Inference with Social Network Dependence

I'm running behind as usual. I meant to post this right after the seminar, about two weeks ago.  Really interesting stuff -- spatial correlation due to network dependence.  A Google search will find the associated paper(s) instantly. Again, really good stuff.  BUT I would humbly suggest that the biostat people need to read more econometrics. A good start is this survey (itself four years old, and distilled for practitioners as the basic insights were known/published decades ago). The cool question moving forward is whether/when/how network structure can be used to determine/inform clustering.

Elizabeth L. Ogburn

Department of Biostatistics

Johns Hopkins University

Social Network dependence,

the replication crisis, and (in)valid inference

                                                               ABSTRACT

In the first part of this talk, I will show that social network structure can result in a new kind of structural confounding, confounding by network structure, potentially contributing to replication crises across the health and social sciences.  Researchers in these fields frequently sample subjects from one or a small number of communities, schools, hospitals, etc., and while many of the limitations of such convenience samples are well-known, the issue of statistical dependence due to social network ties has not previously been addressed. A paradigmatic example of this is the Framingham Heart Study (FHS). Using a statistic that we adapted to measure network dependence, we test for network dependence and for possible confounding by network structure in several of the thousands of influential papers published using FHS data. Results suggest that some of the many decades of research on coronary heart disease, other health outcomes, and peer influence using FHS data may be biased (away from the null) and anticonservative due to unacknowledged network structure.

But data with network dependence abounds, and in many settings researchers are explicitly interested in learning about social network dynamics.  Therefore, there is high demand for methods for causal and statistical inference with social network data. In the second part of the talk, I will describe recent work on causal inference for observational data from a single social network, focusing on (1) new types of causal estimands that are of interest in social network settings, and (2) conditions under which central limit theorems hold and inference based on approximate normality is licensed.

Network Data and Machine Learning

This just arrived, announcing an upcoming conference on the ML/networks interface.  It's definitely worth reading through the synopsis and topics and titles and authors.

"An exciting workshop on Machine Learning for Network Data is taking place at New York University on January 29. The event will discuss emerging challenges on generalizing the successes of image and speech processing to information domains with irregular structure. The workshop includes highlight talks by Yann LeCun and Brian Sadler as well as short talks by a collection of national leaders in the development of machine learning techniques for processing network data. The event is free to attend and open to the public but registration is required because of space limitations. Please visit the workshop site to access the registration form."

Wonderful Network Connectedness Piece

Very cool NYT graphics summarizing U.S. Facebook network connectedness.  Check it out:
https://www.nytimes.com/interactive/2018/09/19/upshot/facebook-county-friendships.html?action=click&module=In%20Other%20News&pgtype=Homepage&action=click&module=News&pgtype=Homepage

They get the same result that Kamil Yilmaz and I have gotten for years in our analyses of economic and financial network connectedness:  There is a strong "gravity effect" -- that is, even in the electronic age, physical proximity is the key ingredient to network relationships. See for example:

 https://www.sas.upenn.edu/~fdiebold/papers2/DDLYpaper.pdf

Maybe not as surprising for facebook friends as for financial institutions (say).  But still... 

STILL MORE on NN's and ML

I recently discussed how the nonparametric consistency of wide NN's proved underwhelming, which is partly why econometricians lost interest in NN's in the 1990s.

The other thing was the realization that NN objective surfaces are notoriously bumpy, so that arrival at a local optimum (e.g., by the stochastic gradient descent popular in NN circles) offered little comfort.

So econometricians' interest declined on both counts. But now both issues are being addressed. The new focus on NN depth as opposed to width is bearing much fruit. And recent advances in "reinforcement learning" methods effectively promote global as opposed to just local optimization, by experimenting (injecting randomness) in clever ways. (See, e.g., Taddy section 6, here.)

All told, it seems like quite an exciting new time for NN's. I've been away for 15 years. Time to start following again...

More on Neural Nets and ML

I earlier mentioned Matt Taddy's "The Technological Elements of Artificial Intelligence" (ungated version here).

Among other things the paper has good perspective on the past and present of neural nets. (Read:  his views mostly, if not exactly, match mine...)  

Here's my personal take on some of the history vis a vis econometrics:

Econometricians lost interest in NN's in the 1990's. The celebrated Hal White et al. proof of NN non-parametric consistency as NN width (number of neurons) gets large at an appropriate rate was ultimately underwhelming, insofar as it merely established for NN's what had been known for decades for various other non-parametric estimators (kernel, series, nearest-neighbor, trees, spline, etc.). That is, it seemed that there was nothing special about NN's, so why bother? 

But the non-parametric consistency focus was all on NN width; no one thought or cared much about NN depth. Then, more recently, people noticed that adding NN depth (more hidden layers) could be seriously helpful, and the "deep learning" boom took off. 

Here are some questions/observations on the new "deep learning":

1.  Adding NN depth often seems helpful, insofar as deep learning often seems to "work" in various engineering applications, but where/what are the theorems? What can be said rigorously about depth?

2. Taddy emphasizes what might be called two-step deep learning. In the first step, "pre-trained" hidden layer nodes are obtained based on unsupervised learning (e.g., principle components (PC)) from various sets of variables. And then the second step proceeds as usual. That's very similar to the age-old idea of PC regression. Or, in multivariate dynamic environments and econometrics language, "factor-augmented vector autoregression" (FAVAR), as in Bernanke et al. (2005). So, are modern implementations of deep NN's effectively just nonlinear FAVAR's? If so, doesn't that also seem underwhelming, in the sense of -- dare I say it -- there being nothing really new about deep NN's?

3. Moreover, PC regressions and FAVAR's have issues of their own relative to one-step procedures like ridge or LASSO.  See this and this. 

Neural Nets, ML and AI

"The Technological Elements of Artificial Intelligence", by Matt Taddy, is packed with insight on the development of neural nets and ML as related to the broader development of AI. I have lots to say, but it will have to wait until next week. For now I just want you to have the paper. Ungated version at http://www.nber.org/chapters/c14021.pdf.

Abstract:

We have seen in the past decade a sharp increase in the extent that companies use data to optimize their businesses.  Variously called the `Big Data' or `Data Science' revolution, this has been characterized by massive amounts of data, including unstructured and nontraditional data like text and images, and the use of fast and flexible Machine Learning (ML) algorithms in analysis.  With recent improvements in Deep Neural Networks (DNNs) and related methods, application of high-performance ML algorithms has become more automatic and robust to different data scenarios.  That has led to the rapid rise of an Artificial Intelligence (AI) that works by combining many ML algorithms together - each targeting a straightforward prediction task - to solve complex problems.  

We will define a framework for thinking about the ingredients of this new ML-driven AI.  Having an understanding of the pieces that make up these systems and how they fit together is important for those who will be building businesses around this technology. Those studying the economics of AI can use these definitions to remove ambiguity from the conversation on AI's projected productivity impacts and data requirements.  Finally, this framework should help clarify the role for AI in the practice of modern business analytics and economic measurement.

Commodity Connectedness

Forthcoming paper here. 
We study connectedness among the major commodity markets, summarizing and visualizing the results using tools from network science.

Among other things, the results reveal clear clustering of commodities into groups closely related to the traditional industry taxonomy, but with some notable differences.

Many thanks to Central Bank of Chile for encouraging and supporting the effort via its 2017 Annual Research Conference.

On the Identification of Network Connectedness

I want to clarify an aspect of the Diebold-Yilmaz framework (e.g., here or here).  It is simply a method for summarizing and visualizing dynamic network connectedness, based on a variance decomposition matrix.  The variance decomposition is not a part of our technology; rather, it is the key input to our technology.  Calculation of a variance decomposition of course requires an identified model.  We have nothing new to say about that; numerous models/identifications have appeared over the years, and it's your choice (but you will of course have to defend your choice). 

For certain reasons (e.g., comparatively easy extension to high dimensions) Yilmaz and I generally use a vector-autoregressive model and Koop-Pesaran-Shin "generalized identification".  Again, however, if you don't find that appealing, you can use whatever model and identification scheme you want.  As long as you can supply a credible / defensible variance decomposition matrix, the network summarization / visualization technology can then take over.

Network Tools for Understanding High-Dimensional Dynamic Models

The slides from my "overview" IMF talk two weeks ago proved popular, so here are some different overview slides on a different topic ("Estimating and Understanding High-Dimensional Dynamic Stochastic Econometric Models"), from my talk at last week's NYU Stern Conference on Volatility and Derivatives.

The Econ Ph.D. Placement Network

Speaking of interesting applications of network connectedness measures, check out Ricky Vohra's latest post in Leisure of the Theory Class. It reports on a fascinating paper by Chu Kin ("Roy") Chan, a talented undergrad who visited Penn for the past year. Congratulations Roy!

Measuring and Monitoring Connectedness

I'm at the IMF soon for a couple days of lecturing on Diebold-Yilmaz's Connectedness. It was published earlier this year, and preparing for the IMF jogged my memory: I brilliantly forgot to announce it in a No Hesitations post. Anyway, it's available at the usual online shops (where you can also read the T.O.C. and first chapter), or directly from Oxford University Press. There's also a web site. Special thanks to Eric Ghysels, who put us in touch with our fine editor, Scott Parris. 

Network Econometrics at Dinner

At a seminar dinner at Duke last week, I asked the leading young econometrician at the table for his forecast of the Next Big Thing, now that the partial-identification set-estimation literature has matured. The speed and forcefulness of his answer -- network econometrics -- raised my eyebrows, and I agree with it. (Obviously I've been working on network econometrics, so maybe he was just stroking me, but I don't think so.) Related, the Acemoglu-Jackson 2014 NBER Methods Lectures, "Theory and Application of Network Models," are now online (both videos and slides). Great stuff!

FinancialConnectedness.org Site Now Up

The Financial and Macroeconomic Connectedness site is now up, thanks largely to the hard work of Kamil Yilmaz and Mert Demirer. Check it out at http://financialconnectedness.org. It implements the Diebold-Yilmaz framework for network connecteness measurement in global stock, sovereign bond, FX and CDS markets, both statically and dynamically (in real time). It includes results, data, code, bibliography, etc. Presently it's all financial markets and no macro (e.g., no global business cycle connectedness), but macro is coming soon. Check back in the coming months as the site grows and evolves.

Network Estimation for Time Series

Matteo Barigozzi and Christian Brownlees have a fascinating new paper, "Network Estimation for Time Series" that connects the econometric time series literature and the statistical graphical modeling (network) literature. It's not only useful, but also elegant: they get a beautiful decomposition into contemporaneous and dynamic aspects of network connectedness. Granger causality and "long-run covariance matrices" (spectra at frequency zero), centerpieces of modern time-series econometrics, feature prominently. It also incorporates sparsity, allowing analysis of very high-dimensional networks.

If I could figure out how get LaTeX/Mathjax running inside Blogger, I could show you some details, but no luck after five minutes of fiddling last week, and I haven't yet gotten a chance to return to it. (Anyone know? Maybe Daughter 1 is right and I should switch to WordPress?) For now you'll just have to click on the Barigozzi-Brownlees paper above, and see for yourself.

It's interesting to see that Granger causality is alive and well after all these years, still contributing to new research advances. And Barigozzi-Brownlees is hardly alone in that regard, as the recent biomedical imaging literature illustrates. Some of Vic Solo's recent work is a great example.

Finally, it's also interesting to note that both the Barigozzi-Brownlees and Diebold-Yilmaz approaches to network connectedness work in vector-autoregressive frameworks, yet they proceed in very different, complementary, ways.