LOGML - Smita Krishnaswamy

LOGML Summer School 2022

Talk Title: Graph Spectral and Signal Processing Tools for Extracting Structure from Scientific Data

Abstract: In this talk, I will show how to leverage data geometry and topology, embedded within modern machine learning frameworks, to understand complex high dimensional scientific data. First, I will show how graphs can model underlying manifolds from which data are sampled and how graph spectral tools such as diffusion operators and signal processing tools such as filters can shed light on characteristics of the underlying manifold including geodesic distances, density, and curvature. Next, I will show how to combine graph diffusion geometry with topology to extract multi-granular features from the data for predictive analysis. Then, I will move up from the local geometry of individual data points to the global geometry of complex objects like data clouds, using graph signal processing to derive representations of these entities and optimal transport for distances between them. Finally, I will demonstrate how two neural networks use geometric inductive biases for generation and inference: GRASSY (geometric scattering synthesis network) for generating new molecules and molecular fold trajectories, and TrajectoryNet for performing dynamic optimal transport between time-course samples to understand the dynamics of cell populations. Throughout the talk, I will include examples of how these methods shed light on the inner workings of biomedical and cellular systems including cancer, immunology and neuroscientific systems. I will finish by highlighting future directions of inquiry.

Speaker Bio: Smita Krishnaswamy is an Associate Professor in the departments of Computer Science (SEAS) and Genetics (YSM). She is part of the programs in Applied Mathematics, Computational Biology & Bioinformatics and Interdisciplinary Neuroscience. She is also affiliated with the Yale Center for Biomedical Data Science, Yale Cancer Center, Wu-Tsai Institute. Smita’s lab works at the intersection of computer science, applied math, computational biology, and signal processing to develop representation-learning and deep learning methods that enable exploratory analysis, scientific inference and prediction from big biomedical datasets. She has applied her methods on datasets generated from single-cell sequencing, structural biology, biomedical imaging, brain activity recording, electronic health records on a wide variety of biological, cellular, and disease systems. Her techniques generally incorporate mathematical priors from graph spectral theory, manifold learning, signal processing, and topology into machine learning and deep learning frameworks, in order to denoise and model the underlying systems faithfully for predictive insight. Currently her methods are being widely used for data denoising, visualization, generative modeling, dynamics. modeling, comparative analysis and domain transfer.

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