Latent structures in high-dimensional systems with complex interactions

Large-scale systems with units interacting via a complex mechanism are ubiquitous in modern research across diverse fields, ranging from spread of epidemics, dynamics of social networks, to recognizing hidden patterns in biological systems such as the brain. Often, the core question of interest in such systems is to identify macroscopic properties that govern their behavior, famously referred to as universality phenomena. In conjunction, it is also of immense interest to use our understanding of these complex systems to develop efficient, scalable algorithms for performing various machine learning tasks. In this talk, I will discuss foundational aspects of these broad questions through the lens of probability and network science and, in more detail, describe my contributions to emerging challenges such as
(a) Universality for percolation on complex networks,
(b) Non-asymptotic and model-free analysis for spread of epidemics, and
(c) Clustering and representation learning algorithms for networks.

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