Events
FDS Colloquium
Learning multiple models with limited and sparse data
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Speaker: Munther Dahleh (MIT) William A. Coolidge Professor, Electrical Engineering and Computer Science Massachusetts Institute of Technology Wednesday, April 9, 2025 11:30AM - 1:00PM Lunch at 11:30am in room 1307
Talk at 12:00pm in room 1327 Location: Yale Institute for Foundations of Data Science, Kline Tower 13th Floor, Room 1327, New Haven, CT 06511 and via Webcast: https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=e70e15d9-744f-42f4-931c-b2760114afe6 |
Abstract: In this talk, we address the challenge of learning models for a large number of agents when only limited data is available for each individual. We assume the existence of an underlying shared structure across agents, enabling us to leverage their commonalities to improve model estimation. This setting arises in various applications, including healthcare, economics, and finance.
We propose two shared-structure modeling approaches. The first assumes that all agent models lie within a low-rank subspace. The second extends this idea to the case of mixture models, where each agent is modeled as a random sample of a fixed number of models. A central challenge in this setting is that the lack of sufficient data per agent makes it difficult to directly estimate their models or identify clusters of similar agents.
To address this, we introduce a framework that harnesses data across all agents to learn the shared structure—and in some cases, the individual agent models. Building on spectral methods for mixtures of linear regressions, we present a moment-based estimator that recovers the underlying low-rank subspace. For mixture models, we further employ tensor decomposition to estimate the mixture components.
Our approach generalizes to more complex settings, including mixtures of autoregressive (AR) processes and input-output (I/O) systems. We also demonstrate how both deterministic and stochastic dynamics can be handled within our framework.
This work is in collaboration with Maryann Rui.
Speaker bio: Munther Dahleh is the William A. Coolidge Professor in Electrical Engineering and Computer Science (EECS) and a member MIT’s Laboratory for Information and Decision Systems (LIDS). Dahleh was the founding director of the Institute for Data, Systems, and Society (IDSS), serving from July 1, 2015 to June 30, 2023. He was previously the associate department head of EECS.
Prof. Dahleh joined LIDS as an assistant professor of EECS in 1987 and became a full professor in 1998. He spent the spring of 1993 as a visiting professor in the Department of Electrical Engineering, California Institute of Technology, and has held consulting positions with several companies in the U.S. and abroad.
Prof. Dahleh is internationally known for his fundamental contributions to robust control theory, computational methods for controller design, the interplay between information and control, the fundamental limits of learning and decision in networked systems, and the detection and mitigation of systemic risk in interconnected and networked systems.
In particular, his research interests include:
-Transportation Systems: Dynamic models of congestion under disruptions, dependence of fragility on network topology, cascaded failures, value of side information on performance
-Networked Systems: Foundational theory for the interaction between physical and information networks, Information propagation, distributed decisions, learning network structure from data.
-Social Networks: Information cascades in stochastic networks, opinion dynamics, global games in modeling outcomes of crises
-Systemic Risk: The development of a foundational theory for the early detection and control of systemic risk resulting from idiosyncratic disturbance affecting components of a networked system
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