Grant: Canada Research Chairs

Over the past decade, data and its analysis have become integral parts of our society. From politics and business to the sciences and engineering, every aspect of society has been transformed by our interaction with data. Indeed, Statistics Canada has estimated that the value of data, databases, and data science in 2017 was up to $200 billion, roughly two-thirds of the value of established oil-reserves in Canada. In this light, obtaining, processing, and understanding this new wealth of data has become a central problem of the 21st century. Data Science is a rapidly emerging discipline at the interface of mathematics, statistics, and computer science that seeks to tackle these problems. Due to the complexity and scale of problems posed by scientists and engineers in the modern era, new fundamental questions have emerged that require ideas from each of these fields: What are the trade-offs between statistical and computational power when tackling complex data? How do we understand the remarkable power of stochastic approximation algorithms and neural networks? How hard are the typical high-dimensional optimization and sampling problems that we face? The goal of this research is to tackle these challenging questions. We tackle these and related challenging questions using recent advances in probability theory originally developed by the PI and others to tackle problems in the statistical physics of disordered media. These tools have had remarkable success in applications to data science in recent years, but this research line is only just at its infancy. We seek to explore the mathematical foundations of data science and put Canada at the forefront of this exciting new field.