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This volume features recent advances in data science ranging from algebraic geometry used for existence and uniqueness proofs of low rank approximations for tensor data, to category theory used for natural language processing applications, to approximation and optimization frameworks developed for convergence and robustness guarantees for deep neural networks. It provides ideas, methods, and tools developed in inherently interdisciplinary research problems requiring mathematics, computer science and data domain expertise. It also presents original results tackling real-world problems with immediate applications in industry and government.
Contributions are based on the third Women in Data Science and Mathematics (WiSDM) Research collaboration Workshop that took place between August 7 and August 11, 2023 at the Institute for Pure & Applied Mathematics (IPAM) in Los Angeles, California, US. The submissions from the workshop and related groups constitute a valuable source for readers who are interested in mathematically-founded approaches to modeling data for exploration, understanding and prediction.
Cristina Garcia-Cardona received the B.Sc. degree in electrical engineering from Universidad de Los Andes, Colombia, the M.Sc. degree in emergent computer sciences from Universidad Central de Venezuela, and the Ph.D. degree in computational science from Claremont Graduate University and San Diego State University Joint Program, CA, USA. She is currently a Staff Scientist with the Computer, Computational and Statistical Sciences (CCS) Division, Los Alamos National Laboratory, Los Alamos, NM, USA. Her research interests include inverse problems, sparse representations, graph algorithms, and machine learning applications.
Harlin Lee received the B.S. and M.Eng. degrees in electrical engineering and computer science from Massachusetts Institute of Technology, USA, and the M.S degree in machine learning and the Ph.D. degree in electrical and computer engineering from Carnegie Mellon University, USA. She completed postdoctoral studies in applied math at the University of California, Los Angeles. She is currently an Assistant Professor at the School of Data Science and Society, University of North Carolina at Chapel Hill, NC, USA. Her research interests include graphs, manifolds, optimal transport, nonconvex optimization, statistical signal processing, machine learning, and healthcare.
Chapter 1: Randomized Iterative Methods for Tensor Regression Under the t-product.- Chapter 2: Matrix exponentials: Lie-Trotter-Suzuki fractal decomposition, Gauss Runge-Kutta polynomial formulation, and compressible features.- Chapter 3: An exploration of graph distances, graph curvature, and applications to network analysis.- Chapter 4: Time-Varying Graph Signal Recovery Using High-Order Smoothness and Adaptive Low-rankness.- Chapter 5: Graph-Directed Topic Models of Text Documents.- Chapter 6: Linear independent component analysis in Wasserstein space.- Chapter 7: Faster Hodgerank Approximation Algorithm for Statistical Ranking and User Recommendation Problems.- Chapter 8: A Comparison Study of Graph Laplacian Computation.- Chapter 9: Supervised Dimension Reduction via Local Gradient Elongation.- Chapter 10: Reducing NLP Model Embeddings for Deployment in Embedded Systems.- Chapter 11: Automated extraction of roadside slope from aerial LiDAR data in rural North Carolina.- Chapter 12: A non-parametric optimal design algorithm for population pharmacokinetics.- Chapter 13: Unrolling Deep Learning End-to-End Method for Phase Retrieval.- Chapter 14: Performance Analysis of MFCC and wav2vec on Stuttering Data.- Chapter 15: Active Learning for Reducing Gender Gaps in Undergraduate Computing and Data Science.- Chapter 16: Quantifying and Documenting Gender-Based Inequalities in the Mathematical Sciences in the United States.
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