Join David P. Woodruff, PhD, as he explores the intricacies of testing positive semidefiniteness and eigenvalue approximation. In this talk, Dr. Woodruff presents optimal algorithms for determining if a matrix 𝐴 is positive semidefinite or has a minimum eigenvalue sufficiently negative. He introduces a novel random walk algorithm that uses only a single vector-matrix-vector product per iteration, offering a significant improvement over classical methods.
Dr. Woodruff also dives into how obtaining additive error estimates for all eigenvalues of
𝐴 using an optimal-sized sketch,𝐺𝐴𝐺𝑇, where 𝐺 is a random Gaussian matrix. Despite the eigenvalues of 𝐺𝐴𝐺𝑇 not being direct approximations of those of 𝐴, he demonstrates a method to recover accurate estimates. This talk is based on his collaborative works with Deanna Needell and William Swartworth, showcasing cutting-edge advancements in matrix analysis and algorithm optimization. Ideal for enthusiasts of machine learning, data science, and AI.
#MachineLearning #DeepLearning #DataScience #AI #ArtificialIntelligence #EigenvalueApproximation #MatrixAnalysis #AlgorithmOptimization #PositiveSemidefiniteness #MLAlgorithms #DataEngineering #ODSC
Timecodes:
0:00 - Intro
6:57 - Matrix-Vector Queries
25:12 - Bilinear Sketches
36:02 - Leveraging Adaptivity
41:29 - Spectrum Estimation
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