These lecture notes are based on [BNS+16] and were compiled for a guest lecture in the course CS229r “Information Theory in Computer Science” taught by Madhu Sudan at Harvard University in Spring 2016. Menu for today’s lecture: • Motivation • Model • Overfitting & comparison to non-adaptive data analysis • What can we do adaptively? • KL Divergence recap • Proof • Differential privacy (time per...

These notes are largely extracted from [9].

1. Definition and Examples (p.2) 2. Transvections and Holonomy (p.7) 3. Killing Fields (p.9) 4. Cartan Involution and Cartan Decomposition (p.11) 5. Locally Symmetric Spaces (p.15) 6. Compact, Noncompact and Euclidean Type; Duality (p.16) 7. The Isometry Group (p.17) 8. Lie Subtriples and Totally Geodesic Subspaces (p.19) 9. Isotropy Representation and Rank (p.19) 10. The Weyl Group (p. 22) Ref...

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