April 20, 2016

In memoriam Prita Shireen Kumarappa Shalizi

4 September 1918 -- 4 April 2016

Posted at April 20, 2016 09:50 | permanent link

April 19, 2016

Course Announcements: Statistical Network Models, Fall 2016

Attention conservation notice: Self-promotion, and irrelevant unless you (1) will be a student at Carnegie Mellon in the fall, or (2) have a morbid curiosity about a field in which the realities of social life are first caricatured into an impoverished formalism of dots and lines, devoid even of visual interest and incapable of distinguishing the real process of making movies from a mere sketch of the nervous system of a worm, and then further and further abstracted into more and more recondite stochastic models, all expounded by someone who has never himself taken a class in either social science or any of the relevant mathematics.

Two, new, half-semester courses for the fall:

36-720, Statistical Network Models
6 units, mini-semester 1; Mondays and Wednesdays 3:00--4:20 pm, Baker Hall 235A
This course is a rapid introduction to the statistical modeling of social, biological and technological networks. Emphasis will be on statistical methodology and subject-matter-agnostic models, rather than on the specifics of different application areas. There are no formal pre-requisites, and no prior experience with networks is expected, but familiarity with statistical modeling is essential.
Topics (subject to revision): basic graph theory; data collection and sampling; random graphs; block models and community discovery; latent space models; "small world" and preferential attachment models; exponential-family random graph models; visualization; model validation; dynamic processes on networks.
36-781, Advanced Network Modeling
6 units, mini-semester 2; Tuesdays and Thursdays 1:30--2:50 pm, Wean Hall 5312
Recent work on infinite-dimensional models of networks is based on the related notions of graph limits and of decomposing symmetric network models into mixtures of simpler ones. This course aims to bring students with a working knowledge of network modeling close to the research frontier. Students will be expected to complete projects which could be original research or literature reviews. There are no formal pre-requisites, but the intended audience consists of students who are already familiar with networks, with statistical modeling, and with advanced probability. Others may find it possible to keep up, but you do so at your own risk.
Topics (subject to revision): exchangeable networks; the Aldous-Hoover representation theorem for exchangeable network models; limits of dense graph sequences ("graphons"); connection to stochastic block models; non-parametric estimation and comparison; approaches to sparse graphs.

720 is targeted at first-year graduate students in statistics and related fields, but is open to everyone, even well-prepared undergrads. Those more familiar with social networks who want to learn about modeling are also welcome, but should probably check with me first. 781 is deliberately going to demand rather more mathematical maturity. Auditors are welcome in both classes.

Corrupting the Young; Networks; Enigmas of Chance

Posted at April 19, 2016 16:00 | permanent link

April 15, 2016

"Network Comparisons Using Sample Splitting"

My fifth Ph.D. student is defending his thesis towards the end of the month:

Lawrence Wang, Network Comparisons Using Sample Splitting
Abstract: Many scientific questions about networks are actually network comparison problems: Could two networks have reasonably come from a common source? Are there specific differences? We outline a procedure that tests the hypothesis that multiple networks were drawn from the same probabilistic source. In addition, when the networks are indeed different, our procedure may characterize the differences between the sources.
We first address the case where the two networks being compared share the same exact nodes. We wish to use common parametric network models and the standard likelihood ratio test (LRT), but the infeasibility of computing the maximum likelihood estimate in our selected families of models complicates matters. However, we take advantage of the fact that the standard likelihood ratio test has a simple asymptotic distribution under a specific restriction of the model family. In addition, we show that a sample splitting approach is applicable: We can use part of the network data to choose an appropriate model space, and use the remaining network data to compute the LRT statistic and appeal to its asymptotic null distribution to obtain an appropriate p-value. Moreover, we show that while a single sample split results in a random p-value, we can choose to do multiple sample splits and aggregate the resulting individual p-values. Sample splitting is a more general framework --- nothing is particularly special about the specific hypothesis we decide to test. We illustrate a couple of extensions of the framework which also provide different ways to characterize differences in network models.
We also address the more general case where the two networks being compared no longer share the same set of nodes. The main difficulty in this case is that there might not be an implicit alignment of the nodes in the two networks. Our procedure relies on the graphon model family which can handle networks of any size, but more importantly can be put in an aligned form which makes it comparable. We show that the framework for alignment can be generalized, which allows this method to handle a larger class of models.
Time and place: 3:30 pm on Monday, 25 April 2016 in Porter Hall A22

Networks; Enigmas of Chance; Kith and Kin

Posted at April 15, 2016 12:00 | permanent link

April 01, 2016

You Think This Is Bad

Attention conservation notice: Note the date.

Any intelligent and well-intentioned person should have a huge, even over-riding preference for leaving existing social and political institutions and hierarchies alone, just because they are the existing ones.

Obviously this can't rest on any presumption that existing institutions are very good, or very wise, or embody any particularly precious values, or are even morally indifferent. They are not. It would also be stupid to appeal to some sub-Darwinian notion that our institutions, just because they have come down to us, and so must have survived an extensive process of selection, are therefore adaptive. At best, that would show the institutions were good at reproducing themselves from generation to generation, not that they had any human or ethical merit. In any case the transmission of any tradition by human beings is inevitably partial and re-interpretive, and so we have no reason to defer to tradition as such.

Stare decisis conservatism rests instead on much less cosy grounds: However awful things are now, they could always be worse, and humanity is both too dumb to avoid making things worse, and too mean to want to avoid making things worse even when it could.

The point about stupidity is elemental. If someone complains that an existing institution is unjust (or unfair, oppressive, etc.), their complaint only has force if a more just alternative is possible. (Otherwise, take it up with the Management.) But it only has political force if that more just alternative is not only possible, but we can figure out what it is. This, we a signally unsuited to do. Social science can tell us many interesting things, but on the most crucial questions of "What will happen if we do this?", we get either dogmatic, experimentally-falsified ideology (economics), or everything-is-obvious-once-you-know-the-answers just-so myths (every other branch of social science). "Try it, and see what happens" is the outer limit of social-scientific wisdom. This is no basis on which to erect a reliable social engineering, or even social handicrafts. When we try to deliberately change our institutions, we are, at best, guided by visions, endemic and epidemic superstitions, evidence-based haruspicy, and the academic version of looking at a list of random words and declaring they all relate to motel service. We have no basis to think that our reforms, if we can even implement them, will rectify the injustice that first aroused our ire, our pity, or our ambition, much less that the attempt won't create even worse problems.

Even getting our pet reform implemented is often going to be hopeless, because so much of our collective knowledge about how to get things done, socially, is tacit. That knowledge is not anything which its holders can put into words, or into a computer, much less into a schedule of prices, but is rather buried in their habits and inarticulate skills. Often these are the habits and skills of a very small number of crucially-placed people, who are, not so coincidentally, vested in the existing institutions and complicit in the existing injustices. Even more, these are habits and skills which only work in a particular environment, usually a social environment. The same people, asked to make a modified institution work, will be less effective, even hopeless. Throwing the bums out gets rid of the people who knew how to get things done.

Finally, and most crucially, think about what happens when existing institutions and arrangements are disturbed. Social life is always full of a clash of conflicting interests. (One of the few things the economists have right is that inside every positive-sum interaction, there is a negative-sum struggle over who gets the gains from cooperation.) When an institution seems settled, eternal, it fades from view, nobody fights over it. Its harsher lines may be softened by compassion (and condescension) on the side of those it advantages, or local and unofficial accommodations and arrangements, or even just from it being too much trouble to exploit it to the hilt. But question the institution, disturb it, make it obvious that there is something to fight over, and what happens? Those who gain from the injustice won't give it up merely because that would be right. Instead, they will press to keep what they have --- and even to claim more. Since this has become an open conflict of power, what emerges is not going to favor the lowly, poor and the weak. Or if that area of social life should, for a time, descend into chaos, well, the tyranny of structurelessness is real, and those who benefit from it are, again, those who are already advantaged, and willing to exploit those advantages. Things might be very different if people were able to agree on justice, and willing to follow it, but they are not.

To recapitulate: People are foolish, selfish and cruel. This means that our institutions are always grossly unjust. But it also means that we don't know how to really make things better. It further means that trying to change anything turns it into a battlefield, where nothing good happens to anybody, least of all the weak and oppressed. Since our current institutions are at least survivable (proof: we've survived them), it's better to leave them alone. They'll change anyway, and that will cause enough grief, without deliberately courting more by ignorant meddling.

Of course, people who actually defend inherited institutions and arrangements just because they're inherited, — such people can usually be counted on the fingers of one fist. Corey Robin would argue — and he has a case — that the impulse behind most actually-existing conservatism is a positive liking for hierarchy. This was an attempt at trying to construct a case for conservatism which would employ all three of Hirschman's tropes of reactionary rhetoric, but also wouldn't fall apart at the first skeptical prod. (Readers who point me at Hayek will be ignored; readers who point me at "neo-reactionaries" will be mocked.) What I have written is still an assembly of fallacies, half-truths and hyperboles, but I flatter myself it would still stand a little inspection.

Modest Proposals; The Running-Dogs of Reaction

Posted at April 01, 2016 00:01 | permanent link

Three-Toed Sloth