Watch a 37-minute lecture from Microsoft Research's Lester Mackey at Harvard CMSA exploring innovative approaches to probability distribution summarization. Learn about two groundbreaking tools that surpass traditional independent sampling and Markov chain Monte Carlo thinning methods. Discover how kernel thinning efficiently reduces n-point summaries to square-root n-points while maintaining integration error accuracy across reproducing kernel Hilbert spaces. Explore Stein thinning's dual capability to compress summaries and enhance accuracy by addressing biases from off-target sampling, tempering, and burn-in. Follow the practical applications in organ and tissue modeling, where each simulation demands thousands of CPU hours. Delve into computational cardiology, maximum mean discrepancies, square-root kernels, and posterior inference for systems of ordinary differential equations, including real-world applications in Goodwin models of oscillatory enzymatic control.
Advances in Distribution Compression - From Kernel Thinning to Stein Thinning
Harvard CMSA via YouTube
Overview
Syllabus
Intro
Motivation: Computational Cardiology
Distribution Compression
Problem Setup
Maximum Mean Discrepancies
Square-root Kernels
Kernel Thinning vs. i.i.d. Sampling: Higher Dimensions
Kernel Thinning vs. Standard MCMC Thinning Posterior inference for systems of ordinary differential equations (ODES) • P-posterior distribution of coupled ODE model parameters given observed data
Compression with Bias Correction
Measuring Distance to P
Stein Thinning Guarantees
Stein Thinning in Action: Correcting for Burn-in Goodwin model of oscillatory enzymatic control
Stein Thinning in Action: Correcting for Tempering
Conclusions
Taught by
Harvard CMSA
