FDS Seminar Series

“Diffusion Earth Mover’s Distance, Distribution Embeddings and Flows”

Speaker: Smita Krishnaswamy
Associate Professor, Dept of Computer Science, Dept. of Genetics
Programs for Applied Math, Computational Biology & Bioinformatics, Interdisciplinary Neuroscience
Yale Cancer Center, Wu Tsai-Institute 

Abstract: We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mover’s Distance (EMD). We model the datasets as distributions supported on a common data graph that is derived from the affinity matrix computed on the combined data. In such cases where the graph is a discretization of an underlying Riemannian closed manifold, we prove that Diffusion EMD is topologically equivalent to the standard EMD with a geodesic ground distance. Diffusion EMD can be computed in {Õ}(n) time and is more accurate than similarly fast algorithms such as tree-based EMDs. We also show Diffusion EMD is fully differentiable, making it amenable to future uses in gradient-descent frameworks such as deep neural networks. We demonstrate an application of Diffusion EMD to single cell data collected from 210 COVID-19 patient samples at Yale New Haven Hospital. Here, Diffusion EMD can derive distances between patients on the manifold of cells at least two orders of magnitude faster than equally accurate methods. This distance matrix between patients can be embedded into a higher level patient manifold which uncovers structure and heterogeneity in patients. Finally, we show DEMD’s incorporation into a neural ode framework we recently developed called MIOFlow (Manifold Interpolating Flows) for learning dynamics from static snapshot data. MIOFlow uses an autoencoder with multiscale diffusion distances to find a manifold embedding of data. Then within this latent space, we use the neural network to learn a continuous time derivative to perform dynamic optimal transport of static snapshot measurements of cells and in the process infer continuous dynamics and single-cell trajectories. We show results of this in a cancer metastasis system measured using single-cell RNA-sequencing. 

Speaker bio: Smita Krishnaswamy is an Associate Professor in the department of Genetics at the Yale School of Medicine and Department of Computer Science in the Yale School of Applied Science and Engineering and a core member of the Program in Applied Mathematics. She is also affiliated with the Yale Center for Biomedical Data Science, Yale Cancer Center, and Program in Interdisciplinary Neuroscience. Smita’s research focuses on developing unsupervised machine learning methods (especially graph signal processing and deep-learning) to denoise, impute, visualize and extract structure, patterns and relationships from big, high throughput, high dimensional biomedical data. Her methods have been applied variety of datasets from many systems including embryoid body differentiation, zebrafish development, the epithelial-to-mesenchymal transition in breast cancer, lung cancer immunotherapy, infectious disease data, gut microbiome data and patient data.

Smita teaches three courses: Machine Learning for Biology (Fall), Deep Learning Theory and applications (spring), Advanced Topics in Machine Learning & Data Mining (Spring). She completed her postdoctoral training at Columbia University in the systems biology department where she focused on learning computational models of cellular signaling from single-cell mass cytometry data. She was trained as a computer scientist with a Ph.D. from the University of Michigan’s EECS department where her research focused on algorithms for automated synthesis and probabilistic verification of nanoscale logic circuits. Following her time in Michigan, Smita spent 2 years at IBM’s TJ Watson Research  Center as a researcher in the systems division where she worked on automated bug finding and error correction in logic.

This presentation will be live and in-person, but remote access is available here: https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=7e3a4115-73f7-4205-976d-af1c01266047

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