Date/Time : 22 Aug 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : Shahar Mendelson, Australian National University

Consider an isotropic measure \mu on R^d (i.e., centred and whose covariance is the identity) and let X_1,…,X_m be independent, selected according to \mu. If \Gamma=m^{-1/2} \sum_{i=1}^m <X_i,->e_i is the random operator whose rows are X_i/\sqrt{m}, how does the random set \Gamma S^{d-1} typically look like? For example, if the extremal singular values of \Gamma are close to 1 then \Gamma S^{d-1} is “well approximated” by a d-dimensional section of S^{m-1} and vice-versa. But is it possible to give a more accurate description of that set?

I will show that under minimal assumptions on \mu, with high probability and uniformly in t \in S^{d-1}, each vector \Gamma t inherits the structure of the one-dimensional marginal <X,t> in a strong sense. If time permits I will also present a few generalisations of this fact – for an arbitrary indexing set.

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Date/Time : 13 Apr 2023 16:00
Venue : S16 #03-06
Speaker : Karthyek Murthy, Singapore University of Technology and Design

Several problems in data-driven decision-making and risk management suffer from data imbalance, a term referring to settings where a small fraction of data has an outsized impact on estimating one or more decision-making criteria. Due to the paucity of relevant samples, such problems are usually approached with the “estimate, then optimize” workflow involving a model estimation from data in the first step before plugging in the trained model to solve various downstream optimization tasks. As biases due to model selection, misspecification, and overfitting to in-sample data are especially difficult to avoid in the first-step estimated model in settings affected by data imbalance, we construct novel locally robust optimization formulations in which the first-step estimation has no effect, locally, on the optimal solutions obtained.

We show that this local insensitivity translates to improved out-of-sample performance freed from the first-order impact of model errors introduced in the first-step estimation. A key ingredient in achieving this local robustness is a novel debiasing procedure that adds a non-parametric bias correction term to the objective. The debiased formulation retains convexity, and the imputation of the correction term relies only on a non-restrictive large deviations behavior conducive for transferring knowledge from representative data-rich regions to the data-scarce tail regions suffering from imbalance. The bias correction gets determined by the extent of model error in the estimation step and the specifics of the stochastic program in the optimization step, thereby serving as a scalable “smart-correction” step bridging the disparate goals in estimation and optimization.

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Date/Time : 13 Apr 2023 10:00
Venue : via Zoom
Speaker : Daniel Sanz-Alonso, University of Chicago

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https://nus-sg.zoom.us/j/81261210349?pwd=M2VlVjUvR1o4dGVodDY4MnBtRzMzUT09

Meeting ID: 812 6121 0349
Passcode: 557052

Semi-supervised learning refers to the problem of recovering an input-output map using many unlabeled examples and a few labeled ones. In this talk I will survey several mathematical questions arising from the Bayesian formulation of graph-based semi-supervised learning. These questions include the modeling of prior distributions for functions on graphs, the derivation of continuum limits for the posterior, the design of scalable posterior sampling algorithms, and the contraction of the posterior in the large data limit.

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Date/Time : 30 Mar 2023 10:00
Venue : via Zoom
Speaker : Xun Huan, University of Michigan

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

Meeting ID: 977 560 6531
Passcode: 123321

Experiments are indispensable for learning and developing models in engineering and science. A careful design of these often-expensive data-acquisition opportunities can be immensely beneficial. Simulation-based optimal experimental design, while leveraging a predictive model, offers a framework to systematically quantify and maximize the value of experiments. We focus on designing a finite sequence of experiments, seeking optimal design policies that can (a) adapt to newly collected data during the sequence (i.e. feedback) and (b) anticipate future changes (i.e. lookahead). We cast this sequential decision-making problem in a Bayesian setting with information-based utilities, and solve it numerically via policy gradient methods from reinforcement learning. In particular, we directly parameterize the policies and value functions by neural networks—thus adopting an actor-critic approach—and improve them using gradient estimates produced from simulated design and observation sequences. We demonstrate the overall method on a problem of optimal sensor movement for contaminant source inversion.

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Date/Time : 16 Feb 2023 16:00
Venue : S16 #05-98
Speaker : Xia Kelin, Nanyang Technological University

Artificial intelligence (AI) based molecular data analysis has begun to gain momentum due to the great advancement in experimental data, computational power and learning models. However, a major issue that remains for all AI-based learning models is the efficient molecular representations and featurization. Here we propose advanced mathematics-based molecular representations and featurization (or feature engineering). Molecular structures and their interactions are represented as various simplicial complexes (Rips complex, Neighborhood complex, Dowker complex, and Hom-complex), hypergraphs, and Tor-algebra-based models. Molecular descriptors are systematically generated from various persistent invariants, including persistent homology, persistent Ricci curvature, persistent spectral, and persistent Tor-algebra. These features are combined with machine learning and deep learning models, including random forest, CNN, RNN, Transformer, BERT, and others. They have demonstrated great advantage over traditional models in drug design and material informatics.

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Date/Time : 06 Jan 2023 14:00
Venue : S17 #05-12 (SR4)
Speaker : Tanya Veeravalli, University of Illinios, Urbana-Champaign

There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include “infinitely wide” neural nets, where the underlying nonlinearity is given by the activation function of an individual neuron. In this talk, we will bring this perspective to function representation by neural stochastic differential equations (SDEs). A neural SDE is an Itô diffusion process whose drift and diffusion matrix are elements of some parametric families. We will show that the ability of a neural SDE to realize nonlinear functions of its initial condition can be related to the problem of optimally steering a certain deterministic dynamical system between two given points in finite time. This auxiliary system is obtained by formally replacing the Brownian motion in the SDE by a deterministic control input. We derive upper and lower bounds on the minimum control effort needed to accomplish this steering; these bounds may be of independent interest in the context of motion planning and deterministic optimal control.

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Date/Time : 22 Dec 2022 10:00
Venue : S17 #05-12 (SR4)
Speaker : Yanni Sun, City University of Hong Kong

Known as the blueprint of life, the genomic sequence contains instructions for controlling a species’ growth, development, survival, and reproduction. From the perspective of Computer Science, the primary structure of the genomic sequences is simply a string/sequence defined on a small alphabet {A, C, G, T}. Different parts of the sequence have different biological functions and thus comprise the “language of life”.

Next-generation sequencing (NGS) technologies, which produce vast amount of sequencing data for various life forms, have provided tremendous information for tackling grand challenges in various fields. NGS enables us to obtain a large amount of data to understand more about the language of life. In this talk, I will focus on my research on using deep learning models to make sense out of the BIG microbial sequencing data obtained from host-associated (such as human gut, skin) or environmental samples (such as water, soil). By using protein clusters as the tokens (“words”), we model viral genomes as a protein-based language and thus use modern language model Transformer for feature learning. In addition, to address the issues of limited labeled biological data, we use graph convolutional network (GCN), a semi-supervised learning model for leveraging both labeled and unlabeled data for feature learning in several tasks. These research projects rendered us with deeper understanding of the advantages and limitations of using deep learning models for biological sequence classification. I will share some of our observations along this line.

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Date/Time : 15 Dec 2022 10:00
Venue : S17 #04-04 (SR3)
Speaker : Ming Ha Quang, RIKEN AIP (Advanced Intelligence Project), Tokyo, Japan

Information geometry (IG) and Optimal transport (OT) have been attracting much research attention in various fields, in particular machine learning and statistics. In this talk, we present results on the generalization of IG and OT distances for finite-dimensional Gaussian measures to the setting of infinite-dimensional Gaussian measures and Gaussian processes. Our focus is on the Entropic Regularization of the 2-Wasserstein distance and the generalization of the Fisher-Rao distance and related quantities. In both settings, regularization leads to many desirable theoretical properties, including in particular dimension-independent convergence and sample complexity. All of the presented formulations admit closed form expressions that can be efficiently computed and applied practically.

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Date/Time : 10 Nov 2022 10:00
Venue : via Zoom
Speaker : Yoonsang Lee, Darthmouth College

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

Meeting ID: 977 560 6531
Passcode: 123321

We propose a neural network-based approach to the homogenization of multiscale problems. The proposed method uses a derivative-free formulation of a training loss, which incorporates Brownian walkers to find the macroscopic description of a multiscale PDE solution. Compared with other network-based approaches for multiscale problems, the proposed method is free from the design of hand-crafted neural network architecture and the cell problem to calculate the homogenization coefficient. The exploration neighborhood of the Brownian walkers affects the overall learning trajectory. We determine the bounds of micro- and macro-time steps that capture the local heterogeneous and global homogeneous solution behaviors, respectively, through a neural network. The bounds imply that the computational cost of the proposed method is independent of the microscale periodic structure for the standard periodic problems. We validate the efficiency and robustness of the proposed method through a suite of linear and nonlinear multiscale problems with periodic and random field coefficients.

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