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         Department of Systems Engineering and Engineering Management

                             The Chinese University of Hong Kong

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Date: 14:00 pm - 15:15 pm on 16 December (Tuesday)

Venue: ERB 513, The Chinese University of Hong Kong

Title: How tractable is statistical learning in high dimensions?

Speaker: Mengqi Lou, School of Industrial and Systems Engineering,

Georgia Institute of Technology





Abstract:

The task of learning the underlying parameters of a statistical model

from noisy samples is ubiquitous in modern signal processing and data

science. Both computational and statistical challenges arise, especially

in high-dimensional settings where the number of parameters is

comparable to (or exceeds) the sample size. On the computational side,

iterative algorithms are commonly used to fit complex models to random

data, but their design and analysis are often guided by worst-case upper

bounds that may not reflect practical performance. On the statistical

side, classical information-theoretic limits on sample complexity or

signal-to-noise ratio may be unattainable by any polynomial-time

procedure, making these limits an impractical benchmark for modern

high-dimensional problems.



In this talk, I will discuss two general frameworks that address these

computational and statistical challenges. In the first part, I will

present a toolkit that yields sharp, iterate-by-iterate

characterizations of solution quality for complex iterative algorithms

on several non-convex model-fitting problems with random data. In the

second part, I will present a toolkit to derive average-case

“reductions’’ between different statistical models, illustrating how

such reductions reveal the computational limits of solving several

structured high-dimensional problems, including resolving a decade-old

conjecture in sparse phase retrieval.



Bio:

Mengqi Lou is a final-year Ph.D. student in the Algorithms,

Combinatorics, and Optimization program at the School of Industrial and

Systems Engineering, Georgia Institute of Technology, where he is

advised by Professor Ashwin Pananjady. In Fall 2021, he was a visiting

student at the Simons Institute for the Theory of Computing at UC

Berkeley. His research interests lie in high-dimensional statistics,

optimization, and statistical–computational trade-offs. His work has

received several recognitions, including an Outstanding Paper Award at

the International Conference on Algorithmic Learning Theory (ALT), 2025.



Everyone is welcome to attend the talk!