Abstract: The rapid proliferation of hierarchical network architectures, such as edge-cloud systems and networks of geographically distributed data centers, has sparked growing interest in efficiently solving large-scale statistical learning tasks, especially when data is inherently distributed and lacks centralized oversight. In these architectures, communication is fast within local clusters but slow and costly across them. Many of these tasks are also high dimensional in the statistical sense: the number of parameters exceeds the sample size, and accurate estimation is possible only by exploiting low-dimensional structure, such as sparsity or low rank. Decentralization makes inference in this regime particularly challenging: no single node may hold enough samples to estimate the model on its own, even when the pooled samples are sufficient, while computation, time, and inter-node communication are tightly constrained. While statistical-computational trade-offs have been thoroughly characterized for high-dimensional inference in centralized settings, our understanding of these trade-offs within decentralized network environments remains comparatively limited. Indeed, methodologies that demonstrate robustness and accuracy in traditional low-dimensional contexts frequently underperform in high-dimensional regimes, and theoretical convergence results often fail to align with observed empirical behaviors. In this talk, we will introduce new algorithmic frameworks and analytical tools specifically tailored for decentralized high-dimensional inferential tasks. Through several vignettes, we will show how integrating statistical insights into the design and analysis of decentralized optimization algorithms sheds new light on existing gaps and misconceptions prevalent in the literature, thereby redefining our understanding of distributed inference methodologies. Time permitting, we will also outline a new decomposition approach, based on message passing, in which the network, rather than serving only to exchange information, becomes part of the algorithm design; exploiting its structure in this way can markedly speed up convergence.

Bio: Gesualdo Scutari is the Pedro and Granadillo Professor in the Edwardson School of Industrial Engineering and the Elmore Family School of Electrical and Computer Engineering at Purdue University, West Lafayette, IN, USA. Research interests focus on continuous optimization (particularly distributed and stochastic methods), equilibrium programming, and their applications in signal processing and statistical learning. Among other honors, he received the 2013 NSF CAREER Award, the 2015 IEEE Signal Processing Society Young Author Best Paper Award, and the 2020 IEEE Signal Processing Society Best Paper Award. He served as an IEEE Signal Processing Society Distinguished Lecturer (2023-2024) and has been on the editorial boards of several IEEE journals. He is currently an Associate Editor for the SIAM Journal on Optimization. He is a Fellow of IEEE.