Date/Time : 22 Apr 2021 16:00
Venue : via Zoom
Speaker : Anqi Qiu, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd The Laplace-Beltrami operator is a generalization of the Euclidean representation of the Laplace operator to an arbitrary Riemannian manifold. It is a self-adjoint operator and its eigenfunctions form a complete set of real-valued orthonormal basis functions. In this talk, I will introduce spectral Laplace-Beltrami wavelets and its computational algorithm. I will then demonstrate its use for smoothing and classification of the data defined on smooth surfaces embedded in the 3-D Euclidean space. Furthermore, I will discuss that the spectral Laplace-Beltrami Wavelets can be used for the construction of geometric convolutional neural network (CNN) and then introduce a vertex-based geometric CNN algorithm for regular surfaces in which translation and downsampling on surfaces can be the same as those in the regular grid. I will show the use of this method for the prediction of Alzheimer’s Disease.

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Date/Time : 21 Apr 2021 08:00
Venue : via Zoom
Speaker : Yudong Chen, Cornell University

Join Zoom Meeting https://nus-sg.zoom.us/j/83859343651?pwd=Yy9pTWRiZ1N1SGs5dVVNbHpaRTBaQT09 Meeting ID: 838 5934 3651 Password: 685719 Estimation of mixture models is a fundamental problems in machine learning and statistics. This problem is inherently nonconvex, and may possess spurious local minimizers that are not globally optimal, both in theory and in practice. In this talk, we will present three positive results for mixture problems in the lens of nonconvex optimization. For a mixture of two components, we show that all local minima are globally optimal, and EM converges to a global optimum from random initialization. This result applies to a broad class of log-concave mixture problems including mixtures of Gaussians and linear regressions. For more than two components, spurious local minima provably exist. One such local minimizer puts multiple centers at one true component, and another center in the middle of multiple true components. We prove that this is essentially the only type of spurious local minima under certain conditions. Consequently, standard algorithms such as gradient descent and EM are guaranteed to converge to a solution that partially identifies the true model. Leveraging the above structural results, we will discuss several algorithmic ideas for avoiding local minima and finding the global optimum. Over-parametrization, in which one over-specifies the number of components, stands out as a promising approach. We characterize the benefit and price of over-parametrization in terms of its computational and statistical efficiency.

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Date/Time : 21 Apr 2021 15:00
Venue : via Zoom
Speaker : Andrea Granelli, Credit Suisse

Join Zoom Meeting https://nus-sg.zoom.us/j/82328711543?pwd=WEllYTc2aE1IbU5ETEk3dERKV1JHQT09 Meeting ID: 823 2871 1543 Passcode: 266585 Understanding variance risk is of key importance in mathematical finance since it affects risk management, asset allocation and derivative pricing. Variance risk is priced in financial markets by the so-called variance risk premium (VRP), which refers to the premium demanded for holding assets whose variance is exposed to stochastic shocks. This paper identifies a new modelling framework for equity indices and presents for the first time explicit analytical formulas for their VRP in a multivariate stochastic volatility setting, which includes multivariate non-Gaussian Ornstein-Uhlenbeck processes and Wishart processes. Moreover, we propose to incorporate contagion within the equity index via a multivariate Hawkes process and find that the resulting dynamics of the VRP represent a convincing alternative to the models studied in the literature up to date. We show that our new model can explain the key stylized facts of both equity indices and individual assets and their corresponding VRP, while popular (multivariate) stochastic volatility models fail. We finally prove the existence of a structure-preserving risk neutral measure for our model. In particular, we establish the class of equivalent probabilities that preserve the self-affecting structure of the Hawkes process.

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Date/Time : 21 Apr 2021 14:00
Venue : via Zoom
Speaker : Ming-Lun Hsieh, Academia Sinica

Join Zoom Meeting https://nus-sg.zoom.us/j/82234939628?pwd=TVRlLzBmS1VsaXhVZ3k5OWtXVlZYdz09 Meeting ID: 822 3493 9628 Password: 838848 Abstract: Darmon, Dasgupta and Pollack in 2011 applied the Eisenstein congruence for Hilbert modular forms to prove the rank one Gross conjecture for Deligne-Ribet p-adic L-functions under some technical assumptions. These assumptions were later lifted by Ventullo. In this talk, we will explain how to apply their ideas in the setting of CM congruence and compute the first derivative of the Katz p-adic L-functions associated with ring class characters of imaginary quadratic fields at the triviall zero. We will present a precise first derivate formula of the Katz p-adic L-functions in terms of certain Gross p-adic regulator and p-adic logarithms of elliptic units. This proves a formula proposed in a recent work of Betina and Dimitrov. This talk is based on a joint work with Masataka Chida.

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Date/Time : 14 Apr 2021 17:00
Venue : via Zoom
Speaker : Karen Seidel, University of Potsdam

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Learning from positive and negative information, so called informant, is one of the models for human and machine learning introduced by Gold. We review existing classical and recent results regarding the learning power of associated settings.

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Date/Time : 14 Apr 2021 16:00
Venue : via Zoom
Speaker : Chaithanya Bandi, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/86983811912?pwd=NDdLMmlEUE1sSWJ0bnVFc3dNSUJ6UT09&from=addon Meeting ID: 869 8381 1912 Password: 628006 We consider the problem faced by an e-retailer that needs to display a limited set of products to a customer with no prior information. In this context, the e-retailer is allowed to query preferences in order to inform its display. A standard approach to this problem follows a two-step approach: First, estimate the preferences of the customer using a choice model, and then optimize the product display. While this approach is applicable to many settings with stationary customer preferences, this is not applicable to scenarios with changing customer preferences. In this paper, we develop a novel product-driven online framework for efficiently learning customer preferences using a structured questionnaire design. We demonstrate that our approach provably outperforms state-of-the-art methods which focus on eliciting the preference vector. Further, we formulate a robust algorithm for eliciting the optimal display set when the customer responses are noisy.   We establish theoretical foundations for our question-design mechanism and develop efficiency guarantees for our product-driven algorithm. We also present results of our implementation on a real data set obtained from a major fashion retailer.  We demonstrate that we are able to efficiently and customer preferences to inform the optimal product display, and outperform existing approaches based on “estimate, then optimize”. Joint work with Yam Huo (NU), and based on work with Jonathan Amar and Nikos Trichakis (MIT).

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Date/Time : 09 Apr 2021 09:00
Venue : via Zoom
Speaker : Irene M. Gamba, University of Texas at Austin

Join Zoom Meeting https://nus-sg.zoom.us/j/85868905071?pwd=SVJOYzdvY3NOSlZJOVVOS0lUelg4Zz09 Meeting ID: 858 6890 5071 Password: 422756 We will focus on recent advances on numerical schemes resolving recent approaches of hybrid computational solvers of two kinds: conservative spectral based and Finite Element Method (FEM) based for the Boltzmann equation binary interactions. We will show that recently developed functional analysis tools enable proofs of consistency schemes, construction of error estimates and convergence to statistical equilibrium results, both, in the conservative spectral method as well as on FEM approach. Finally, a new approach to grazing collision limits will be presented that enable us to calculate the approximation of the Boltzmann to the Fokker Plank Landau model for Coulomb interactions with a velocity dependent Coulomb logarithm as much envisioned by the original calculations of Rutherford and Landau in the first part of the 20th century. Numerical simulations show a clear difference between the classical constant angular cut-off versus the velocity dependent angular cut-off.

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Date/Time : 08 Apr 2021 16:00
Venue : via Zoom
Speaker : Yinping YANG, Institute of High Performance Computing, A*Star, Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd What are social technologies? Why they are useful in understanding people in the digital era? How do these technologies help to understand how the population respond to the pandemic throughout its development? This joint presentation will introduce A*STAR’s affective and social research and advanced emotion analysis technologies, and discuss how they are developed and put in good use in a range of practical industry applications, including the context of COVID-19. We will first review conceptual concepts surrounding human emotions, machine learning, natural language processing, and system architecture that lay the foundation of our social technologies. We will then share a few key learning points from our COVID-19 social media analytics studies in collaboration with communication scientists and public health practitioners. Among our first published findings at JMIR Public Health and Surveillance, we discovered that at a global scale, public emotions shifted strongly from fear to anger over the course of the pandemic, while sadness and joy also surfaced. Our presentation will be concluded with a few key takeaways and discussion for future research.

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Date/Time : 07 Apr 2021 14:00
Venue : via Zoom
Speaker : Shu-Yen Pan, National Tsing Hua University

Join Zoom Meeting hhttps://nus-sg.zoom.us/j/82917531325?pwd=QzVzVVdNbUZhOHlwc09MRG5nWldudz09 Meeting ID: 829 1753 1325 Password: 555209 Let $(G,G’)$ be a reductive dual pair inside a finite symplectic group. By restricting the Weil representation to the dual pair, there exists a relation (called the finite Howe correspondence) between the irreducible representations of the two groups $G,G’$. In this talk, we would like to discuss some progress on the understanding of the correspondence by using Lusztig’s classification on the representations of finite classical groups. In particular, we will focus on the following three subjects: 1. the decomposition of the uniform projection of the Weil character. 2. the commutativity between the Howe correspondence and the Lusztig correspondence. 3. the description of the Howe correspondence on unipotent characters in terms of the symbols by Lusztig.

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