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SUMMARY:Mean-shift interacting particle systems for optimal quantization a
 nd beyond - Youssef Marzouk (Massachusetts Institute of Technology)
DTSTART:20250624T130000Z
DTEND:20250624T140000Z
UID:TALK232222@talks.cam.ac.uk
DESCRIPTION:Approximating a probability distribution using a set of partic
 les is a fundamental problem in machine learning and statistics\, with app
 lications including clustering and quantization. We formalize this problem
  by seeking a weighted mixture of Dirac measures that best approximates th
 e target distribution in the sense of maximum mean discrepancy (MMD). We a
 rgue that a Wasserstein--Fisher--Rao gradient flow is well-suited to desig
 ning such weighted quantizations\, and show that this flow can be discreti
 zed using a system of interacting particles that satisfy simple closed-for
 m ODEs. To more efficiently reach a stationary solution of these ODEs\, we
  derive a new fixed-point algorithm called mean shift interacting particle
 s (MSIP). We show that MSIP extends the classical mean shift algorithm\, w
 idely used for identifying modes in kernel density estimates. Moreover\, w
 e show that MSIP can be interpreted as a preconditioned gradient descent w
 ith important acceleration properties\, and that it acts as a relaxation o
 f Lloyd&rsquo\;s algorithm for clustering. This unification of gradient fl
 ows\, mean shift\, and MMD-optimal quantization yields algorithms that are
  more robust and efficient than state-of-the-art methods\, as demonstrated
  empirically.\nTime permitting\, we will also discuss links between MMD qu
 antization and Bayesian quadrature\, and present extensions of MSIP to the
  problem of sampling given access to the unnormalized target density and s
 core.\nThis is joint work with Ayoub Belhadji and Daniel Sharp.
LOCATION:Seminar Room 1\, Newton Institute
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