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DTSTAMP:20260602T125052Z
DESCRIPTION:Title:\n\nFunction-space regularized information divergences an
 d optimal transport for enhanced generative modeling\n\nAbstract: \n\nWe p
 resent recent work on new variational representations for probability dive
 rgences and metrics with applications to machine learning and uncertainty 
 quantification (UQ). The newly constructed information-theoretic divergenc
 es interpolate between f-divergences (e.g. KL-divergence) and Integral Pro
 bability Metrics (IPM) such as the Wasserstein or the MMD distances.\n\nTh
 ese divergences show improved convergence and stability properties in stat
 istical learning applications (in particular for generative adversarial ne
 tworks (GANs)) as well as tighter uncertainty regions in UQ.\n\nThese dive
 rgences also provide new mathematical and computational insights on Lipsch
 itz regularization methods (e.g. spectral normalization in neural networks
 ) which have recently emerged as an important algorithmic tool in Deep Lea
 rning. A version of the Data Processing Inequality allows flexibility in s
 electing the functions to be optimized over in the variational representat
 ion of the divergences.\n\nThis feature comes in particularly handy when l
 earning distributions which preserve additional structure such as group sy
 mmetries\, or more general constraints.\n\nCombining our new divergences w
 ith recent advances in invariant and equivariant neural networks allowed u
 s to introduce Structure-Preserving GANs (SP-GAN) as a data-efficient appr
 oach for learning distributions with symmetries.\n\nOur theoretical insigh
 ts lead to a reduced invariant discriminator space\, as well as to careful
 ly constructed equivariant generators\, avoiding flawed designs that can e
 asily lead to a catastrophic “mode collapse” for the learned distribution.
 \n\nOur experimental and theoretical results show a drastic improvement in
  sample fidelity and diversity\, and importantly in the amount of data nee
 ded to learn invariant distributions.\n\n \n\n \n
DTSTART:20230403T203000Z
DTEND:20230403T213000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Markos Katsoulakis (University of  Massachusetts-Amherst)
URL:/mathstat/channels/event/markos-katsoulakis-univer
 sity-massachusetts-amherst-347223
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