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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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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Date/Time : 03 Nov 2022 10:00
Venue : S17 #05-11 (SR5)
Speaker : Michael Choi, National University of Singapore

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Meeting ID: 977 560 6531
Passcode: 123321

This talk centers around a technique that we call landscape modification. The core idea is that the Hamiltonian function is suitably modified in a way for rapid mixing while maintaining proximity with the original target distribution. We first present model-independent results that give rapid mixing and tunneling in the low-temperature regime. Building upon these results, we investigate the effect of landscape modification on some prototypical statistical physics models including the Ising model on various deterministic and random graphs as well as Derrida’s random energy model. This talk highlights a novel use of the geometry and structure of the landscape, in particular the global minimum value or its estimate, to the design of accelerated samplers or optimizers.

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

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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 : 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 : 22 Sep 2022 10:00
Venue : S17 #05-11 (SR5)
Speaker : Kengo Kamatani, Institute of Statistical Mathematics

Abstract:  We construct a class of non-reversible Metropolis kernels as a multivariate extension of the guided-walk kernel proposed by Gustafson 1998. The main idea of our method is to introduce a projection that maps a state space to a totally ordered group. By using Haar measure, we construct a novel Markov kernel termed Haar-mixture kernel, which is of interest in its own right. This is achieved by inducing a topological structure to the totally ordered group. Our proposed method, the Delta-guided Metropolis–Haar kernel, is constructed by using the Haar-mixture kernel as a proposal kernel. The proposed non-reversible kernel is at least 10 times better than the random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for the logistic regression and a discretely observed stochastic process in terms of effective sample size per second.

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