am looking at easier, by giving me some of the letters. We don't just divide the clues at random, we naturally each tend to look at the ones we are most likely to solve. Researchers in the USA have in fact shown that group intelligence is more related to the diversity of group members and the extent to which all individuals are able to participate than it is to the intelligence of the individuals themselves. 

In the example of the crossword, this diversity of skills is a happy accident. But in other cases there are incentives for people to be specialised. Adam Smith noted that division of labour made industrial production much more efficient. Similarly, markets such as the stock exchange can reward a diversity of knowledge - the best way to make a profit is to know something about a company that other people do not. Some of my recent research has looked at how these incentives can be manipulated, and we find exactly this: rewarding people for accurately predicting something that other people were unable to predict creates the best environment for fostering collective intelligence. 

What is the future for collective intelligence. Globalisation, increasing urbanisation and the internet have created ever greater rewards for specialisation. This has fostered economic growth and associated improvements in health and education, especially in what were once under-developed countries now enjoying the fruits of industrialisation. There has thus naturally been a drive to follow this trend further. But we should be wary of continuing this drive to specialisation indefinitely for the sake of group performance. One of the most depressing anecdotes I have ever heard [2] relates to specialisation: an accountant, finding his job rather unfulfilling, began spending large amounts of time playing the online multiplayer game World of Warcraft. In this game [3], players typically join together in 'guilds' to complete 'quests' together. Completing quests can gain players experience points and prizes which can be used to improve their characters in the game. However, when a guild completes quests together, the resources they expend or win, and the new materials they buy or sell must be managed and divided equitably. Slowly over time this accountants guild found they needed to devote more and more time to managing resources - a task that called for some specialisation. Eventually our hero finds himself coming home from 8 hours of real world accountancy only to spend his evening doing the guild's accounts, while other players do the fighting on his behalf! As this anecdote illustrates, if we follow our specialities too closely we may eventually become alienated and lose our motivation to participate in the group at all, which will then reduce the group performance.
Feel the wrath of my double-entry bookkeeping [4]
In contrast, as I noted at the start, I am not a particularly good crossword solver. It can easily take me 4-5 hours in total to solve one of the 'Jumbo' crosswords on Saturdays. Given that one is unlikely to win the prize even if the crossword is completed correctly, and that the prize is a set of books that one could get for about £50 on Amazon, this is not an efficient way for me to acquire an atlas and a dictionary. I complete the crosswords because I find the puzzle intrinsically interesting and diverting. What's more, I value my ability to do a range of tasks, some of which I might even be actively bad at (as erstwhile members of Uppsala Wanderers FC will attest). Robert Heinlein said 'specialisation is for insects', and I'm inclined to agree; while a degree of specialisation is useful, too much goes against what makes us human, and deprives us of motivation and intrinsic reward in activities. To perform well, and to lead fulfilling lives, we need not just diversity between individuals, but also diversity within ourselves and our own minds - to experience the joy of mastering multiple tasks, and to have agency over our own lives rather than to feel like ever smaller cogs in an every larger machine. This also makes us more flexible and robust. Mastering one task makes you vulnerable to that task becoming redundant. Being able to work in many different groups in a multitude of ways makes you more able to contribute as society's needs change. 

So in conclusion, as someone who studies collective intelligence, I am most interested in finding how this can be fostered without crushing individual autonomy. I don't want us to end up looking like an insect colony. I'd rather we ended up like Graham and me, coming together to solve tasks that bring us satisfaction in a job collectively well done. I for one will be enjoying my atlas far more than any I could have bought on Amazon!
To the victor, the spoils

[1] Though not in the case of my immortal triumph in Cryptic Jumbo 1313!
[2] I vaguely recall this coming from Daniel Strömbom, of robot sheepdog fame.
[3] My knowledge of WoW is all at least 3rd hand so please excuse any inaccuracies in this description.
[4] As an academic statistician, I'm aware that I really shouldn't be nerd-shaming anyone.