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Algebraic solvers are fundamental tools
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Interplay of Linear Algebra, Machine Learning, and HPC - JuliaCon 2021 Keynote
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- 1 Welcome!
- 2 Introduction by the speaker
- 3 Acknowledgments
- 4 Algebraic solvers are fundamental tools
- 5 Mathematical libraries in which development we were involved
- 6 Two main themes of the talk
- 7 Kernel methods in ML
- 8 Kernel Ridge Regression (KRR)
- 9 Solving large sense linear systems
- 10 Low-rank compression
- 11 Classes of low-rank structured matrices
- 12 Cluster tree of matrix
- 13 Fast algebraic algorithm: sketching
- 14 Problem: we don't know the target rank
- 15 Stochastic norm estimation
- 16 Example: compression of HSS matrix
- 17 Fast geometric algorithm: approximate nearest neighbor
- 18 Approximate nearest neighbor with iterative merging
- 19 Comparison of algebraic and geometric algorithms
- 20 STRUMPACK (STRUctured Matrix PACKage)
- 21 Linear algebra and machine learning
- 22 Bayesian optimization
- 23 Modeling phase
- 24 Search phase
- 25 Parallelization of code execution
- 26 Examples of ML improved linear algebra computations
- 27 Summary
- 28 Q&A: What do we need more: linear algebra code for new architectures or for new applications?
- 29 Q&A: How we can give users the ability to use ML to get performance?
- 30 Q&A: What developments do you want to see in the Julia ecosystem?
- 31 Q&A: What high-performance algorithms can make use of specific code generation?
- 32 Q&A: Do you think that Julia can replace C++ as the language for linear algebra?
- 33 Q&A: Do you search for rank revealing LU?
- 34 Announcements
