Today, we're excited to hear from Guangdong on network based learning for understanding collective human behaviour.
He's a lecturer in the Department of Engineering here at Oxford and a former postdoc in The Last Media Lab, where he is still an affiliate shoutin,
works with graphs to model relational structure of data and develop new technologies that sit at the intersection of machine learning,
signal processing and complex networks. So it's kind of a cool opportunity.
We've touched quite a bit peripherally on mentioning networks, but now we're going to get to hear a little bit more in depth.
And we're also lucky to be creating. Speaking of networks, a little bit of traffic closer here because at MIT Media Lab, he was in Sandy Petaling lab,
which several friends and former members of of the six informal in other years and speakers this year, like Abdullah speaking at Princeton.
Mm hmm. So we were creating friends of a friend of a friend.
So, yeah, thank you very much for that saying. Yeah, thank you.
So I hope this this is OK, you can hear it. Thank you very much for the kind introduction and the invitation.
It's a great pleasure to be here and also to talk about some recent stuff that we did.
So I'm in engineering here technically so, which means I have an engineering background.
So that means when I talk about computational social science, I definitely have more on the computational side rather than the social side.
So I will not pretend to be a social scientist here. So if I make an imprecise statement, please forgive me.
Nevertheless, I think it's good to present some recent work that we have done to apply computational approaches to understand
collective human behaviour and which I hope will bring some fresh ideas from a more computational learning perspective,
which would be complementary to the traditional approaches. So for this reason, please feel free to interrupt during the presentation.
If you have any questions or comments, I'll be happy to answer.
So, yes, this works. So since we are in this summer Institute for Computational Social Science,
I thought it would be good for us to first to look at a few historical development
in applying computational methods to understand the society and behaviour.
And you will see most of the many ideas were actually originated from the field of physics.
So in early 19th century and inspired by a Newtonian physics society,
was conceptualised as a machine and Auguste Collins was regarded as the father of sociology by many people at that
time defined the concept of social physics as the study of the laws of societies and the science of the civilisation.
In fact, the term sociology was invented, by our count, to designate the concept of social physics.
And so if we want to study the laws of society, then we need information and, uh, what we call data today.
So at the same time, and to be precise in 1830 for the London Statistical Society Statistical Society of London was founded,
which eventually became the Royal Statistical Society.
Nowadays, with the aim to procure a wrench and publish facts to illustrate the conditions and the prospects of society.
So that was the of data collection. But in Victorian times,
the way that we collected data was basically to go to different villages in this country
and then to collect somewhat disconnected and fragmented pieces of information.
So they're not good enough for us to illustrate the whole picture of the society,
let alone to build computational models to understand that the behaviour of people.
So this is a kind of the first wave of studies.
The second wave took place in the mid-20th century, and again, the concept of social physics was reinvented.
There was actually a research group called Department of Social Physics in Princeton in the 1950s.
They existed for 20 years or something.
So the main drivers of this wave was that many social indicators have been found to have statistical regularities,
such as the zip distribution or gravity law.
So zip distribution is one type of power or distribution, which was popularised by American linguist George Ziff,
who studied the distribution of the frequencies of the words in a document.
And he found that out that the frequencies of a word in a document is proportional to the rank of the word in the frequency table.
So that means the most frequent. The word appears two times as many as often as the second most frequent and three times as many
as the search for frequency and the same distribution has been discovered for other indicators,
such as the populations of cities in countries or income distribution.
And the gravity law is another example of which was also kind of proposed by Ziff, who studied the intercity movement in the United States.
So he he discovered that the number of people who move between two different communities
in the United States is proportional to the population of the two communities.
But inversely proportional to the transportation distance between them. So like a P one, p two divided by D has the name Gravity Law, so.
And then more recently, the third wave emerges where more people find the statistical regularities also within human movement and communication.
So examples could be concepts such as tragic culture.
So how people form a group so like a join groups of form ties.
If a is a friend of both B and C, and B and C are likely to be a friend in future.
Other concepts could be strong and weak ties. So these were the ideas originally proposed by Grant, the latter in the 70s.
So he was basically saying that the links of a president in a social network can be divided in roughly two groups.
The strong ties, which are close friends and weak ties, which are distant acquaintances of the weak ties in this case essentially are
like links between that span the boundaries of different communities or groups,
which are believed to be essential to a exchange of information and creation of new economic opportunities.
So as a consequence, people who maintain what is weak ties are likely to be more successful in their career.
The same idea has been tested at the community level. In a study in 2010 by Ego,
so they basically looked at the communication network of communities across the whole country
of U.K. and then they find the very strong correlation between the diversity of the community,
of the communication patterns of the communities and the socio economic status.
And so this paper itself has also some criticism,
but I think it's one of the first studies that try to test these ideas at the national level, which is good.
But the limitations of this kind of work would be mostly we don't really study the mechanism
behind the social interactions or what is the cause of the observed statistical regularities,
which could be due to a lack of appropriate data or computational methods to do so.
So both things change dramatically more recently. So since 10 years ago, we haven't won more data about human behaviour.
So you can think about social media location data that are that are collected by pervasive technologies such as mobile phones and credit cards.
So one thing about these type of data is that they're passively collected so they are not, like obtained the survey.
So potentially they contain less personal bias because usually the data are not collected
where the people actually are knowing that they're actively being correctly collected.
And also, of course, they are easy to scale to the population scale.
So at the same time, we obviously have more advanced computational methods.
You probably heard about machine learning or deep learning these kind of techniques that can allow us to make the best out of the data that we have.
So the combination of these two basically leads to computational social science,
in my view, which gives a few new perspectives in social science studies.
So we can obviously think about moving away from static information collected by surveys to the actual behaviour of the people.
So from demographics, age, gender to the actual behaviour of the people.
And also from a single prison to a connected network,
so you're not just looking at individuals separately, but you look at how they behave collectively,
you look at this relationship between different people in a dynamic way, which means that the relationship can evolve over time.
And obviously, you can easily look at a much larger population.
So the practical impact of that could be if we think about most current population management solutions,
they're mostly focussed on demographics, individual records and static information.
And think about how banks give credit limits to to you or the network providers to keep videos about mobile phone contracts.
It's mostly about your individual records in history without looking at a kind of a network of people.
So the new way could be to actually look at the actual behaviour of people in a collective way and also dynamically.
But these, of course, need more and more those and the matters because we need to understand better the structures and the complexities.
And and this also poses challenges in developing advanced computational methods in the context of social science research.
So the topic today will mostly be this part.
So how we move from individual behaviour to collective behaviour because I think that will be something important to understand,
also interesting to understand. And so our focus on two pieces of studies, I was pleased to talk equally more or less.
The first question is how social network will affect the decision making.
So we all know that, for example, if I tell you something about a restaurant, maybe you are likely to go sometime in the future.
So that's like an influence. But how this influence propagates in social network is an interesting and open question.
Second, in many cases, we don't observe a social network. We just observe the decisions that are taken by people.
So it will be very interesting to see if we can do the some of the reverse problem.
We observed the actions and then we tried to infer the connexions between them so that we can understand that the communities, et cetera.
So our first talk about that, the the first question. So the kind of motivation here is it's basically we all know that nowadays we live
in a connected society and we want people who are very worried if we are connected.
While few hopes of acquaintances and ideas of the six degrees of separation was mostly first realised by Milgram's experiment in the 70s.
Once you did this, just to ask a present in who lives in salary in the US, Nebraska to to send a letter to somebody in Massachusetts.
And the rule is just to send a letter to one of the people the sender knows.
And so eventually he did a study and then eventually, I think 25 percent of the letters arrived.
But amongst the letters that arrived, the average hope that took is like five point five.
So that was one of the original experiments that gave the idea of six degrees of separation.
And but we are not just connected in a society in like a factual way.
Actually, we also influence each other if we are connected.
So there is several studies by Christakis and Fowler that look at the spreading of behaviours,
certain type of phenomenon in the social network, such as obesity, happiness or smoking behaviour.
And they find that this kind of behaviour can spread two to three hops away from you.
So it's remarkable the way if you think about it may be a person that you don't even know.
In some cases. So the thing that remains open is how this influence propagate in the social network a scenario.
So how might decision will be affected by you if I received some information from you?
And especially in the offline setting, there are a few studies on in the online setting like Facebook, these kind of platforms.
But offline settings are difficult because it's not easy, usually to carry out a large scale offline experiment.
And we also need more advanced methods compared to the traditional asset based methods to to basically quantify the influence.
So that's basically the motivation of this study.
We we looked at a particular dataset, which is a mobile phone dataset collected during an international event called Cirque du Soleil.
It's basically a performance event in many countries. This one is in Andorra in Europe, took place every July, I think, and last for the whole month.
So basically, we try to ask the question.
How influence,
how social influence can play a role in an individual decision making in the sense that whether or not to attend this event is likely to
be affected by the fact that either you receive a phone call from an attendee or maybe somebody who has been contacted by the attending.
These are just some basic statistics that I will explain further to, citing that we have a quite intuitive so we build the information cascade.
So it's basically a phone communication network for a given observational period.
You can take one day if you like. So the idea here is that let's say we have and who is who is the initial adopter.
So he attended the event. And then after that, within this observational period, we observed that she made a phone call to three other people.
OK, then you and Bob, since these people, after receiving the call from and there were further make calls to the other people.
So this is basically the information cascade that we define.
And here we basically define the shortest distance between any person to the original adopter as a hope index.
So you can see Bob Casey and Daniel Day one hop away and all the other people to hopefully the
people who have never been connected in this information cascade are the people who are outside.
So in that sense, we do find all these people to be influenced and the people outside are not influenced, basically.
So then we can observe whether all the rest of the people will make our adoption in this case, attend the event for the rest of the month, basically.
So this is the basic setup.
But one technical challenge in this case would be the decisions on adoption, or a lot of things may be attributed to two factors usually.
One is called Homophily. The Chinese influence the Homophily is basically it means that a.
Friendship is more likely to be formed between people who share certain characteristics in this case or to people like music,
then they're likely to form a link between them instead of between a person who likes music and the person who likes books.
That's the basic idea how links can be formed. So that means if we observe that these two people they both attend, let's say this is attendee.
And then after the phone call, this person goes that we are not really sure whether that person goes because of the phone call,
because it might be that they are just both interested in music by default.
So it's kind of a bias that is caused by this concept of Homophily.
So if we really want to quantify the influence of a phone call and which is the kind of treatment in our case, then we need to separate them.
So this is the other scenario that we would like to consider if all of them are kind of matched based on their interest.
So by default, they are kind of having the same amount of interest of attending the event.
And then in that case, the phone call or basically play the role of affecting the decision making and the most of the studies this this influence,
what we call is actually the combination of two things first, exposure. So I tell you the event.
Second, my experience will basically affects what you do in the future.
Usually, in most of the studies, we don't separate exposure and under the actual influence.
So that's also the case here. OK, so to do this, basically our idea is to kind of use an idea similar to a randomised experiment.
And so we do a matched sample estimation where propensity score matching sounds.
You might have heard about this concept. The basic idea is that the propensity score is the likelihood of being treated given a set of calories.
So in this case, the treatment is basically receiving a phone call.
The koalas in this case obviously would be the, let's say, individual preferences by default, how much they like music or something else.
So the idea here is basically to pair the individuals that have a very similar propensity score such
that we kind of mimic the treatment assignment in randomised experiments to remove selection bias.
So typically, the way that we match people based on demographic information, age,
gender like this stratification in this case, and we would like to explore some new options.
Basically, what we looked at is the review of the preferences of individuals through their mobile phone choices or mobility history.
So there is a series of review with preferences and economics that especially with business and the marketing,
which says that your preferences is sometimes reviewed by what you do, like the products that you buy, for example.
So in this case, we we basically look at the mobility histories, which means the frequencies of the people visiting different locations in the past.
And we hope that the fact that they visit different locations will kind of captured their interest.
Yeah. So is this because you didn't have information on observed demographics or this is in addition to the observed demographic?
So, so for us, we don't have demographics here.
That's true. Second, on demographics, they also have limitations.
For example, they are a information. They are not dynamic.
Uh, so uh, what we hope here is basically to see whether this kind of a more dynamic
representation of the preferences can lead to a better matching based method.
And I think we have partial demographic information in this case.
Maybe gender, I'm not sure. So we did some simple comparison to see whether there was a difference or not.
But the main motivation of using this kind of a new koala is, in some sense,
is to actually condition the matching based on the actual behaviour of the person in the past, rather than some static information like demographics.
And so obviously, individual mobility history is is very.
So how do you sort of decide how much further back in the past?
Oh yeah. So in this case, we just look at the past six months.
So here you can see basically, we have this little cells so that they are basically like a cell towers.
So we just look at the frequency of the president visiting different places.
So you can see in this case, the press. And on the left, he's my explorative because he goes to different places, more or less equal frequency.
The president on the right, he's more exploitative because he has backs back to single location that he likes.
So this gives us an idea of how to basically link this type of behaviour,
which is reflected in the past history to the likelihood of doing something in this case that I can attending the event.
So but obviously, there's no good answer how much you should look back so that you capture the the kind of genuine behaviour of the person.
In these kind of spatial things, did you focus on weekend time if the person on the left, maybe their job just takes them around?
It's mostly weekend weekends. Yeah, it's mostly weekend mobility.
Yeah, which we hope captures the later related activities.
And so at the same time, we also want to study the effect of influence with respect to the communication distance.
So I introduced the concept, the Hope Index,
which is like how far away in some sense you are from attending because maybe you don't receive a direct information,
but maybe you receive the information from a friend who received a phone call from the person who attended and maybe the information got propagated.
So that's in fact the main motivation of the study.
For that reason, we basically have one treatment group for each hope index.
So that means for people who receive the phone calls directly from the attendee,
we basically put them as a treatment group and then we take a we construct the
corresponding control group from the people who are outside of the cascade,
but conditioned on the fact that the propensity score would be similar based on their past mobility history.
So we just pair them like that.
And if we do that, then basically the difference in future adoption rate, we establish upper bound of social influence.
In fact, after you control the whole monthly basis, is this.
So wait, so this only works if you have.
The same call records from the same company for everyone, right?
So like if I if I call you and you call her, but her is, but she's not in our phone company, you can't see what she's doing afterwards.
Yeah, yeah, definitely.
So the hope is that, well, in this case, because there is only a single network provider in the country, also with high penetration rate.
But but in a country where you have more than one network provider, then that will usually what we see is true because I think in that case,
most of the providers would only have a market of 20 30 percent of the people.
So it's kind of the it's larger scale than surveys, but still it's a kind of a biased in some ways.
So this is only based in Andorra and Andorra. There's only one provider.
So mostly mostly, yeah, we have people from France and Spain, but mostly Andorra.
OK. Yeah. Yes. And that's it connects to that.
To do this, people say, You know what? You can have information on my call data or, uh, so could you friend again?
These people give permission? Oh yeah. Well, yeah.
The assumption is that when they basically signed a mobile phone contract and then they give the permission to these kind of studies.
But I think that's a there's a big question that we can discuss separately because that's related to to the ethical concerns and the privacy.
Yeah. And I'm quite interested.
I think an implicit assumption you're making is that when somebody makes a phone call, we just assume that they are talking about the concept.
That's right, because you can never actually track the content. So you don't know if actually they talked about the event or not.
So you're there and we are just absolutely OK.
Yeah, which is kind of one of the limitations that we can talk in the end because you don't carry out the survey.
Therefore, you don't know exactly what I mean. You can't track the the content of the course.
So, yeah, uh, so it's an upper bound of social influence because obviously there are many different observe the variables that may affect adoption,
such as like offline TV advertisement or, you know, everything that you observe on the street or something like that.
And so, uh, so yeah.
So here I said, I said that we we have one treatment group for each hoping that because we want to understand who has this influence, a difference.
Uh, for for people who are of different distance from the original attendee.
And then basically we have this uh uh and uh, in fact, a treatment effect for each hope, uh, as I just defined.
So what we see here basically is a curve where the access is to help index.
So that means the, uh, distance away from the initial attendee.
The y axis is the difference is the difference in the likelihood of attending the event in the future, uh,
divided by the likelihood of attending and by the people in the control group, which is basically estimated using a logistic regression.
So that basically means this number here means that if you received a phone call directly from an attendee,
then you get one hundred and fifty percent more likely to due to adopt it in the future compared to a person who who has not been influenced.
It's interesting that we see it's obviously we see a positive effect of social influence that's kind of expected.
Uh, but it's mostly a dramatically for the direct contact, which makes sense.
So if we receive a direct phone call, then then then that presumably gives a strong, uh, influence.
But we also see that this effect remains significant for people who are further away.
So we are mostly talking about a blue curve here for the moment.
So you see, that is it remains significant.
Even two, three or four hops away in this case, which indicates that the influence of the initial adopter reaches far beyond the immediate circle.
It can even influence people who they probably don't know.
Uh, so uh, do you understand the robustness of the results?
We also did some tests. Uh, the first is basically to do exactly the same thing, but without controlling for Homophily.
So that means we don't match people based on the past history.
If you do that, you observe this purple curve is a random matching.
You see the overestimation and the overestimation is mostly due to Homophily, and this is almost twice as much.
And this is similar to the founding in this paper, uh, in 2009.
The other thing that we did is basically to do a shuffling test of the Hope Hop Index,
so if the president has a direct, uh, contact, we randomly change that number from one to five or six like that.
And after that, we again do the magic.
So the purpose of doing this is basically to see whether some of the variables were related to the decay patterns that we see.
But the red curve basically shows that there is no such pattern.
So the observed results is not likely to be mainly driven by something that we don't observe.
So to understand how these patterns decay, so what is the mechanism that lead to this decay effect of social inference?
We do the simple Bayesian model to to to understand it.
So the basic idea is that in a communication cascade, an individual will basically updates for estimation of the product.
So the product is defined that broadly, so whatever that you want to adopt,
it can be a new app or it can be a piece of music or whether you want to attend the event or not.
So an individual will update our estimation of the product characteristics.
So what is the event like? Things like that after they talk to you, the people around him or her.
And then after that, they will dynamically update the estimates by aggregating information from the neighbours.
So then we assume that this estimation, together with the president's own preference by default,
will basically form an evaluation of of the person for the event.
So if the present estimates,
the event is kind of like a pop music event with a huge crowd and his own preference is basically he likes these large scale events.
And then he put together these two pieces of information to form his own evaluation, which is this is the event that I like to go.
And then he will basically make the adoption decision following a simple binary probability distribution.
And so the estimation is basically done like here.
So Greg basically received a phone call from Bob,
and then he will basically updated his estimation based on the evaluation of Bob and the fact that he knows that Bob likes certain things.
And then basically, this will keep going, keep going like that.
And and then after a while, we could basically see the estimation of the event by all the individuals.
And now we can see how this estimation basically change when we move further away from the initial adopter.
So what we measure here is the difference in the estimation between the individuals who are in the Cascades and the initial adopter.
So the x axis here is again the distance, the hope index. The Y is basically the mean squared difference between the evaluation.
What you see here is that this difference increases as the Hope Index increases.
So this could mean the estimation of the event become less accurate and contains mobiles because the estimation of individuals contain bias.
And this bias can accumulate along the information cascade.
And also the fact that if you receive inference from multiple people can also have this aggregation effect.
So in the end, people here they have a less accurate estimation of the event,
which might be related to the decline pattern of the inference in this case.
But this is still something that we're wanting to investigate further. So it's kind of like a conjecture that we hope to test further.
So the main findings in this study is that first, we we try to use the revealed preferences instead of static demographics as covariance,
uh, to, uh, quantify the inference in matching based estimation.
Uh, and and we think this can actually overcome a lot of difficulties in traditional our city based approaches because,
uh, sometimes, uh, for privacy reasons, you don't have the corroborates as you like.
Sometimes you have, but they remain static, so you can't capture the dynamic changes.
If there are, uh, the empirical finding is that we observed these long range effects of social influence, uh,
which may have implications in scenarios like our marketing or public health management when you try to basically use a.
Online communication to influence people's decision making,
all these situations and the limitations are mostly the identification of the initial
adopters is not precise because we don't really know whether the person at hand or not.
We just know that the person had some activities within the very small range from the venue of the event, but we didn't actually ask the people.
So we don't know whether they actually attended or they just passed by Keith.
So to come back to this point about matching was on on static demographics versus the more dynamic ones dynamic characteristics,
I mean, to some extent, dynamic attributes, there's a certain androgyny do there because things that are changing are they
could be changing because people are themselves being influenced themselves.
And we don't really observe that experience. So how do we?
So while I'm sympathetic to your point,
I also kind of wonder about that issue of indulgent idea of the fact that mobility itself reflects influence processes that are happening.
I go to this museum where someone told me to go to. Yeah, I think that's true.
I didn't present a result where we basically compare the two different matching wines based on demographics.
The other is based on demographics plus the mobility history.
And the results are mostly similar, which makes us think like the mobility histories contain the information of the demographics in some sense.
But this by itself is a very interesting question to ask,
like whether these observe the behaviour to which extent they captured the static attributes that we use in the traditional case.
But more importantly, if you are not allowed to collect these kind of demographics, then then then these can be more useful.
And other obvious things is that the dramatic exists multiple treatment effect where you receive multiple phone calls.
But right now, the distance that we define is basically the shortest distance to the attendees.
So. So obviously, that's something that we can do further.
But the main idea is that given the social network in this case, we want to see how this influence payroll and the how it can propagate, basically.
But in some cases, you don't observe this communication network.
But we just observe that the adoption behaviour of people so they decide to do something if.
Yes. So could you speak a bit more about how the estimate of the product was done because you calculated it means great difference?
So I guess these estimates were actual numbers and what went into the calculation of these?
Yeah, so so do we initialised as following a certain distribution.
And then after that, let's say, if you called me, then basically you will have your estimation, which leads to your your evaluation.
And we also assume that each person has the initial vector of preferences.
So based on what I receive from you, I will basically just use a baseline rule to compute the posterior of my estimation,
conditioned on the fact that I observe the information from you also.
So it's basically the posterior is basically the prior proportional to the prior times.
The likelihood the prior is basically my original sorry, the prior is basically the estimation from the past timestamp.
The likelihood is basically what is the likelihood of this given estimation, such that it leads to the information that I received from you?
So you just a simulate all these quantities by putting distributions on top of them and then you just compute.
This estimate is sort of an average of the vector is it's a vector.
Is it a vector? Yeah. Yeah, OK. And then this is basically a square that is just a difference between the vector.
Yeah. So the second question that we want to ask, which is just kind of conceptually the reverse of the problem,
if you observe some and adoption actions or whatever actions, what could be the opposite of the social network that lets you these actions?
We will use a slightly different framework here, which is based on game theory.
So we are going to make a small transition here. But the conceptual, uh, clustering is the reverse of the first one that we ask.
So let's start with some simple examples consider a group of students making choices on an educational effort.
So how much time you use? You want to put just two to a certain study, so they will basically follow a number of rules.
The first rule will be the the making effort is costly, obviously for me, but I will benefit from my own efforts, obviously.
And in this case, I also benefit from my friend's effort because it's a collective study.
It's, of course, projects like that. So if we have these kind of rules, then the president will tend to put more effort.
The friends of the president put more effort. So one scenario could be this where the colours divide how much effort they want to put in.
So you see the president here, it was a lot of effort because many of his friends put a lot of effort, and the opposite is true for this blue guy and.
A second example is to consider a group of students making choice to buy a book, whether each individual wants to buy a book or not.
Obviously, in this case, buying a book is costly.
I cost the time and money, so if a friend of mine will buy, then I will not buy based on the assumption that I can easily borrow.
But even now, my friends will abide by it because I definitely need the book.
So if we have this kind of rules, then we are likely to end up in a situation like these.
The right guys decide to buy a book because none of their neighbours decides to
buy and the Brueghel they don't buy because at least one neighbour about the book.
So this is another scenario.
Both of the scenarios you can see that the existence of strategic interactions between people, which can be modelled as games.
Game theory is basically a mathematical models of a rational decision making between individuals,
and usually it contains key concepts such as a player actions and actions kind of binary, whether by a book or not.
It can also be continuous, like the amount of effort that you put, and the payoff is basically how much reward you got for your action.
What is so all the these concepts they remain in what we call on game social networks,
but for the concepts here we have an additional information, which is the interaction network.
So friendship network, for example. So the interesting idea here would be to see how they're in.
The virtual actions can be related to the structure of the network.
So I can give you an example. In the previous cases, if you are central in the network, you are well connected,
then obviously that will affect how much effort that you're put in projects or whether you are going to buy a book or not.
So the relationship between the individual decision making and the structure of the
network is the most interesting aspect in these models of the games on networks.
And obviously, the basic assumption is that the payoff of one individual depends on her action, but also the actions of the neighbours.
So the two things that we talked about are actually examples of what we call strategic accomplishments and substitute.
So I think this is quite a self-explanatory. So there are many studies dedicated to this feud, which is a subject of economics.
And if not, people look at the equilibrium of games played on networks and on a given or preferred network.
They're mostly interested in how action and the payoff depends on the network structure.
Uh, in computer science, the same ideas is studied under the name of graphical games.
Uh, what they're interested in is mostly to develop algorithms to compute the equilibrium in the computational sense.
And so what we have more interested in this work is a reverse problem, which is trying to infer the network given the conditions that we observe.
So we don't assume that we have a network,
but we assume that the people play games in the hidden network and then we want to basically recover that structure.
You can find a lot of examples. We observe individual decisions, adoptions, but not social networks.
We observed the research and development activities of firms,
but we don't observe the collaboration network of firms or policies of countries, but not the political alliances.
So obviously, the the difficulty here is the complexity of the network, which makes the inference more difficult.
As a result, we have to kind of put some structure to the game.
Otherwise, it would be very difficult to make any inference the specific structure.
I mean, the the broad definition could be the payoff of a player UI is basically a function of his own action A.I.
Which are the actions of his neighbours in the observer network or in this case,
we can say is observe the network and then the connectivity, basically.
So one particular formulation of the payoff is this linear quadratic model.
It's quite easy to understand.
Here we have individual actions A.I. and then we have this marginal benefit by which basically decides independent from independent from the others.
If I increase my action, how much of a benefit I would get. And then we have this network factor beta in front of this term.
So this time we can basically. Think about is the eight times the summation of the neighbours action,
so you can clearly see that the first two terms corresponds to a kind of individual effort.
This is the individual benefits this is the cost is an active squad's time and then this training is basically the network effect.
So if you have a lot of people who are your neighbours and they they all have a very high age,
then you know, if you put a higher rate than it would increase your own utility.
So that's basically one specific model that we use.
And why do we choose this specific function, payroll function first?
It's a continuous. It can capture continuous actions.
That aid doesn't have to be discrete or in many cases, the A's are assumed to be discrete in the literature.
Also, it's very easy for us to capture both strategic accomplishments and the substitute.
You just need to choose a positive beta or negative beta, the negative beta,
which basically mean that there is a kind of a negative network effect and this is a simple quadratic model,
but it can also be used to approximate the more complex nonlinear payoffs.
So that's also makes it general. And this is also that while adopting the model in the literature of games on networks again,
we have a lot of examples that I just gave before that these games can think about educational
efforts or collaboration or even individual mobility choices in the context of urban dynamics.
So let's focus on the most important advantage of this specific model in game theory were mostly interesting equilibrium.
So what is the kind of a stable situation where a person will not tend to make a change of his action, if not all of his neighbours, which ends?
So the concept of national equilibrium is to capture this stable situation.
In this case, the equilibrium is easy to derive.
We can simply take it the first order condition of stability,
so we take the derivative of this utility with respect to the individual action, and then we end up in the equation here.
So B here is basically a vector of the marginal benefit if you remember the A's of active actions.
So you see that the actions A's basically the inverse of this matrix times B.
And so we need a few assumptions to to guarantee that this inversion exists,
which is basically the spectral radius of this matrix is smaller than one.
And the spectral radius is basically the largest single the value of the of the matrix.
If that's the case, then you can guaranteed a matrix.
Inversion exists, and the equilibrium is unique and unstable, so that's just a technical conditions.
But if we observe this equilibrium more carefully, we can we can find something interesting.
This inversion can be rewritten as even if some of the terms here, so be it.
And this is closely related to a concept in network science,
which is called the voltage centrality that just counts the total number of works from one single person to anybody in the network.
So and the interesting thing here is that if you look at the payload function here,
it looks like this pair of interdependency only existing, well, hot neighbour.
But if you look at the equation here, actually, you see that under the equilibrium,
this pair of dependency spreads indirectly through the whole network, which is something interesting to observe.
And you can also have some other interpretation far more signal processing viewpoint.
But I will skip that because probably that's not very easy to explain in the short period of time.
But under this model, we basically come up with a learning algorithm that helps us to basically infer the G from the air.
So that's the the the idea that we had from the beginning, and we we basically consider K independent games.
All of them have different marginal benefit vectors, so you can think about the adoption of different types of products.
The marginal benefits for each of them will be different for individuals.
Therefore, the equilibrium actions will be different, but the network is assumed to be the same.
So we. Try to infer the network structure G and together with the marginal benefit to be given only the Action A and the parameter beta.
What we do is to solve this following optimisation problem.
The first to here we can see is just a condition that is matched when the equilibrium of the action is observed.
So you want to minimise this term so that it basically means that your actions close to equilibrium, then we want to put some other conditions on.
The variable that we want to optimise for the G is basically the network structure.
So we want it to be symmetric non-active and then also constraint on the total sum of the weights of the edges.
This just guarantees that the variable that we solve in the end is a valid graph topology, a structure.
We also need some constraint or prior information on this, be the marginal benefits.
The simple thing that we consider is, again, an idea taken from this idea of Homophily.
So two people are likely to form a link if they have similar characteristics.
This characteristic here is, in fact, that's the marginal benefit. So you like music?
Therefore, taking certain actions will lead to a higher power, for example.
So if we think of this, uh, marginal benefit as a single value, let's say, instead of a vector,
we just think of either like a single value and then we represent that value as a bar in a network.
So the the the bars that are upwards are positive, the blue ones, they are negative.
So in this case, because two people will form a likely to form a link if they are marginal, benefits are similar.
Therefore, if you look at this information, which is the marginal benefits on top of this network,
you will see that the transitions of these values will be kind of smooth across the edges because
that's based on the assumption that a link will only form between people who have similar attributes.
So in computer science, you can use a term which is this thing based on what is called a passive matrix of the network to quantify.
This is basically say that if there is a connexion which is non-zero, then I want beyond Vee-Jay to be similar.
So in our context, we use this term here, which basically means we assume a kind of a homogenous distribution of the marginal benefits.
And then after we have this term, we can basically solve this problem, uh,
using specific computational methods, uh, which I will probably not talk too much.
And basically, it's you have this adjointe, a variable GMB, which leads to a non convex optimisation,
but you can use the alternating minimisation to solve all both of them iteratively.
If I'm just, like, probably over oversimplify a lot of this, but just because not yet, anyways.
So part of it is that you have the same network, but your training algorithm, which is there's a variation in the marginal benefit of different.
Yeah, different. Yeah, that's right. So you're saying I have the same network many, many times, but yeah.
Yeah. And then I'm trying to guess a person's position. Network.
Yeah, that's right. Yeah. It can be extended to cases where networks are changing.
But right now, we just consider six to topology, but a different marginal benefits.
And did you put any constraints on the different types of networks, like the topology of the networks?
That's a very good question. Right now, we don't because this constraint is very general.
It's the basic constraint that guarantees a value, the network topology.
You can put things like a degree distribution or other things,
which we studied in the experiments, but now we don't put them in the constraint, the explicitly.
You can if you have some, you know, prior information about something and then you try to put that as a constraint.
Uh, the basic intuition is that if this spectrum radius role Beta G is zero, then obviously, you know,
you don't have any information of the network from a because you just got a minus B, right?
So so there is no hope that you can infer the G from from that.
But if this a b g becomes a bigger and bigger, then obviously a will containing the information from the network.
The extreme case, if Peter G has a radius of one,
then we can work out that this action is proportional to the eigenvectors ontology of the network and that eigenvectors.
Ontology, in fact, has a strong information about the.
Activity of the network, so that that's kind of an intuition, why from action a we can go back to to get to the topology, see.
So we tested this idea in both the synthetic and real world, the data.
So these are basically the different types of pathologies that you mentioned.
These are random graph models that are typically studied in network science.
They basically capture different types of activities. And what we do is basically to first to generate a grant to run the network.
Then we basically use this idea to compute an action based on a simulation of the amorphous marginal benefits,
which is assumed to be a Gaussian distribution here. So we got the G.
We compute the B following these and then we got a.
And now we just use the algorithm to infer GMB from a that's the basic procedure.
And then we basically compare it with some other, like a well known methods in computer science, mostly, and they evaluate the performance.
And this is one set of experiments that we do. Each figure is basically one type of random graph.
What we observe here are the x axis is the spectrum radius of the Beta G matrix, and the Y is the evaluation,
which is the similarity between what we infer and the ground shows that we start with.
So you can see that when we increase the spectral radius, the performance increases, which follows the intuition that I just explained.
And then. The method that we have here in general achieves a better performance than a simple baseline, which is sample correlation.
And also another well-known method in computer science, which is called the graphical lasso.
I'm not sure if you're familiar with sound,
but the idea is to see whether this new formulation can actually improve the performance compared to some existing models.
The more interesting question in this case would be whether the algorithm works equally well three and four different types of graphs,
like graphs of different kind of activity. So to do that, basically, we test it for these three different types of graph.
Each of these running graph models have parameters to decide that the densities of the edges.
So, for example, in others or any network, edges are created independently with a given probability distribution.
So if the P is high, then the network becomes dense.
Another example would be this Barbash Aabot network,
which is a generative model that each time you just add a new vertex and that connects the new vertex to the existing nodes in the graph.
So if you decide every time you put new nodes,
that means every time you just add new edges and the rule is that you only
connect yourself at the new nodes to the notes that are already well connected.
So that in the end, you have these preferential attachment.
So they are just different networks.
But what we observed here is that when these parameters are high, which leads to denser networks, the performance drops.
And one reason for that could be if you have a very dense network,
then the Connexions basically have this influence, which are kind of mingled against with each other.
So it becomes very difficult for you to recover from just the observed actions.
If the network is sparse, then the likely correlation between the actions indicates more the existence of a link.
So that's the basic intuition. We also did some real world data to infer so.
In this case,
it's an inference of a social network structure where the data basically are the almost two hundred households in a village in rural India.
This is one classical study economics and the games in this case are basically the number of facilities adopted by each household.
And so it's arguably a and strategic accompaniments game because of the conformity to social norms,
which basically lead to higher benefits in the village. And then we basically take the data, which is the actions,
and then gets the social network and to compare that with self-reported the social network to see how it works.
So in this case, we can get a good performance better than the baseline.
The other example is a dream for a trade network. So that's a similar idea.
But the slight the difference is that in this case, it's more like a strategic substitute instead of a compliment.
But the basic idea is to observe actions which are important Oxford X worth of countries,
and we want to see whether they're looking for help us to infer a trade network that we don't observe.
So that's basically a high level idea. So again, here, I think the interesting thing would be the application in the practical scenarios.
If you only observe the actions by nodes, the network, then obviously if you can infer the network,
you can use it to detect the communities, which is useful for stratification.
You can compute the centrality measures which can help you to design targeting interventions,
and you can basically achieve planning objectives by looking at the network.
So the two examples here could be if you want to maximise the total utility of the players,
then you can adjust the marginal benefits that you learnt, uh,
so that it is proportional to the eigenvectors ontology,
which is proving this paper you can think about in reducing inequality between different players like different communities in the city.
Uh, by adjusting the connexions between the different communities after you interact so you can encourage new links and discourage existing links.
There are several open issues here.
The determination of the parameter data, um, the theoretical understanding of the algorithm when it works with what guarantee,
that's more like a, uh, a guarantee that we would like to have so that we can actually apply it in a real scenario as.
Then obviously other payroll functions or applications.
So the high level idea here is kind of opposite to the first problem that I talked if we observe certain actions.
Can we try to basically go back to infer the hidden links between them?
So these two basically combine together and in a sense,
that I think collective decision making is key to understand the behaviour and the
network based on learning can provide some natural models and to us to do that.
The caveat here is more like the learning and inference they need to be done in combination with social series for better interpretability.
Otherwise, they just become a computer science exercise without the implications in policymaking.
More importantly, you need to think about the ethical implications and consequences when you build models to understand human behaviour.
It might lead to marginalisation of some disadvantaged groups in some sense or situation, so.
And you need to be basically extra careful when you make these modelling assumptions,
but that basically needs help from social scientists to work in a more collaborative setting.
And so finally, there are a few papers and the co-authors of this paper, so we start out and thank you for your attention.
Take the question. Oh, you can trade off that.
And one of my well, just for clarity sake, if you wanted to infer the the the location of someone in the network, do you using your method,
you need to know what the network like topology is first to be able to identify where they're in that point,
you just because your gains held topology constant. Right?
No, I think you just need to to observe these actions, which are vectors.
OK. And then basically, you get what is called adjacency matrix, right?
And that addresses a matrix supposedly captures the kind of activity pattern. So you don't need the you don't need the network topology eventually.
Yeah, that's basically what you want to infer. So who is just one individual location, but the entire topology of the network?
So yeah, so that in some sense,
I think the location of the network is doesn't matter that much because you can redraw the network in whatever way, right?
So so they just I think they depend on the specific layout of the graph, if you like.
But but the information is basically by the A's connected to be so whether there
is the existence of that link that's completely captured by the adjacency matrix.
So we infer that just from the electoral observation of actions.
OK.
And just following up on that, a lot of what we've been discussing lately is that with digital trace data, we we don't know what we're missing so far.
And this method seems like it could be one way to start getting at that in the context of social network data.
We could try. Yeah. Although this particular matter is based on the assumption of network games,
which means that the actions people take are kind of based on strategic interactions.
Some abilities, whether they. So there is an interesting example in urban dynamics that can feed this,
which is a think about artificial city, where we only have two locations wines to centre.
The other is the periphery.
Now everybody needs to basically decide how many times they go to the city centre for social benefits, like by interacting with down there.
So in that case, the number of visits is basically the action. And then you obviously want to visit more if you are central in the social
network because there is a high likelihood that you can target with more people.
So in that specific scenario, you can think of inferences the hidden social natural connexion from the action,
which is the number of visits to page to the city centre.
I guess if the digital traces can fit into something like that, like the fact that I move to a certain place,
this is likely to be affected by the fact that you are so gorgeous in place.
Then then it might be possible to do this because my action we're not just dependent on my own action, but also you actually let it make sense.
Yeah. All right.
Thank you for the talk. I was wondering about the first beach we're talking about on the network through telephone
if where you could insert some alternative demographics by just looking at how people call.
Yeah, yeah. Well, I think there are people who do that.
Uh, I have some colleagues who try to use communication patterns, mostly in what is called the ego network.
So it's just to me under the first hope neighbours of myself to even for demographics.
And you can do that with reasonable accuracy of what the results are still usually like between 70 and 80 percent accuracy,
even without making the link explicitly to demographics in itself will be interesting to maybe do some clustering on just the type of communication.
Yeah, yeah, yeah, definitely. I think these kind of predictions are based on that.
So, for example, females and males have different communication patterns during the weekdays on the weekends, so that's how they the predictor.
So getting back to your point, if you don't have demographics, maybe you can use that to predict and then use that to condition the matching.
But there is one actual stop in the middle that you don't guarantee that the prediction is perfect.
On the other hand, you can use social media activities to predict. I think Scott hail from the I did something recently.
And they just look at Twitter activities and they use that to predict demographics.
I think it's kind of similar idea.
So I'm wondering in your inference of the Netflix apology, do you have in this case, you had this kind of quadratic function?
Yeah, but I guess it's quite generally two different kinds of functions.
Yeah. So I'm yeah, I'm trying to understand perhaps variations, where have you thought or have you built?
Have you tried to do this with other functions as well to try and see how it, how it looks like?
Or or um. Yeah.
So the answer is that we haven't really tried the other health functions, too.
The thing is that the first we want wanted to be general enough.
Second, the equilibrium needs to be explicitly computable because we want to have this notion of natural Grootboom actions.
If you have, let's say, uh, arbitrary analytical function of the of,
as long as you can take the first or the derivative, you can you fit into the optimisation.
But in that case, there is no economic theory to guarantee that the equilibrium will be stable and unique,
which means you kind of lose something from the, uh, economic interpretation.
Right?
So one of the things that we've discussed a lot in the Summer Institute is is that some of these very detailed types of data that you've talked about,
for example,
mobile networks calling networks or other forms of of rich behavioural data are often in the hands of private companies and hard to get access to.
And while they're very they can shed light to new kinds of ways as you were in the dark,
perhaps you could comment a bit on on on your experiences trying to access these kinds of data, especially, for example, the mobile study in Andorra.
And what were the steps or the pathways that enabled you to get access to them?
Because I think it would be helpful for us here as well.
To know about that Andorra study, I think was based on kind of a contract signed between a few groups in the Media Lab and the government of Andorra,
because at the time they were trying to diversify the economy and then trying to attract more tourists, basically.
And now understand whether they can keep them to stay overnight so that they can, and they have some huge problems in terms of traffic jams.
So so they basically want to work with a few groups in the media lab to build the new models first to solve these problems.
But they also want to make Android like a place of innovation in Europe by testing new ideas like these and self-driving cars.
And that was like five years ago when they were trying to put some vehicles on the
street and then see how people react in that case because of that special relationship.
We got this access to data from the.
Telecom, Andorra, I think, and mostly what I know the way that you got access to this kind of data is through this kind of research contracts.
But I would say it's more and more common compared to 10 years ago, 10 years ago,
it was really very difficult because people do not understand whether it's safe to share it or whether they can actually get some benefit.
But nowadays, I would say specifically for mobile phone data,
it becomes more popular because more and more network providers realise that
there is a reasonably good way to share anonymized data for some benefits.
So, uh, I don't know if you know there is a dedicated conference called Net Mobile, which actually happens the week after next in Oxford.
So that's a dedicated conference for people working on mobile phone data.
So there you can see that they have all sorts of data from different countries.
But in general, I think the problem is that the reason why people do not necessarily want to share the data is because of these ethical concerns.
They are not sure whether it will be safe and what would be the best way to share what is the best way to anonymize.
If they don't know, then it becomes very difficult for them to share a name for your approach, tending to be difficult.
So I think the idea would be to I think people are convinced that they are helpful.
But now this means that the other side of the development needs to catch up,
basically to show that we can have safe and meaningful ways to share the data, which can help us to solve something important problems.
I think that can help us convince the data holder in this case.
But it takes time because I could tell you, if you compare 10 years ago and now,
10 years ago, maybe June, if only a few groups in the world that have this kind of data.
But now I would say much, much more common. Still, I think.
It's kind of a slow process in some ways.
So. I think you have a question regarding the network model that you that you showed before,
when I got that right with the inverse of the policy areas in the model that you get some kind of like the temporal process that I'm influencing,
like my network neighbours and like other neighbours.
And it also comes back to me, doesn't it like that? So in this case, if I understand your question, this is more like a one shot game.
So it's not a sequential game. So it's just like I just observed action where people do not know the decisionmaking, so the other people beforehand.
So they basically make simultaneous actions and the network is basically a network structure in a particular time.
OK, so you observe this simultaneous actions and then you in four network in a given point in time, but is not sequentially done?
But wouldn't I be like if I just solve the the inverse inverse term or I'd be there as well?
Like, uh, like, isn't that wouldn't it look modern?
Kind of like that. My effort depends on my effort somewhat. Yeah, you.
I mean, actually, it's like there is a loop, right? So your your efforts depends on the others and the others are depending on the third person.
It's like that. Isn't it only possible in time like this?
You just model one simultaneously is, uh, not necessary.
You can. You can basically have these examples that I presented at the beginning where basically we say
that say you are in a social network and now you know your neighbours and then in your mind,
you basically work out like what would be the equilibrium, right? If I do something, I can expect, what is the action right?
So if everybody just to if everybody's assumed to be rational,
they will basically compute this equilibrium in their mind and they would basically make a simultaneous action.
And then that's a gripping you observe, basically,
because the idea of recruitment means that if the others do not change, then I don't have the incentive to change.
Right. Yeah. But you can generalise, generalise into to a sequential setting.
I think where you say, OK, I observe the past joint decision of all the people and that may be the network attention the next.
Timestamp. Maybe the actions will depend on the actions in this new point in time.
Plus the game that played in the past, but not here so.
So I have another question about data collection, so one of the I mean, I think like network data are things that, of course,
are very exciting, but also not as as as widely available as as one would like, partly because they're difficult to connect data on.
And I am wondering if based on your examples, given that you do a lot of work on you use with networks,
are there kind of examples of good data sets that are also publicly available that that you know you'd like to talk or share?
Let us know about. Because I mean, this has been recently enough in college.
There was a workshop on, I think, a couple of years ago or last year,
which was on sort of the challenges of network data collection and the fact that there
are just so few available and often there are maybe very small samples if they are.
And so and you mentioned that now a lot more data sources are available, especially for networks.
So perhaps you could just give us more examples of that to leverage those that would be very helpful.
Yeah. If you if you talk about the like or, for example, real world social network data,
at least in the computer science literature, there are many, many repositories.
I would say you can find all sorts of networks in real world situations because
those are the networks that a computer scientists to test the algorithms on.
They can be static or they can be dynamic that can be directed to can be for all different types of applications.
I can share a few links, maybe. And the more difficult thing would be the data that you mentioned first, like the more private.
Yeah. Or data that are privately held by companies and governments.
That's more difficult and that's more difficult also because of the nature of the data, which has a like a higher risk.
If you think about the social network, the risks, it kind of lasts because you just have the Connexions.
If you don't have any other information on the nodes, it's just like a graph. It's a matrix doesn't really allow any identification.
But if you have a trace system, then that's a different story. So.
All right, well, we want to thank Joe Dunn for Joe and for speaking with us.
And if you have any more questions, open the door. Yeah.
OK, so we'll come to lunch if you have more questions. And after lunch is just continue to work on your group, projects will be sending out soon.
A little brief on what we would like in the presentations tomorrow.
So anyone have any questions? OK. Thank you.