Date/Time : 25 Feb 2022 09:00
Venue : via Zoom
Speaker : Daniel Russo, Columbia University

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https://nus-sg.zoom.us/j/86446962104?pwd=cFFTQzhtOU9OTFd5RUZhOHBPSjcwQT09

Meeting ID: 864 4696 2104
Passcode: 673331

Abstract: Multi-armed bandit algorithms minimize experimentation costs required to converge on optimal behavior. They do so by rapidly adapting experimentation effort away from poorly performing actions as feedback is observed. But this desirable feature makes them sensitive to confounding, which is the primary concern underlying classical randomized controlled trials. We highlight, for instance, that popular bandit algorithms cannot address the problem of identifying the best action when day-of-week effects may confound inferences. In response, this paper proposes deconfounded Thompson sampling, which makes simple, but critical, modifications to the way Thompson sampling is usually applied. Theoretical guarantees suggest the algorithm strikes a delicate balance between adaptivity and robustness to confounding. It attains asymptotic lower bounds on the number of samples required to confidently identify the best action — suggesting optimal adaptivity — but also satisfies strong performance guarantees in the presence of day-of-week effects and delayed observations — suggesting unusual robustness.

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Date/Time : 24 Feb 2022 09:00
Venue : via Zoom
Speaker : Leonard Wong, University of Toronto

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https://nus-sg.zoom.us/j/81306548290?pwd=RmRhYmVUemtRMjEvTW1EeFVkazFrdz09

Meeting ID: 813 0654 8290
Passcode: 312153

Abstract: Divergences such as Bregman and Kullback-Leibler divergences are fundamental in probability, statistics and machine learning. We begin by explaining how divergences arise naturally from the geometry of optimal transport. Then, we study a family of logarithmic costs – originally motivated by financial applications – which may be regarded as a canonical deformation of the negative dot product in Euclidean quadratic transport. It induces a logarithmic divergence which has remarkable probabilistic and geometric properties. As an application, we introduce a generalization of continuous-time mirror descent.

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Date/Time : 22 Feb 2022 14:00
Venue : S17 #06-11 (SR6)
Speaker : David Hansen, Max Planck Institute for Mathematics in Bonn

Abstract:  I’ll talk about some recent foundational developments in etale cohomology:

i) A flexible six-functor formalism for “Zariski-constructible” sheaves on rigid spaces (joint work with Bhargav Bhatt).

ii) A new “relative” variant of perverse sheaves (joint work with Peter Scholze).

If time permits, I’ll mention some tantalizing open problems in these directions.

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Date/Time : 18 Feb 2022 10:00
Venue : via Zoom
Speaker : Yang Haizhao, Purdue University

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract: Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This talk introduces the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

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Date/Time : 16 Feb 2022 16:30
Venue : via Zoom
Speaker : Rupert Hoelzl, Universitaet der Bundeswehr, Muenchen

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract: A Martin-Loef test U is universal if it captures all sequences which are not Martin-Loef random. It is optimal if for every Martin-Loef test V there is a constant c such that, for all n, V_{n+c} subseteq U_n. We study the computational differences between universal and optimal Martin-Loef tests as well as the effects of these differences on both the notions of layerwise computability and the Weihrauch degree of LAY, the function that produces a bound on the randomness deficiency of a given Martin-Loef random sequence. We prove several robustness and idempotence results concerning the Weihrauch degree of LAY and we show that layerwise computability is more restrictive than Weihrauch reducibility to LAY. Along similar lines, we also study the principle RD, a variant of LAY outputting the precise randomness deficiency of sequences instead of only an upper bound as LAY.

This is joint work with Paul Shafer. The paper is available as in the Annals of Pure and Applied Logic, https://doi.org/10.1016/j.apal.2015.05.006

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Date/Time : 15 Feb 2022 10:00
Venue : via Zoom
Speaker : Min Ru, University of Houston

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: In this talk, I’ll first discuss an Nevanlinna-Diophantine inequality obtained by Ru-Vojta. Then I’ll describe its applications in the study of the GCD problems (the work of Guo-Wang, and Wang-Yasufuku), as well as in the study of the divisibility, hyperbolicity and integral points problems (the work of Rousseau, Turchet and Wang).

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Date/Time : 14 Feb 2022 10:00
Venue : via Zoom
Speaker : Minh-Binh Tran, Southern Methodist University

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https://nus-sg.zoom.us/j/86090852474?pwd=TmJ2eUNPbTNEZW5aT3ZPRyt1cEhLZz09

Meeting ID: 860 9085 2474
Passcode: 995447

Abstract: Wave turbulence describes the dynamics of both classical and non-classical nonlinear waves out of thermal equilibrium. Recent mathematical interests on wave turbulence theory have their roots from the works of Bourgain, Staffilani and Colliander-Keel-Staffilani-Takaoka-Tao. In this talk, I will present some of our recent results on wave turbulence theory. In the first part of the talk, I will discuss our rigorous derivation of wave turbulence equations. The second part of the talk is devoted to the analysis of wave turbulence equations as well as some numerical illustrations. The last part concerns some physical applications of wave turbulence theory. The talk is based on my joint work with Staffilani (MIT), Soffer (Rutgers) and Pomeau (ENS Paris).

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Date/Time : 11 Feb 2022 09:00
Venue : via Zoom
Speaker : Geordie Williamson, University of Sydney

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https://nus-sg.zoom.us/j/86817881669?pwd=T1dVRWRQVjJRTjZNbDE0QUpsa3E0QT09

Meeting ID: 868 1788 1669
Passcode: 432904

Abstract: The combinatorial invariance conjecture is a fascinating conjecture in Representation Theory. Basically it says that certain important polynomials (“Kazhdan-Lusztig polynomials”) are determined in a very non-trivial way by a directed graph. About 2 years ago, I began working on this problem with DeepMind, an AI lab based in London. (DeepMind is famous for their AlphaGo program which was the first program to defeat the best human Go players.) Our goal was to try to discover whether modern Machine Learning techniques are helpful in approaching problems in Pure Mathematics. I will outline how the Machine Learning models work, how successful they were and (by far the trickiest part) how we went about extracting new mathematics from these models. The result is a formula which sheds light on the combinatorial invariance conjecture. This is joint work with the DeepMind team: Charles Blundell, Lars Buesing, Alex Davies and Petar Veličković.

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Date/Time : 11 Feb 2022 10:00
Venue : via Zoom
Speaker : Soufiane Hayou, National University of Singapore

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract: The theoretical analysis of infinite-width neural networks has led to many interesting practical results (choice of initialization schemes, choice of Bayesian priors etc.). However, the traditional infinite-width framework focuses on fixed depth networks and omits the large depth behavior of these models. In this talk, I will cover different topics on the infinite-width-then-infinite-depth networks and show how we can leverage some theoretical results to obtain principled algorithms. The following papers will be covered in this talk:

• On the Impact of the activation function on deep neural networks training. ICML 2019. (Joint work with A. Doucet and J. Rousseau)
• Stable ResNet. AISTATS 2021. (Joint work with E. Clerico, B. He, G. Deligiannidis, A. Doucet, and J. Rousseau)

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