Three-Toed Sloth

These are my preprints; also, publishers are to be destroyed

Attention conservation notice: Advertisements for myself and my co-authors. If these were of interest, you'd probably already have seen them on arxiv.

I don't seem to have publicized new papers at all this year. Except for the first, they're all working their way through the peer-review system.

CRS, "Comment on `Why and When ``Flawed'' Social Network Analyses Still Yield Valid Tests of No Contagion'", Statistics, Politics, and Policy 3 (2012): 5 [PDF reprint]

Abstract: VanderWeele et al.'s paper is a useful contribution to the on-going scientific conversation about the detection of contagion from purely observational data. It is especially helpful as a corrective to some of the more extreme statements of Lyons (2011). Unfortunately, this paper, too, goes too far in some places, and so needs some correction itself.

Comment: As you can tell, this is an invited comment on a paper by VanderWeele, Ogburn and Tchetgen Tchetgen, which is on VanderWeele's website.. It began life as my referee report on their paper.

Editores delenda sunt: The journal Statistics, Politics, and Policy used to be published by the Berkeley Electronic Press, but the title was recently taken over by De Gruyter. The latter did not, of course, devote any resources to helping me write my paper, or to ensure its scholarly merit (such as it might have), since peer reviewers and editors are unpaid volunteers. De Gruyter provided copy editing, which amounted to mis-understanding how LaTeX's hyperref package works and telling me to "fix" it, and not catching any of my actual mistakes (e.g., the editing fragment "could at be" on p. 2). For all this, they charge readers \$42 for a copy of my paper, i.e., \$14 per page of text. (Of course fees like that are really to force libraries to subscribe to the whole journal, for a more dependable revenue stream.) The experience left me feeling dirty, and not in a good way. Again, for-profit journal publishing is a racket and should be destroyed.

Georg M. Goerg and CRS, "LICORS: Light Cone Reconstruction of States for Non-parametric Forecasting of Spatio-Temporal Systems", arxiv:1206.2398

Abstract: We present a new, non-parametric forecasting method for data where continuous values are observed discretely in space and time. Our method, "light-cone reconstruction of states" (LICORS), uses physical principles to identify predictive states which are local properties of the system, both in space and time. LICORS discovers the number of predictive states and their predictive distributions automatically, and consistently, under mild assumptions on the data source. We provide an algorithm to implement our method, along with a cross-validation scheme to pick control settings. Simulations show that CV-tuned LICORS outperforms standard methods in forecasting challenging spatio-temporal dynamics. Our work provides applied researchers with a new, highly automatic method to analyze and forecast spatio-temporal data.

Comment: This descends from the old "Our New Filtering Techniques Are Unstoppable" paper, and so from the work on self-organization and prediction on networks, and ultimately from the last chapter of my own dissertation. One reason I use the sloth as an emblem is that I really am very slow this way. (Georg is not, as a comparison of this to his dissertation proposal will show.) All of the older methods had to assume that space, time, and the field being predicted were all discrete. The last point, the discretized field, was annoying, since the mathematical theory had no such restriction, and the discretizing data before working with it is dubious.

What Georg did here was figure out how, exactly, to use non-parametric density estimation and high-dimensional two-sample tests to work with continuous-valued fields. (We still need space and time to be discrete.) To prove consistency, we assumed a limited number of predictive states, but we let that number grow with the sample size.

We are indebted to Larry Wasserman for a great deal of advice, and most of all for the acronym LICORS, pronounced like "liquors".

Xiaoran Yan, Jacob E. Jensen, Florent Krzakala, Cristopher Moore, CRS, Lenka Zdeborova, Pan Zhang and Yaojia Zhu, "Model Selection for Degree-corrected Block Models", arxiv:1207.3994

Abstract: A central problem in analyzing networks is partitioning them into modules or communities, clusters with a statistically homogeneous pattern of links to each other or to the rest of the network. One of the best tools for this is the stochastic block model, which in its basic form imposes a Poisson degree distribution on all nodes within a community or block. In contrast, degree-corrected block models allow for heterogeneity of degree within blocks. Since these two model classes often lead to very different partitions of nodes into communities, we need an automatic way of deciding which model is more appropriate to a given graph. We present a principled and scalable algorithm for this model selection problem, and apply it to both synthetic and real-world networks. Specifically, we use belief propagation to efficiently approximate the log-likelihood of each class of models, summed over all community partitions, in the form of the Bethe free energy. We then derive asymptotic results on the mean and variance of the log-likelihood ratio we would observe if the null hypothesis were true, i.e., if the network were generated according to the non-degree-corrected block model. We find that for sparse networks, significant corrections to the classic asymptotic likelihood-ratio theory (underlying \( \chi^2 \) hypothesis testing or the AIC) must be taken into account. We test our procedure against two real-world networks and find excellent agreement with our theory.

Comment: Initially, I was unthinkingly sure the log-likelihood ratio would have a \( \chi^2 \) distribution. Writing this was most educational in many ways, and gave me a new appreciation of how interestingly weird network data really is.

Georg M. Goerg and CRS, "Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction", arxiv:1211.3760

Abstract: We introduce "mixed LICORS", an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data which can be used for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm Goerg and Shalizi (2012) from hard clustering of predictive distributions to a non-parametric, EM-like soft clustering. This retains the asymptotic predictive optimality of LICORS, but, as we show in simulations, greatly improves out-of-sample forecasts with limited data. We also implement the proposed methodology in the R package LICORS.

Comment: We as a community really ought to understand nonparametric expectation-maximization better.

Daniel J. McDonald, CRS, and Mark J. Schervish, "Time series forecasting: model evaluation and selection using nonparametric risk bounds", arxiv:1212.0463

Abstract: We derive generalization error bounds --- bounds on the expected inaccuracy of the predictions --- for traditional time series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space models. These bounds allow forecasters to select among competing models and to guarantee that with high probability, their chosen model will perform well without making strong assumptions about the data generating process or appealing to asymptotic theory. We motivate our techniques with and apply them to standard economic and financial forecasting tools --- a GARCH model for predicting equity volatility and a dynamic stochastic general equilibrium model (DSGE), the standard tool in macroeconomic forecasting. We demonstrate in particular how our techniques can aid forecasters and policy makers in choosing models which behave well under uncertainty and mis-specification.

Comment: Another chapter or two from Daniel's dissertation. Keeping our set-up close to what time-series-wallahs usually do — the ARMA alphabet soup plus state-space models, mean-squared error, etc. — was very much the goal of the project. (At the same time, assuming any of those models is ever correctly specified is silly.) Controlling mean-squared error in particular is why I've grown so interested in generalization error guarantees for unbounded loss functions.

I would say more about the economic implications of the results here, but we're preparing a separate paper on that, aimed at economists, and I don't want to blunt its edge.

20 December: more on Georg's thesis work.

Self-Centered; Enigmas of Chance; Networks; Complexity; The Dismal Science; Learned Folly