On the Role of Data Structure in High-Dimensional Learning

Explore the intricacies of high-dimensional learning in this 57-minute seminar by Joan Bruna Estrach from New York University. Delve into the experimental revolution of deep learning and its challenges, examining geometric function classes and harmonic analysis on the sphere. Investigate invariant kernels, optimization aspects, and overparametrisation while considering algorithm-specific hardness. Analyze the computational hardness of shallow learning, the shortest vector problem, and continuous learning with errors. Discover algorithmic upper bounds, the LLL algorithm, and random subset problems. Expand your understanding beyond generalized linear models in this comprehensive exploration of data structure's role in high-dimensional machine learning.

Intro
DEEP LEARNING TODAY: EXPERIMENTAL REVOLUTION
CHALLENGES OF HIGH-DIMENSIONAL LEARNING
GEOMETRIC FUNCTION CLASSES
HARMONIC ANALYSIS ON THE SPHERE
INVARIANT KERNELS
OPTIMIZATION ASPECTS
OVERPARAMETRISATION
ALGORITHM-SPECIFIC HARDNESS
COMPUTATIONAL HARDNESS OF SHALLOW LEARNING
SHORTEST VECTOR PROBLEM
CONTINUOUS LEARNING WITH ERRORS
ALGORITHMIC UPPER BOUNDS
LLL AND RANDOM SUBSET PROBLEM
BEYOND GENERALISED LINEAR MODELS
CONCLUSIONS