Live plenary talks

Video can be found here.

Abstract: Recent progress in machine learning provides us with many potentially effective tools to learn from datasets of ever-increasing sizes and make useful predictions. How do we know that these tools can be trusted in critical and highly-sensitive domains? If a learning algorithm predicts the GPA of a prospective college applicant, what guarantees do we have concerning the accuracy of this prediction? How do we know that it is not biased against certain groups of applicants? To address questions of this kind, this talk reviews a wonderful field of research known under the name of conformal inference/prediction, pioneered by Vladimir Vovk and his colleagues 20 years ago. After reviewing some of the basic ideas underlying distribution-free predictive inference, we shall survey recent progress in the field touching upon several issues: (1) efficiency: how can we provide tighter predictions?, (2) data-reuse: what do we do when data is scarce? (3) algorithmic fairness: how do we make sure that learned models apply to individuals in an equitable manner?, and (4) causal inference: can we predict the counterfactual response to a treatment given that the patient was not treated?

Thursday, August 27th, 0am and 3pm UTC in the "Conference hall"

Slides can be found here, video here.

Abstract: Quantum gauge theories are the most successful models for the description of nature at its fundamental level. Unfortunately, despite decades of intense effort, their mathematical foundations remain murky. In this lecture, I will present recent results yielding some first steps towards the construction of quantum Yang-Mills theories in space-time dimensions 2 and 3. I will focus on the probabilistic aspects, so no prior knowledge of QFT is required. This is joint work with A. Chandra, I. Chevyrev and H. Shen.

Monday, August 24th, 8am and 4pm in UTC in the "Conference hall"

Slides can be found here.

Abstract: So-called ‘citizen science’ is increasingly being employed for scientific endeavours and as a new data source. In this presentation I will describe some of our early efforts to utilise these data for statistical modelling. I will focus on three case studies: a more traditional example of using data obtained from local citizens, a more modern challenge of using data obtained from crowds and a slightly different example of using data from wearable sensors. In the first study, the derived stochastic model facilitates evaluation of the impact of various scenarios of climate change. In the second study, the Bayesian statistical models account for the proficiency of the citizens and the difficulty of the tasks in order to produce relevant ecological measures. The last study focuses on obtaining and understanding the intrinsic dimension of team sport. This work was undertaken with a range of collaborators who will be acknowledged in the presentation.

Monday, August 24th, 9pm in UTC and Tuesday, August 25th, 7am in UTC in the "Conference hall"

Video can be found here.

Abstract: Consider critical percolation, or a critical FK-percolation model in a half-plane. Color each cluster in green or blue independently with probability p or 1-p. How do we expect the probability that a given boundary point is in a green cluster of radius at least R to decay as R goes to infinity? We will try to describe some of the many ingredients that go into the determination of those critical exponents. This includes SLE paths and their generalizations, Conformal loop ensembles, Liouville Quantum Gravity ideas and features of stable growth-fragmentation trees. This is based on joint work with Jason Miller and Scott Sheffield.

Friday, August 28th, 8am in UTC and 3pm in UTC in the "Conference hall"

Slides can be found here, video here.

Abstract: Hierarchical latent attribute models are a type of discrete latent variable models that have been attracting increasing attention in educational, psychological, and behavioral sciences. The key ingredients of such models include a binary structural matrix and a directed acyclic graph specifying hierarchical constraints on the configurations of latent attributes. These ingredients encode practitioners’ design information and carry important scientific meanings. In exploratory latent attribute analysis, it is of great practical interest to develop methods to estimate the significant latent attribute patterns and the attribute hierarchy graph. More fundamentally, it is an important yet open theoretical question of whether and when the structural matrix and the attribute hierarchy are uniquely identifiable. In this talk, on the theoretical side, I present sufficient and necessary identifiability conditions for structured and hierarchical latent attribute models. Under the attribute hierarchy, the identifiability results sharply characterize the different impacts on identifiability cast by different attributes in the graph. The developed identifiability conditions advance the theoretical knowledge and provide insights into real designs of diagnostic tests. Methodologically, I propose a statistically consistent method to select significant latent patterns and estimate the attribute hierarchy graph in high dimensions. An application of the method to data from an international educational assessment reveals meaningful knowledge structures of the student population. This is joint work with Gongjun Xu.

Tuesday, August 25th, 10pm in UTC and Wednesday, August 26th, 1pm in UTC in the "Conference hall"

Slides can be found here, video here.

Abstract: Data lying in a high-dimensional ambient space are commonly thought to have a much lower intrinsic dimension. In particular, the data may be concentrated near a lower dimensional subspace or manifold. There is an immense literature focused on approximating the unknown subspace and the unknown density, and exploiting such approximations in clustering, data compression, and building of predictive models. Most of the literature relies on approximating subspaces and densities using a locally linear, and potentially multi-scale, dictionary with Gaussian kernels. We propose a simple and general alternative, which instead uses pieces of spheres, or spherelets, to locally approximate the unknown subspace. I will also introduce a curved kernel called the the Fisher–Gaussian (FG) kernel which outperforms multivariate Gaussians in many cases. Theory is developed showing that spherelets can approximate the unknown manifold with smaller covering numbers and the posterior consistency of the Dirichlet process mixture of FG kernels. Results relative to state-of-the-art competitors show gains in ability to accurately approximate the subspace and the density with fewer components and parameters. Time permitting, I will also present some applications of spherelets, including classification, geodesic distance estimation and clustering.

Tuesday, August 25th, 9pm in UTC and Wednesday, August 26th, 12pm in UTC in the "Conference hall"

Video is available here.

Abstract: A plethora of latent variable models are used to learn from data generated by people. Specific examples include the Bradley--Terry--Luce and multinomial logit models for comparison and choice data, the Dawid--Skene model for crowdsourced question answering, and the Rasch model for categorical data that arises in psychometric analysis. In this talk, I will present a class of "permutation-based" models that borrows from the literature on sociology and economics and significantly generalizes classical approaches in these contexts, thereby improving their robustness to mis-specification. The talk will focus on the mathematical statistics of fitting these models, and describe a methodological toolbox that is inspired by considerations of adaptation as well as computation. These considerations highlight connections between the theory of adaptation in nonparametric statistics and conjectures in average-case computational complexity. This talk will present vignettes from two papers, one jointly with Cheng Mao and Martin Wainwright, and another jointly with Richard Samworth.

Monday, August 24th, 10pm in UTC and Tuesday, August 25th, 6am in UTC in the "Conference hall"