Date/Time : 25 Mar 2021 16:00
Venue : via Zoom
Speaker : Joe Kileel, University of Texas at Austin

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Tensors are higher-order matrices, and decomposing tensors can reveal structure in datasets. In recent years, tensor decomposition has found applications in statistics, computational imaging, signal processing, and quantum chemistry. In this talk, we will present a new numerical method for low-rank symmetric tensor decomposition, building on the usual power method and ideas from classical algebraic geometry. The approach achieves a speed-up over the state-of-the-art by roughly one order of magnitude. We will also describe an “implicit” variant of the algorithm for the case of moment tensors which avoids the explicit formation of higher-order moments, analogously to matrix-free techniques in linear algebra. Time permitting, we will include a quantitative analysis of the non-convex optimization landscape associated with our algorithm. This is based on joint works with Joao Pereira, Tammy Kolda and Timo Klock.

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Date/Time : 18 Mar 2021 16:00
Venue : via Zoom
Speaker : Yifei Wang, Stanford University

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Abstract We introduce a framework for Newton’s flows in probability space with information metrics, named information Newton’s flows. Extending the relationship between overdamped Langevin dynamics and Wasserstein gradient flows of Kullback-Leibler (KL) divergence, we derive Newton’s Langevin dynamics from Wasserstein Newton’s flows. We design sampling efficient variational methods in affine models and reproducing kernel Hilbert space (RKHS) to approximate Wasserstein Newton’s directions. Convergence results of the proposed information Newton’s method with approximated directions are established. Several numerical examples from Bayesian inference problems are shown to demonstrate the effectiveness of the proposed method.

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Date/Time : 11 Mar 2021 16:00
Venue : via Zoom
Speaker : Vaibhav Rajan, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Abstract:  The increasing availability of digitized clinical and genomic data presents an unprecedented opportunity to study and gain deeper understanding of diseases, develop new treatments and improve healthcare ecosystems. However, clinical data also poses modelling challenges due to the heterogeneity of data sources, e.g., structured demographic variables, text in clinical notes, images in MRI scans etc. In this talk, I’ll describe a deep multi-view learning technique, developed in my group, for unsupervised learning of representations from arbitrary collections of matrices. I’ll outline how our technique can be used for predicting gene-disease associations and drug targets in cancer.

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Date/Time : 04 Mar 2021 16:00
Venue : via Zoom
Speaker : Ariel Neufeld, Nanyang Technological University

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Abstract: In this talk, we first recall the mathematical concept of neural networks and its universal approximation property. Then we will show how one can combine neural networks together with tools from Stochastic Calculus, particularly the Feynman-Kac representation, to build a neural network based algorithm that can approximately solve high-dimensional nonlinear PDEs in up to 10’000 dimensions with short run times. We apply this algorithm to price high-dimensional financial derivatives under default risk.

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