Fall 2018 MATH 8660 Topics in
Probability
Course
Instructor:
Wei-Kuo Chen
Office: 537 Vincent Hall
Email: wkchen@umn.edu
Description of the course:
The aim of this course will be focused on
establishing the the probabilistic and statistical mechanical
methods for spin and graphical models in high dimension and
introducing their emerging applications in a variety of fields.
The lecture will be divided into two major components. The first
part will be covering some fundamental tools in high dimensional
probability including concentration phenomena, random matrix
theory, and chaining. The second part will mostly involve the
recent popular topics in computer and data sciences.
Reference: [1] High-Dimensional Probability, by R. Vershynin
(available on author's website).
[2] Information, Physics, and Computation, by M. Mezard and A.
Montanari
[3] Ten Lectures and Forty-Two Open Problems in the Mathematics of
Data Science, by B. Afonso (available on author's website)
Tentative topics (More will be updated later):
- Principle Component Analysis: Ch. 1 in [3]
- Positive Semi-definite Programming and Grothendick's inequality:
Ch. 2 & 5 in [1]
- Concentration Inequalities: Ch. 1 in [1]
- Random Matrix and Some Applications: Ch. 3 in [1]
- Some basics on Information Theory and Statistical Mechanics: Ch. 1
& 2 in [2]
- Detection and Recovery Problems: See this paper, Phase transitions in
spiked matrix estimation: Information-Theoretic Analysis, by
Leo Miolane
- Graphical Models and Factor Graphs: Ch. 9 in [2]
- Belief-Propagation: Ch. 14 in [2]
Time: MWF from 11:15 AM to 12:05 PM
Classroom: Vincent Hall 301
Grades: The final grade will be determined by a few
homework assignments, which will be posted on the Moodle
site.
Office hour: 537VH, TBD