Statistics seminars

Arka Banerjee introduces k-nearest-neighbor distributions as summaries of cosmological survey data that capture information beyond two-point statistics. They respond to moments of all N-point correlations while retaining a computational cost comparable to two-point measurements. The talk covers auto-correlations and cross-correlations in discrete and continuous datasets, their relationship to other higher-order summaries, and applications that improve detection significance or parameter constraints. It also explores modeling these distributions with methods already successful for two-point functions in real and redshift space.

Nassim Nicholas Taleb examines three technical problems in applied probability. First, he considers how errors in probabilities derived from fat-tailed survival functions can translate into disproportionately large, potentially unbounded errors in thresholds. He relates this to uncertainty in disease growth rates and forecasting. Second, he discusses what he regards as fundamental probability errors in psychology papers. Third, he examines how correlation and relative distances can mislead in the geometry of information, proposing heuristics for applying entropy-based methods to genetic distances. The lecture connects these examples through the consequences of using probabilistic quantities outside the conditions under which they are informative.

Victor Chernozhukov develops sharp bounds on omitted-variable bias for a broad class of causal quantities. The framework covers averages of potential outcomes, average treatment effects, average derivatives, and policy effects generated by shifts in covariate distributions within general nonparametric causal models. Using the Riesz–Fréchet representation of the target quantity, the analysis expresses the bias bound through the additional variation that unobserved variables introduce into the outcome and the relevant Riesz representer. Debiased machine learning then provides flexible statistical inference for the components of these bounds that can be learned from observed data. The approach connects sensitivity analysis for unmeasured confounding with modern causal estimation.

Alex Gittens studies how many data points must be labelled to fit a linear regression model with nearly the predictive power of a fully labelled dataset. Existing coreset and iterative approaches handle constant-factor approximations, but tighter approximations that improve with dataset size need different methods. The talk presents a polynomial-time algorithm that reduces label complexity by an additive O(sqrt(n)), using a sharp analysis of regression error for a coreset formed by backward selection.

Cognitive science and cognitive neuroscience researchers have agreed that the replication of findings is important for establishing which ideas (or theories) are integral to the study of cognition across the lifespan. Recently, high-profile papers have called into question findings that were once thought to be unassailable. Much attention has been paid to how p-hacking, publication bias, and sample size are responsible for failed replications. However, much less attention has been paid to the fidelity by which researchers enact study protocols. Researchers conducting education or clinical trials are aware of the importance in fidelity – or the extent to which the protocols are delivered in the same way across participants. Nevertheless, this idea has not been applied to cognitive contexts. This seminar discusses factors that impact the replicability of findings alongside recent models suggesting that even small fidelity deviations have real impacts on the data collected.

A major challenge for causal inference from time-series data is the trade-off between computational feasibility and accuracy. Motivated by process motifs for lagged covariance in an autoregressive model with slow mean-reversion, we propose to infer networks of causal relations via pairwise edge measure (PEMs) that one can easily compute from lagged correlation matrices. Motivated by contributions of process motifs to covariance and lagged variance, we formulate two PEMs that correct for confounding factors and for reverse causation. To demonstrate the performance of our PEMs, we consider network interference from simulations of linear stochastic processes, and we show that our proposed PEMs can infer networks accurately and efficiently. Specifically, for slightly autocorrelated time-series data, our approach achieves accuracies higher than or similar to Granger causality, transfer entropy, and convergent crossmapping -- but with much shorter computation time than possible with any of these methods. Our fast and accurate PEMs are easy-to-implement methods for network inference with a clear theoretical underpinning. They provide promising alternatives to current paradigms for the inference of linear models from time-series data, including Granger causality, vector-autoregression, and sparse inverse covariance estimation.

Motor learning is typically assessed in the lab, affording a high degree of control over the task environment. However, this level of control often comes at the cost of smaller sample sizes and a homogenous pool of participants (e.g. college students). To address this, we have designed a web-based motor learning experiment, making it possible to reach a larger, more diverse set of participants. As a proof-of-concept, we collected 1,581 participants completing a visuomotor rotation task, where participants controlled a visual cursor on the screen with their mouse and trackpad. Motor learning was indexed by how fast participants were able to compensate for a 45° rotation imposed between the cursor and their actual movement. Using a cross-validated LASSO regression, we found that motor learning varied significantly with the participant’s age and sex, and also strongly correlated with the location of the target, visual acuity, and satisfaction with the experiment. In contrast, participants' mouse and browser type were features eliminated by the model, indicating that motor performance was not influenced by variations in computer hardware and software. Together, this proof-of-concept study demonstrates how large datasets can generate important insights into the factors underlying motor learning.

Neuroscientists have many questions about connectomes that revolve around the ability to compare networks. For example, comparing connectomes could help explain how neural wiring is related to individual differences, genetics, disease, development, or learning. One such question is that of bilateral symmetry: are the left and right sides of a connectome the same? Here, we investigate the bilateral symmetry of a recently presented connectome of an insect brain, the Drosophila larva. We approach this question from the perspective of two-sample testing for networks. First, we show how this question of “sameness” can be framed as a variety of different statistical hypotheses, each with different assumptions. Then, we describe test procedures for each of these hypotheses. We show how these different test procedures perform on both the observed connectome as well as a suite of synthetic perturbations to the connectome. We also point out that these tests require careful attention to parameter alignment and differences in network density in order to provide biologically meaningful results. Taken together, these results provide the first statistical characterization of bilateral symmetry for an entire brain at the single-neuron level, while also giving practical recommendations for future comparisons of connectome networks.

Does that title put you to sleep or pique your interest? The goal of my presentation is to introduce a powerful yet under-utilized mathematical equation that is surprisingly effective at uncovering spatiotemporal patterns that are embedded in data -- but that might be inaccessible in traditional analysis methods due to low SNR or sparse spatial distribution. If you flunked calculus, then don't worry: the math is really easy, and I'll spend most of the time discussing intuition, simulations, and applications in real data. I will also spend some time in the beginning of the talk providing a bird's-eye-view of the empirical research in my lab, which focuses on mesoscale brain dynamics associated with error monitoring and response competition.

This research panel explores how large and unconventional datasets can produce high-frequency inflation forecasts. Its starting point is renewed concern about inflation following substantial monetary and fiscal stimulus. Alberto Cavallo presents research on real-time inflation measurement. Yves Lemperiere, Adam Rej, José Scheinkman and Michael Woodford join the discussion of alternative data and its economic and financial applications. The panel connects timely measurement with the problem of assessing inflation while conventional economic statistics arrive with a delay.

Complex systems can be modeled at various levels of granularity, e.g., we can model a person at the cognitive level, on the neuronal level, or down to the biochemical level. When multiple models represent the same system at different scales, we would like to be able to reason about the causal effects of interventions on each level in such a way that the models remain consistent across levels. In the first part of this talk, I consider which conditions must be fulfilled for two structural equation models (SEMs) to stand in such a causally consistent relation. In the second part of the talk, I present recent work on learning causally consistent SEMs across multiple levels, distinguishing between bottom-up (micro- to macro-level) and top-down (macro- to micro-level) approaches.

Fast computation often trades statistical accuracy for speed. In nearest-neighbor prediction, achieving optimal accuracy generally requires the number of neighbors to grow as a root of the sample size, creating a corresponding computational burden even with fast search. This talk shows how bias or variance corrections after data quantization or subsampling, together with black-box fast-search techniques, can retain accuracy while reducing prediction-time computation to O(log n). The analysis explains how much quantization or subsampling is compatible with optimal accuracy. Extensive experiments on large datasets from several domains test these theoretical insights. The talk draws on work with N. Verma and L. Xue.

Locality-sensitive hashing is widely used for high-dimensional nearest-neighbor search. This talk develops another view of hashing as a biased sampling method for density-estimation queries. Given a point set and a query, one may estimate kernel density by summing distance-dependent influence functions, or count points within a chosen radius. A linear scan is costly for large datasets and many queries. The presentation surveys recent methods that preprocess the data and use locality-sensitive hashing to construct unbiased estimators for these problems and their extensions. It covers joint work with Arturs Backurs, Piotr Indyk, Vishnu Natchu, Paris Syminelakis, and Xian (Carrie) Wu.

Nassim Nicholas Taleb examines distributions whose behaviour is dominated by extremes and tail events. He classifies these distributions and identifies circumstances in which familiar statistical tools become unreliable, including slow or problematic convergence of sample averages under the law of large numbers. The lecture questions the robustness of commonly used statistical procedures in fat-tailed settings, the reliability of frequency-based forecasting, and the use of past averages as guides to future outcomes. Taleb then develops implications for decision-making and the changes in method needed when extreme observations have disproportionate influence.

Worst-case bounds described as optimal can remain loose for the data encountered in practice. This talk develops distribution-specific analyses for local, nonparametric methods, focusing on nearest neighbors. The statistical results give closely matching upper and lower bounds for classification convergence for each data distribution, characterize metric measure spaces supporting universal consistency, and motivate a smoothness concept adapted to nearest-neighbor methods. The algorithmic results characterize the performance of tree-based nearest-neighbor search through the configuration of the data, with specializations to common forms of structure. The talk concludes with open statistical and algorithmic questions.

Nassim Nicholas Taleb develops two approaches to reasoning about extreme risk. In the first part, on the law of large numbers in the real world, he defines fat-tailed distributions and examines why conventional statistical procedures can perform poorly for economic variables. He stresses the much larger data requirements and the choice of estimators when rare observations dominate outcomes. The second part considers how to detect fragility in portfolios. Taleb describes fragility as sensitivity to volatility and argues for analysing the shape of an exposure and its response to shocks when reliable numerical estimates of tail probabilities are unavailable. The lecture connects limitations of statistical estimation with practical heuristics for identifying vulnerability.

Ariel Pakes introduces the foundations of demand estimation for differentiated products. Starting from individual preferences and choices, he explains how consumer heterogeneity can be aggregated into market demand and used to study prices, substitution and welfare. The lecture compares modelling products directly with representing them through characteristics, including observed and unobserved attributes. It examines how different assumptions about tastes generate substitution patterns, using examples involving cars and other differentiated goods. Pakes discusses logit models, vertical and horizontal differentiation, and the implications of demand assumptions for markups, competition and policy analysis.