Date/Time : 06 Oct 2022 10:00
Venue : via Zoom
Speaker : Ruqi Zhang, Purdue University

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

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Probabilistic modeling provides a principled framework for learning from data, with the key advantage of offering rigorous solutions for uncertainty quantification. In the era of big and complex data, there is an urgent need for new inference methods in probabilistic modeling to extract information from data effectively and efficiently.

This talk will show how to do theoretically guaranteed scalable and reliable inference for modern machine learning. First, I will introduce a general and theoretically grounded framework to enable fast and asymptotically correct inference, with applications to Metropolis-Hastings and Gibbs sampling. Then, I will highlight the key challenges of probabilistic inference in deep learning, and present a novel approach for fast posterior inference of neural network weights. This method has achieved state-of-the-art results and has been regarded as one of the benchmarks in deep probabilistic modeling.

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Date/Time : 05 Oct 2022 15:00
Venue : S17 #05-12 (SR4)
Speaker : Abdul Basit, Johns Hopkins University

Abstract:  A celebrated conjecture of Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint triangles. We will discuss some recent results regarding a generalization of this conjecture to hypergraphs which was proposed by Aharoni and Zerbib.

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Date/Time : 05 Oct 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Yang Yue, National University of Singapore

Abstract: Yang Yue will talk about his past and concurrent research in Reverse Mathematics and also provide the background of other researchers on the same topic. Please see the abstract on

https://www.comp.nus.edu.sg/~fstephan/logicseminar20221005abs.pdf

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Date/Time : 04 Oct 2022 17:00
Venue : S17 #04-06 (SR1)
Speaker : Sun Rongfeng, National University of Singapore

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https://nus-sg.zoom.us/j/85460997100?pwd=S2FVVXUzSGU0U0tSN3Z4MURVSGhVUT09

Meeting ID: 854 6099 7100
Passcode: 504631

Abstract: The stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation are singular stochastic partial differential equations, for which robust solution theories have been developed in dimension 1. But in the critical dimension 2 for SHE and KPZ, no robust solution theory exists. I will review joint work with Caravenna and Zygouras on the scaling limit of the 2-dimensional directed polymer model, a space-time discretisation of the SHE, which implies that the 2-dimensional SHE and KPZ undergo a phase transition. Below the critical point, both SHE and KPZ have Gaussian fluctuations. At the critical point, we recently showed that the directed polymer model has a unique limit, which can be interpreted as the solution of the critical 2-dimensional SHE.

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Date/Time : 30 Sep 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Chung-Ru Lee, National University of Singapore

Abstract: One of the main application of the Relative Langlands Program is providing a description of distinguished representation, which itself has profuse interpretations. In this talk series I will introduce a method to study such problem through the comparison of relative trace formulae, where the theory of endoscopy plays a significant role. In particular, the study of representations on unitary groups that are distinguished by an orthogonal subgroup remains mysterious due to the presence of a type N-spherical root, which requires extra caution when dealt with.

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Date/Time : 30 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Huang Fukeng, National University of Singapore

Abstract: Recently it has been observed that when the interfacial tension is lower than normal liquids by two to three orders, the pinch-off dynamics is dominated by bulk diffusion [PRL 123, 134501 (2019)], showing a scaling behavior distinct from that dominated by Stokes flow. We employ the Cahn-Hilliard-Navier-Stokes model to investigate the pinch-off dynamics of a liquid thread surrounded by a viscous external fluid. A characteristic length scale is introduced to measure the competition between diffusion and viscous flow in interfacial motion. The crossover between the Stokes regime and the diffusion-dominated regime is investigated numerically and analytically to reveal how the scaling behaviors of similarity solutions are to be qualitatively changed as the characteristic length scale is accessed by the pinching neck of the interface.

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Date/Time : 30 Sep 2022 14:00
Venue : S17 #04-05 (SR2)
Speaker : Mengdi Wang, Princeton University

Abstract:  Consider the estimation of policy gradient (PG) using data that maybe collected in off-policy manners. The talk presents a Policy Gradient Bellman Equation and shows how to leverage Q function approximator for policy gradient estimation via a double fitted iteration. We show that the double fitted iteration is equivalent to a plug-in estimator. Further, the PG estimation error bound is determined by a restricted chi-square divergence that quantifies the interplay between distribution shift and function approximation. A matching Cramer Rao lower bound is also provided.

Next, we show how to extend policy gradient method to reinforcement learning beyond cumulative rewards. In particular, consider the objective that is a general concave utility function of the state-action occupancy measure, containing as special cases maximal exploration, imitation and safety constrained RL. Such generality invalidates the Bellman equation and Sutton’s Policy Gradient Theorem. We derive a new Variational Policy Gradient Theorem for RL with general utilities, which establishes that the parametrized policy gradient may be obtained as the solution of a stochastic saddle point problem. We also exploit the hidden convexity of the Markov decision process and prove that the variational policy gradient scheme converges globally to the optimal policy for the general objective, though the optimization problem is nonconvex.

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Date/Time : 29 Sep 2022 10:00
Venue : via Zoom
Speaker : He Haiyun, 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:  Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively refine the model parameters. In contrast to most previous works that bound the gen-error, we provide an exact expression for the gen-error and particularize it to the binary Gaussian mixture model. Our theoretical results suggest that when the class conditional variances are not too large, the gen-error decreases with the number of iterations, but quickly saturates. On the flip side, if the class conditional variances (and so amount of overlap between the classes) are large, the gen- error increases with the number of iterations. To mitigate this undesirable effect, we show that regularization can reduce the gen-error. The theoretical results are corroborated by extensive experiments on the MNIST and CIFAR datasets in which we notice that for easy- to-distinguish classes, the gen-error improves after several pseudo-labelling iterations, but saturates afterwards, and for more difficult-to-distinguish classes, regularization improves the generalization performance.

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Date/Time : 28 Sep 2022 15:00
Venue : via Zoom
Speaker : István Tomon, Umeå University

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https://nus-sg.zoom.us/j/88686191741?pwd=ZHVWbmcvejludWpPRmRLUlBjZ00yQT09

Meeting ID: 886 8619 1741
Passcode: 23571113

Abstract:  At least how many hyperplanes are needed to cover the finite space $\mathbb{F}_p^{n}$ if we require that the normal vectors of the hyperplanes span the whole space, and none of the hyperplanes is redundant? This question is related to a number of long-standing conjectures in linear algebra and group theory, such as the Alon-Jaeger-Tarsi conjecture on non-vanishing linear maps, the Additive Basis conjecture, and a conjecture of Pyber about irredundant coset covers. I will talk about some progress on this question, which in particular leads to a solution of the first conjecture in a strong form, makes substantial progress on the second conjecture, and fully resolves the third conjecture. This is based on a joint work with Janos Nagy and Peter Pal Pach.

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