Explore the power and versatility of sampling methods in this comprehensive lecture by Peter W. Glynn from Stanford University. Delve into the historical context, philosophical underpinnings, and modern applications of sampling across various fields. Learn about statistical sampling in surveys, Monte Carlo methods in computational mathematics, and the role of sampling in distributed control systems and machine learning algorithms. Understand key concepts such as dimensional insensitivity, the "curse of dimensionality," and the differences between statistical and Monte Carlo sampling. Gain insights into how subtle modifications in sampling techniques can significantly impact results and why sampling-based approaches are crucial in overcoming computational challenges in high-dimensional problems. Through examples and visualizations, discover the practical applications of sampling in real-world scenarios, from presidential elections to server farm job assignments.
Overview
Syllabus
Date: 14 August 2019, 16:00 to
Introduction to speaker
The Power of Sampling
What should a well-educated scientist know about sampling?
Thesis of Lecture:
According to Wikipedia:
Some History:
First sampling-based survey:
Second known instance of sampling
Today, statistical sampling is used everywhere
Such randomized trials form one setting where one can legitimately claim evidence of a causal effect
Key Philosophical Underpinning:
1936 US Presidential Election
Problems with Literary Digest survey:
Moral of the Story:
Subtle modifications in sampling can have a big impact
Why?
Many other such subtleties exist in applying sampling methods
Active research area:
Sampling in Computational Mathematics
High-dimensional Integration:
High-level Perspective:
History
Analysis of Monte Carlo Method:
If it's so slow, why is it so widely used?
The Numerical Alternative to Monte Carlo
Better integration rules:
Tracking discontinuities is easy in d = 1
Versatility of Monte Carlo Method:
"Curse of Dimensionality"
Result
What about Monte Carlo?
Example: Compute volume of region A c [0, 1]d
So, Monte Carlo is dimensionally insensitive...
Coding Flexibility and Visualization: Aan Example
Modify model so that time spent in just one state is non-exponential...
Monte Carlo Alternative:
A Key Difference between Statistical Sampling and Monte Carlo Sampling
Sampling in Synthesizing Distributed Controls
The agents typically need state information to make good decisions
Example: Assigning incoming jobs to servers on a server farm
Approach 1: Centralized controller assigns incoming jobs to shortest queue
Sampling plays a key role in many machine learning algorithms
Final words:
Q&A
Taught by
International Centre for Theoretical Sciences
