<div class="csl-bib-body">
<div class="csl-entry">Aubin, P.-C. (2024, May 15). <i>Optimizing my distributions and proving convergence, or how to look into the mirror</i> [Presentation]. SWM Colloquium, Wien, Austria.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/198624
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dc.description.abstract
Many problems in machine learning and applied statistics can be formulated as optimizing a functional over the space of probability measures, e.g. the Kullback–Leibler (KL) divergence. But can we guarantee that we have a converging algorithm? Starting from Expectation-Maximization (EM), I will show that it can always be written as a mirror descent and present two cases, 1) the joint distribution is an exponential family and 2) we have a non-parametric distribution, but only over the latent space. In these cases, EM only involves convex functions and we have a (sub)linear convergence rate. Moving to variational inference in disguise, namely entropic optimal transport, I will then focus on the convergence of Sinkhorn's algorithm, a.k.a IPFP or RAS, outlining the similarities with EM.
Finally, I will show that both these algorithms fall within a general majorize-minimize framework for which we prove novel rates of convergence based on a five-point property introduced by Csiszár and Tusnády (in 1984).
The talk is based on joint works with Anna Korba (ENSAE, France) and Flavien Léger (INRIA Paris), see https://arxiv.org/abs/2305.04917 , Sections 1, 4.7 and 4.8 for an overview.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
Optimization
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dc.subject
Gradient descent
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dc.subject
Convergence
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dc.title
Optimizing my distributions and proving convergence, or how to look into the mirror
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
P 36344N
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dc.type.category
Presentation
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tuw.publication.invited
invited
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tuw.project.title
Unilateralität und Asymmetrie in der Variationsanalyse
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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tuw.linking
https://arxiv.org/abs/2305.04917
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tuw.publication.orgunit
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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tuw.event.name
SWM Colloquium
en
tuw.event.startdate
15-05-2024
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tuw.event.enddate
15-05-2024
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Wien
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tuw.event.country
AT
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tuw.event.institution
E105 SWM, TU Wien
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tuw.event.presenter
Aubin, Pierre-Cyril
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.openairetype
conference presentation
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item.openairecristype
http://purl.org/coar/resource_type/R60J-J5BD
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item.cerifentitytype
Publications
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item.grantfulltext
none
-
item.fulltext
no Fulltext
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item.languageiso639-1
en
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crisitem.author.dept
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik
