10th World Congress in Probability and Statistics

Plenary Lectures

Plenary Wed-1

Laplace Lecture (Tony Cai)

Conference
9:00 AM — 10:00 AM KST
Local
Jul 20 Tue, 8:00 PM — 9:00 PM EDT

Transfer Learning: Optimality and adaptive algorithms

Tony Cai (University of Pennsylvania)

16
Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this talk, we consider statistical transfer learning in various settings with a focus on nonparametric classification based on observations from different distributions under the posterior drift model, which is a general framework and arises in many practical problems. We first establish the minimax rate of convergence and construct a rate-optimal weighted K-NN classifier. The results characterize precisely the contribution of the observations from the source distribution to the classification task under the target distribution. A data-driven adaptive classifier is then proposed and is shown to simultaneously attain within a logarithmic factor of the optimal rate over a large collection of parameter spaces.

Session Chair

Runze Li (Pennsylvania State University)

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Plenary Wed-2

Public Lecture (Young-Han Kim)

Conference
10:00 AM — 11:00 AM KST
Local
Jul 20 Tue, 9:00 PM — 10:00 PM EDT

Structure and Randomness in Data

Young-Han Kim (University of California at San Diego and Gauss Labs Inc.)

4
In many engineering applications ranging from communications and networking to compression and storage to artificial intelligence and machine learning, the main goal is to reveal, exploit, or even design structure in apparently random data. This talk illustrates the art and science of such information processing techniques through a variety of examples, with a special focus on data storage systems from memory chips to cloud storage platforms.
Keywords: Information theory, noise, manufacturing, computer vision, distributed computing, probability laws.

Session Chair

Joong-Ho Won (Seoul National University)

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Plenary Wed-3

Wald Lecture 2 (Martin Barlow)

Conference
7:00 PM — 8:00 PM KST
Local
Jul 21 Wed, 6:00 AM — 7:00 AM EDT

Low dimensional random fractals

Martin Barlow (University of British Columbia)

7
The behaviour of the random walk can often can be described by two indices, called by physicists the ‘fractal’ and ‘walk’ dimensions, and denoted by d_f and d_w. This lecture will look at the tools which enable us to calculate these, and obtain the associated transition probability or heat kernel bounds. Three kinds of estimate are needed:
(1) control of the size of balls (2) control of the resistance across annuli, and (3) a smoothness result (a Harnack inequality). In the ‘low dimensional case’ the Harnack inequality is not needed, and (2) can be replaced by easier bounds on the resistance between points. Many random fractals of interest are low dimensional: examples include critical branching processes, the incipient infinite cluster (IIC) for percolation in high dimensions, and the uniform spanning tree. Critical percolation in d=2 remains a challenge however.

Session Chair

Takashi Kumagai (Kyoto University)

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Plenary Wed-4

IMS Medallion Lecture (Gerard Ben Arous)

Conference
8:00 PM — 9:00 PM KST
Local
Jul 21 Wed, 7:00 AM — 8:00 AM EDT

Random determinants and the elastic manifold

Gerard Ben Arous (New York University)

3
The elastic manifold is a paradigmatic representative of the class of disordered elastic systems. These are surfaces with rugged shapes resulting from a competition between random spatial impurities (preferring disordered configurations), on the one hand, and elastic self-interactions (preferring ordered configurations), on the other. The elastic manifold model is interesting because it displays a depinning phase transition and has a long history as a testing ground for new approaches in statistical physics of disordered media, for example for fixed dimension by Fisher (1986) using functional renormalization group methods, and in the high-dimensional limit by Mézard and Parisi (1992) using the replica method. We study the energy landscape of this model, and compute the (annealed) topological complexity both of total critical points and of local minima, in the Mezard-Parisi high dimensional limit. Our main result confirms the recent formulas by Fyodorov and Le Doussal (2020). It gives the phase diagram and identifies the boundary between simple and glassy phases. Our approach relies on new exponential asymptotics of random determinants, for non-invariant random matrices.

This is joint work with Paul Bourgade and Benjamin McKenna (Courant Institute, NYU).

Session Chair

Arup Bose (Indian Statistical Institute)

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