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Research & Publications Office to host seminar on ‘No-Regret Generative Modeling via Parabolic Equations’

Prof. Nabarun Deb, University of Chicago, will deliver the talk on 3 July 2025

27 June, 2025, Bengaluru: The Office of Research & Publications at IIM Bangalore will host a research seminar, ‘No-Regret Generative Modeling via Parabolic Equations’, to be delivered by Prof. Nabarun Deb, Decision Sciences area, University of Chicago Booth School of Business, on 3 July 2025, at 2.30 PM, in Classroom P-21 at IIMB.

Abstract:

The talk will provide a brief introduction to Euclidean mirror descent, score matching methods, the "classification trick", and methods for regret analysis. The study introduces a novel generative modeling framework based on a discretized parabolic Monge-Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in optimal transport. The method used performs iterative refinement in the space of Brenier maps using a mirror gradient descent step. The authors establish theoretical guarantees for generative modeling through the lens of no-regret analysis, demonstrating that the iterates converge to the optimal Brenier map under a variety of step-size schedules. As a technical contribution, they derive a new Evolution Variational Inequality tailored to the parabolic Monge-Ampère PDE, connecting geometry, transportation cost, and regret. Their framework accommodates non-log-concave target distributions, constructs an optimal sampling process via the Brenier map, and integrates favorable learning techniques from generative adversarial networks and score-based diffusion models. As direct applications, the authors illustrate how their theory paves new pathways for generative modeling and variational inference.

Speaker Profile:

Prof. Nabarun Deb is an Assistant Professor in the Econometrics & Statistics Group at the University of Chicago Booth School of Business, joining in July 2023. He earned his Ph.D. in Statistics from Columbia University (2017–2022) and completed his postdoctoral work at UBC’s PIMS Kantorovich Initiative (2022–23). His research interests include nonparametric inference, theory of optimal transport and its applications in statistics, kernel methods and nearest neighbor graphs, network (Ising) models, fluctuations, and theory of dependent data

Webpage Link: https://www.chicagobooth.edu/faculty/directory/d/nabarun-deb

Add to Calendar 2025-07-03 05:30:00 2025-06-28 11:10:48 Research & Publications Office to host seminar on ‘No-Regret Generative Modeling via Parabolic Equations’ Prof. Nabarun Deb, University of Chicago, will deliver the talk on 3 July 2025 27 June, 2025, Bengaluru: The Office of Research & Publications at IIM Bangalore will host a research seminar, ‘No-Regret Generative Modeling via Parabolic Equations’, to be delivered by Prof. Nabarun Deb, Decision Sciences area, University of Chicago Booth School of Business, on 3 July 2025, at 2.30 PM, in Classroom P-21 at IIMB. Abstract: The talk will provide a brief introduction to Euclidean mirror descent, score matching methods, the "classification trick", and methods for regret analysis. The study introduces a novel generative modeling framework based on a discretized parabolic Monge-Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in optimal transport. The method used performs iterative refinement in the space of Brenier maps using a mirror gradient descent step. The authors establish theoretical guarantees for generative modeling through the lens of no-regret analysis, demonstrating that the iterates converge to the optimal Brenier map under a variety of step-size schedules. As a technical contribution, they derive a new Evolution Variational Inequality tailored to the parabolic Monge-Ampère PDE, connecting geometry, transportation cost, and regret. Their framework accommodates non-log-concave target distributions, constructs an optimal sampling process via the Brenier map, and integrates favorable learning techniques from generative adversarial networks and score-based diffusion models. As direct applications, the authors illustrate how their theory paves new pathways for generative modeling and variational inference. Speaker Profile: Prof. Nabarun Deb is an Assistant Professor in the Econometrics & Statistics Group at the University of Chicago Booth School of Business, joining in July 2023. He earned his Ph.D. in Statistics from Columbia University (2017–2022) and completed his postdoctoral work at UBC’s PIMS Kantorovich Initiative (2022–23). His research interests include nonparametric inference, theory of optimal transport and its applications in statistics, kernel methods and nearest neighbor graphs, network (Ising) models, fluctuations, and theory of dependent data Webpage Link: https://www.chicagobooth.edu/faculty/directory/d/nabarun-deb IIM Bangalore IIM Bangalore communications@iimb.ac.in Asia/Kolkata public
3 Jul 2025

Research & Publications Office to host seminar on ‘No-Regret Generative Modeling via Parabolic Equations’

Add to Calendar 2025-07-03 05:30:00 2025-06-28 11:10:48 Research & Publications Office to host seminar on ‘No-Regret Generative Modeling via Parabolic Equations’ Prof. Nabarun Deb, University of Chicago, will deliver the talk on 3 July 2025 27 June, 2025, Bengaluru: The Office of Research & Publications at IIM Bangalore will host a research seminar, ‘No-Regret Generative Modeling via Parabolic Equations’, to be delivered by Prof. Nabarun Deb, Decision Sciences area, University of Chicago Booth School of Business, on 3 July 2025, at 2.30 PM, in Classroom P-21 at IIMB. Abstract: The talk will provide a brief introduction to Euclidean mirror descent, score matching methods, the "classification trick", and methods for regret analysis. The study introduces a novel generative modeling framework based on a discretized parabolic Monge-Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in optimal transport. The method used performs iterative refinement in the space of Brenier maps using a mirror gradient descent step. The authors establish theoretical guarantees for generative modeling through the lens of no-regret analysis, demonstrating that the iterates converge to the optimal Brenier map under a variety of step-size schedules. As a technical contribution, they derive a new Evolution Variational Inequality tailored to the parabolic Monge-Ampère PDE, connecting geometry, transportation cost, and regret. Their framework accommodates non-log-concave target distributions, constructs an optimal sampling process via the Brenier map, and integrates favorable learning techniques from generative adversarial networks and score-based diffusion models. As direct applications, the authors illustrate how their theory paves new pathways for generative modeling and variational inference. Speaker Profile: Prof. Nabarun Deb is an Assistant Professor in the Econometrics & Statistics Group at the University of Chicago Booth School of Business, joining in July 2023. He earned his Ph.D. in Statistics from Columbia University (2017–2022) and completed his postdoctoral work at UBC’s PIMS Kantorovich Initiative (2022–23). His research interests include nonparametric inference, theory of optimal transport and its applications in statistics, kernel methods and nearest neighbor graphs, network (Ising) models, fluctuations, and theory of dependent data Webpage Link: https://www.chicagobooth.edu/faculty/directory/d/nabarun-deb IIM Bangalore IIM Bangalore communications@iimb.ac.in Asia/Kolkata public

Prof. Nabarun Deb, University of Chicago, will deliver the talk on 3 July 2025

27 June, 2025, Bengaluru: The Office of Research & Publications at IIM Bangalore will host a research seminar, ‘No-Regret Generative Modeling via Parabolic Equations’, to be delivered by Prof. Nabarun Deb, Decision Sciences area, University of Chicago Booth School of Business, on 3 July 2025, at 2.30 PM, in Classroom P-21 at IIMB.

Abstract:

The talk will provide a brief introduction to Euclidean mirror descent, score matching methods, the "classification trick", and methods for regret analysis. The study introduces a novel generative modeling framework based on a discretized parabolic Monge-Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in optimal transport. The method used performs iterative refinement in the space of Brenier maps using a mirror gradient descent step. The authors establish theoretical guarantees for generative modeling through the lens of no-regret analysis, demonstrating that the iterates converge to the optimal Brenier map under a variety of step-size schedules. As a technical contribution, they derive a new Evolution Variational Inequality tailored to the parabolic Monge-Ampère PDE, connecting geometry, transportation cost, and regret. Their framework accommodates non-log-concave target distributions, constructs an optimal sampling process via the Brenier map, and integrates favorable learning techniques from generative adversarial networks and score-based diffusion models. As direct applications, the authors illustrate how their theory paves new pathways for generative modeling and variational inference.

Speaker Profile:

Prof. Nabarun Deb is an Assistant Professor in the Econometrics & Statistics Group at the University of Chicago Booth School of Business, joining in July 2023. He earned his Ph.D. in Statistics from Columbia University (2017–2022) and completed his postdoctoral work at UBC’s PIMS Kantorovich Initiative (2022–23). His research interests include nonparametric inference, theory of optimal transport and its applications in statistics, kernel methods and nearest neighbor graphs, network (Ising) models, fluctuations, and theory of dependent data

Webpage Link: https://www.chicagobooth.edu/faculty/directory/d/nabarun-deb