BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Luca Tamanini (Universite Paris Dauphine)
DTSTART:20210621T150000Z
DTEND:20210621T154000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/1
DESCRIPTION:Title: Small-time asymptotics of the metric Schrödinger problem\nby Luc
a Tamanini (Universite Paris Dauphine) as part of BIRS workshop: Entropic
Regularization of Optimal Transport and Applications\n\n\nAbstract\nThe Sc
hrödinger problem as "noised" optimal transport is by now a well-establis
hed interpretation. From this perspective several natural questions stem\,
as for instance the convergence rate as the noise parameter vanishes of m
any quantities: optimal value\, Schrödinger bridges and potentials... As
for the optimal value\, after the works of Erbar-Maas-Renger and Pal a fir
st-order Taylor expansion is available. First aim of this talk is to impr
ove this result in a twofold sense: from the first to the second order and
from the Euclidean to the Riemannian setting (and actually far beyond). F
rom the proof it will be clear that the statement is in fact a particular
instance of a more general result. For this reason\, in the second part of
the talk we introduce a large class of dynamical variational problems\, e
xtending far beyond the classical Schrödinger problem\, and for them we p
rove $\\Gamma$-convergence towards the geodesic problem and a suitable gen
eralization of the second-order Taylor expansion. (based on joint works w
ith G. Conforti\, L. Monsaingeon and D. Vorotnikov)\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Nenna (Université Paris-Saclay)
DTSTART:20210621T155000Z
DTEND:20210621T163000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/2
DESCRIPTION:Title: From Schrödinger to Lasry-Lions\nby Luca Nenna (Université Pari
s-Saclay) as part of BIRS workshop: Entropic Regularization of Optimal Tra
nsport and Applications\n\n\nAbstract\nThe minimization of a relative entr
opy (with respect to the Wiener measure) is a very old problem which dates
back to Schrödinger. C. Léonard has established strong connections and
analogies between this problem and the Monge-Kantorovich problem with quad
ratic cost (namely the standard Optimal Transport problem). In particular\
, the entropic interpolation leads to a system of PDEs which present stron
g analogies with the Mean Field Game system with a quadratic Hamiltonian.
In this talk\, we will explain how such systems can indeed be obtained by
minimization of a relative entropy at the level of measures on paths with
an additional term involving the marginal in time. If time permitted we wi
ll also show the multi-population case and its connection with some equati
ons in Quantum Mechanics.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Young-Heon Kim (University of British Columbia)
DTSTART:20210621T164000Z
DTEND:20210621T172000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/3
DESCRIPTION:Title: Optimal transport in Brownian motion stopping\nby Young-Heon Kim
(University of British Columbia) as part of BIRS workshop: Entropic Regula
rization of Optimal Transport and Applications\n\n\nAbstract\nWe consider
an optimal transport problem arising from stopping the Brownian motion fro
m a given distribution to get a fixed or free target distribution\; the fi
xed target case is often called the optimal Skorokhod embedding problem in
the literature\, a popular topic in math finance pioneered by many people
. Our focus is on the case of general dimensions\, which has not been well
understood. We explain that under certain natural assumptions on the tran
sportation cost\, the optimal stopping time is given by the hitting time t
o a barrier\, which is determined by the solution to the dual optimization
problem. In the free target case\, the problem is related to the Stefan p
roblem\, that is\, a free boundary problem for the heat equation. We obtai
n analytical information on the optimal solutions\, including certain BV e
stimates. The fixed target case is mainly from the joint work with Nassif
Ghoussoub and Aaron Palmer at UBC\, while the free target case is the rece
nt joint work (in-progress) with Inwon Kim at UCLA.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert McCann (University of Toronto)
DTSTART:20210621T173000Z
DTEND:20210621T181000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/4
DESCRIPTION:Title: Inscribed radius bounds for lower Ricci bounded metric measure spaces
with mean convex boundary\nby Robert McCann (University of Toronto) a
s part of BIRS workshop: Entropic Regularization of Optimal Transport and
Applications\n\n\nAbstract\nInscribed radius bounds for lower Ricci bounde
d metricConsider an essentially nonbranching metric measure space with the
measure contraction property of Ohta and Sturm. We prove a sharp upper bo
und on the inscribed radius of any subset whose boundary has a suitably si
gned lower bound on its generalized mean curvature. This provides a nonsmo
oth analog of results dating back to Kasue (1983) and subsequent authors.
We prove a stability statement concerning such bounds and --- in the Riema
nnian curvature-dimension (RCD) setting --- characterize the cases of equa
lity. This represents joint work with Annegret Burtscher\, Christian Kette
rer and Eric Woolgar.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yongxin Chen (Georgia Tech)
DTSTART:20210621T203000Z
DTEND:20210621T211000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/5
DESCRIPTION:Title: Graphical Optimal Transport and its Applications\nby Yongxin Chen
(Georgia Tech) as part of BIRS workshop: Entropic Regularization of Optim
al Transport and Applications\n\n\nAbstract\nMulti-marginal optimal transp
ort (MOT) is a generalization of optimal transport theory to settings with
possibly more than two marginals. The computation of the solutions to MOT
problems has been a longstanding challenge. In this talk\, we introduce g
raphical optimal transport\, a special class of MOT problems. We consider
MOT problems from a probabilistic graphical model perspective and point ou
t an elegant connection between the two when the underlying cost for optim
al transport allows a graph structure. In particular\, an entropy regulari
zed MOT is equivalent to a Bayesian marginal inference problem for probabi
listic graphical models with the additional requirement that some of the m
arginal distributions are specified. This relation on the one hand extends
the optimal transport as well as the probabilistic graphical model theori
es\, and on the other hand leads to fast algorithms for MOT by leveraging
the well-developed algorithms in Bayesian inference. We will cover recent
developments of graphical optimal transport in theory and algorithms. We w
ill also go over several applications in aggregate filtering and mean fiel
d games.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Peyré (CNRS and Ecole Normale Supérieure)
DTSTART:20210622T150000Z
DTEND:20210622T154000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/6
DESCRIPTION:Title: Scaling Optimal Transport for High dimensional Learning\nby Gabri
el Peyré (CNRS and Ecole Normale Supérieure) as part of BIRS workshop: E
ntropic Regularization of Optimal Transport and Applications\n\n\nAbstract
\nOptimal transport (OT) has recently gained lot of interest in machine le
arning. It is a natural tool to compare in a geometrically faithful way pr
obability distributions. It finds applications in both supervised learning
(using geometric loss functions) and unsupervised learning (to perform ge
nerative model fitting). OT is however plagued by the curse of dimensional
ity\, since it might require a number of samples which grows exponentially
with the dimension. In this talk\, I will explain how to leverage entropi
c regularization methods to define computationally efficient loss function
s\, approximating OT with a better sample complexity. More information and
references can be found on the website of our book "Computational Optimal
Transport" https://optimaltransport.github.io/\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Korba (École Nationale de la Statistique et de l'Administrat
ion Économique)
DTSTART:20210622T155000Z
DTEND:20210622T163000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/7
DESCRIPTION:Title: Wasserstein Proximal Gradient\nby Anna Korba (École Nationale de
la Statistique et de l'Administration Économique) as part of BIRS worksh
op: Entropic Regularization of Optimal Transport and Applications\n\n\nAbs
tract\nWasserstein gradient flows are continuous time dynamics that define
curves of steepest descent to minimize an objective function over the spa
ce of probability measures (i.e.\, the Wasserstein space). This objective
is typically a divergence w.r.t. a fixed target distribution. In recent ye
ars\, these continuous time dynamics have been used to study the convergen
ce of machine learning algorithms aiming at approximating a probability di
stribution. However\, the discrete-time behavior of these algorithms might
differ from the continuous time dynamics. Besides\, although discretized
gradient flows have been proposed in the literature\, little is known abou
t their minimization power. In this work\, we propose a Forward Backward (
FB) discretization scheme that can tackle the case where the objective fun
ction is the sum of a smooth and a nonsmooth geodesically convex terms. Us
ing techniques from convex optimization and optimal transport\, we analyze
the FB scheme as a minimization algorithm on the Wasserstein space. More
precisely\, we show under mild assumptions that the FB scheme has converge
nce guarantees similar to the proximal gradient algorithm in Euclidean spa
ces.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Niles-Weed (New York University)
DTSTART:20210622T164000Z
DTEND:20210622T172000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/8
DESCRIPTION:Title: Asymptotics for semi-discrete entropic optimal transport\nby Jona
than Niles-Weed (New York University) as part of BIRS workshop: Entropic R
egularization of Optimal Transport and Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zaid Harchaoui
DTSTART:20210622T173000Z
DTEND:20210622T181000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/9
DESCRIPTION:Title: chrödinger Bridge with Entropic Regularization: two-sample test\, ch
aos decomposition\, and large-sample limits\nby Zaid Harchaoui as part
of BIRS workshop: Entropic Regularization of Optimal Transport and Applic
ations\n\n\nAbstract\nWe consider an entropy-regularized statistic that al
lows one to compare two data samples drawn from possibly different distrib
utions. The statistic admits an expression as a weighted average of Monge
couplings with respect to a Gibbs measure. This coupling can be related to
the static Schrödinger bridge given a finite number of particles. We est
ablish the asymptotic consistency as the sample sizes go to infinity of th
e statistic and show that the population limit is the solution of Föllmer
's entropy-regularized optimal transport. The proof technique relies on a
chaos decomposition for paired samples. This is joint work with Lang Liu a
nd Soumik Pal.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Promit Ghosal (MIT)
DTSTART:20210622T203000Z
DTEND:20210622T211000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/10
DESCRIPTION:Title: Geometry and large deviation of entropic optimal transport\nby P
romit Ghosal (MIT) as part of BIRS workshop: Entropic Regularization of Op
timal Transport and Applications\n\n\nAbstract\nOptimal transport (OT) the
ory has flourished due to its connections with geometry\, analysis\, proba
bility theory\, and other fields in mathematics. A renewed interest in OT
stems from applied fields such as machine learning\, image processing and
statistics through the introduction of entropic regularization. In this ta
lk\, we will discuss the convergence of entropically regularized optimal t
ransport. Our first result is about a large deviation principle of the as
sociated optimizers in entropic OT and the second result is about the stab
ility of the optimizers under weak convergence. To prove these results\, w
e will introduce a new notion called 'cyclical invariance' of measures.
This is a joint work with Marcel Nutz and Espen Bernton.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beatrice Acciaio (ETH Zürich)
DTSTART:20210623T150000Z
DTEND:20210623T154000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/11
DESCRIPTION:Title: PQ-GAN: a market generation model consistent with observed spot pric
es and derivative price\nby Beatrice Acciaio (ETH Zürich) as part of
BIRS workshop: Entropic Regularization of Optimal Transport and Applicatio
ns\n\n\nAbstract\nOptimal transport (OT) theory has flourished due to its
connections with geometry\, analysis\, probability theory\, and other fiel
ds in mathematics. A renewed interest in OT stems from applied fields such
as machine learning\, image processing and statistics through the introdu
ction of entropic regularization. In this talk\, we will discuss the conve
rgence of entropically regularized optimal transport. Our first result is
about a large deviation principle of the associated optimizers in entropi
c OT and the second result is about the stability of the optimizers under
weak convergence. To prove these results\, we will introduce a new notion
called 'cyclical invariance' of measures. This is a joint work with Marc
el Nutz and Espen Bernton.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfred Galichon (New York University)
DTSTART:20210623T155000Z
DTEND:20210623T163000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/12
DESCRIPTION:Title: Dynamic Matching Problems (joint w Pauline Corblet and Jeremy Fox)\nby Alfred Galichon (New York University) as part of BIRS workshop: Ent
ropic Regularization of Optimal Transport and Applications\n\n\nAbstract\n
For the purposes of economics applications\, we formulate a class of dynam
ic matching problems. We investigate in particular the stationary case\, a
nd computation and estimation issues are investigated.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ting-Kam Leonard Wong (University of Toronto)
DTSTART:20210623T164000Z
DTEND:20210623T172000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/13
DESCRIPTION:Title: Logarithmic divergences and statistical applications\nby Ting-Ka
m Leonard Wong (University of Toronto) as part of BIRS workshop: Entropic
Regularization of Optimal Transport and Applications\n\n\nAbstract\nWe con
sider the Dirichlet optimal transport which is a multiplicative analogue o
f the Wasserstein transport and is deeply connected to the Dirichlet distr
ibution. The log-likelihood of this distribution defines a logarithmic div
ergence\, in the same way that the square loss comes from the normal distr
ibution. Using this divergence\, which can be extended to a family of gene
ralized exponential families\, we consider statistical methodologies inclu
ding clustering and nonlinear principal component analysis. Our approach e
xtends a well-known duality between exponential family and Bregman diverge
nce. Joint work with Zhixu Tao\, Jiaowen Yang and Jun Zhang.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Huesmann (Universität Münster)
DTSTART:20210624T150000Z
DTEND:20210624T154000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/14
DESCRIPTION:Title: Fluctuations in the optimal matching problems\nby Martin Huesman
n (Universität Münster) as part of BIRS workshop: Entropic Regularizatio
n of Optimal Transport and Applications\n\n\nAbstract\nThe optimal matchin
g problem is one of the classical random optimization problems. While the
asymptotic behavior of the expected cost is well understood only little is
known for the asymptotic behavior of the optimal couplings - the solution
s to the optimal matching problem. In this talk we show that at all mesosc
opic scales the displacement under the optimal coupling converges in suita
ble Sobolev spaces to a Gaussian field which can be identified as the curl
-free part of a vector Gaussian free field. (based on joint work with Mic
hael Goldman)\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathias Beiglböck (University of Vienna)
DTSTART:20210624T155000Z
DTEND:20210624T163000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/15
DESCRIPTION:Title: The Wasserstein space of stochastic processes\nby Mathias Beiglb
öck (University of Vienna) as part of BIRS workshop: Entropic Regularizat
ion of Optimal Transport and Applications\n\n\nAbstract\nWasserstein dista
nce induces a natural Riemannian structure for the probabilities on the Eu
clidean space. This insight of classical transport theory is fundamental f
or tremendous applications in various fields of pure and applied mathemati
cs. We believe that an appropriate probabilistic variant\, the adapted Was
serstein distance AW\, can play a similar role for the class FP of filtere
d processes\, i.e. stochastic processes together with a filtration. In con
trast to other topologies for stochastic processes\, probabilistic operati
ons such as the Doob-decomposition\, optimal stopping and stochastic contr
ol are continuous w.r.t. AW. We also show that (FP\,AW) is a geodesic spac
e\, isometric to a classical Wasserstein space\, and that martingales form
a closed geodesically convex subspace.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Kausamo
DTSTART:20210624T164000Z
DTEND:20210624T172000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/16
DESCRIPTION:Title: Multi-marginal entropy-regularized optimal transportation for singul
ar cost functions\nby Anna Kausamo as part of BIRS workshop: Entropic
Regularization of Optimal Transport and Applications\n\n\nAbstract\nI will
introduce multi-marginal optimal transportation (MOT) for singular cost f
unctions and mention some of its applications. Then I move on to the entro
py-regularised framework\, focusing on the Gamma-convergence proof of the
regularized minimizers for the singular MOT problem towards a non-regulari
sed solution when the regularisation parameter goes to zero. When one goes
from two to many marginals and from attractive to singular cost function\
, different levels of difficulty are introduced. One of the aims of my tal
k is to show how these difficulties can be tackled.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Conforti (Ecole Polytechnique Paris – Mathematics)
DTSTART:20210624T173000Z
DTEND:20210624T181000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/17
DESCRIPTION:Title: Hamilton Jacobi equations for controlled gradient flows: the compari
son principle\nby Giovanni Conforti (Ecole Polytechnique Paris – Mat
hematics) as part of BIRS workshop: Entropic Regularization of Optimal Tra
nsport and Applications\n\n\nAbstract\nThis talk is devoted to the study o
f a class of Hamilton-Jacobi equations on the space of probability measur
es that arises naturally in connection with the study of a general form of
the Schrödinger problem for interacting particle systems. After present
ing the equations and their geometrical interpretation\, I will move on to
illustrate the main ideas behind a general strategy for to prove uniquene
ss of viscosity solutions\, i.e. the comparison principle. Joint work with
D.Tonon (U. Padova) and R.Kraaij (TU Delft).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geoffrey Schiebinger (University of British Columbia)
DTSTART:20210624T203000Z
DTEND:20210624T211000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/18
DESCRIPTION:Title: Towards a mathematical theory of development\nby Geoffrey Schieb
inger (University of British Columbia) as part of BIRS workshop: Entropic
Regularization of Optimal Transport and Applications\n\n\nAbstract\nNew me
asurement technologies like single-cell RNA sequencing are bringing 'big d
ata' to biology. My group develops mathematical tools for analyzing time-c
ourses of high-dimensional gene expression data\, leveraging tools from pr
obability and optimal transport. We aim to develop a mathematical theory t
o answer questions like How does a stem cell transform into a muscle cell\
, a skin cell\, or a neuron? How can we reprogram a skin cell into a neuro
n? We model a developing population of cells with a curve in the space of
probability distributions on a high-dimensional gene expression space. We
design algorithms to recover these curves from samples at various time-po
ints and we collaborate closely with experimentalists to test these ideas
on real data.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max von Renesse (Universitaet Leipzig)
DTSTART:20210625T150000Z
DTEND:20210625T154000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/19
DESCRIPTION:Title: On Overrelaxation in the Sinkhorn Algorithm\nby Max von Renesse
(Universitaet Leipzig) as part of BIRS workshop: Entropic Regularization o
f Optimal Transport and Applications\n\n\nAbstract\nWe discuss a simple bu
t potent modification of the Sinkhorn algorithm based on overrelaxation. W
e provide an a priori estimate for the crucial overrelaxation parameter wh
ich guarantees both global and improved local convergence.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Flavien Léger (Sciences Po Paris)
DTSTART:20210625T155000Z
DTEND:20210625T163000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/20
DESCRIPTION:Title: Taylor expansions for the regularized optimal transport problem\
nby Flavien Léger (Sciences Po Paris) as part of BIRS workshop: Entropic
Regularization of Optimal Transport and Applications\n\n\nAbstract\nWe pro
ve Taylor expansions of the regularized optimal transport problem with gen
eral cost as the temperature goes to zero. \nOur first contribution is a m
ultivariate Laplace expansion formula. We show that the first-order terms
involve the scalar curvature in the corresponding Hessian geometry. \nWe t
hen obtain: \n - first-order expansion of the potentials\; \n - second-ord
er expansion of the optimal transport value. \nJoint work with Pierre Rous
sillon\, François-Xavier Vialard and Gabriel Peyré.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunan Yang (New York University)
DTSTART:20210625T164000Z
DTEND:20210625T172000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/21
DESCRIPTION:Title: Optimal transport-based objective function for physical inverse prob
lems\nby Yunan Yang (New York University) as part of BIRS workshop: En
tropic Regularization of Optimal Transport and Applications\n\n\nAbstract\
nWe have proposed the quadratic Wasserstein distance from optimal transpor
t theory for inverse problems\, including nonlinear medium reconstruction
for waveform inversions and chaotic dynamical systems parameter identifica
tion. Traditional methods for both applications suffered from longstanding
difficulties such as nonconvexity and noise sensitivity. As we advance\,
we discover that the advantages of using optimal transposed-based metrics
apply in a broader class of data-fitting problems where the continuous dep
endence between the parameter and the data involves the change of data pha
se or support of the data. The implicit regularization effects of the Wass
erstein distance similar to a weak norm also help improve stability of par
ameter identification.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katy Craig (University of California Santa Barbara)
DTSTART:20210625T173000Z
DTEND:20210625T181000Z
DTSTAMP:20260422T185536Z
UID:BIRS-21w5120/22
DESCRIPTION:Title: A blob method for diffusion and applications to sampling and two lay
er neural networks\nby Katy Craig (University of California Santa Barb
ara) as part of BIRS workshop: Entropic Regularization of Optimal Transpor
t and Applications\n\n\nAbstract\nGiven a desired target distribution and
an initial guess of that distribution\, composed of finitely many samples\
, what is the best way to evolve the locations of the samples so that they
more accurately represent the desired distribution? A classical solution
to this problem is to allow the samples to evolve according to Langevin dy
namics\, the stochastic particle method corresponding to the Fokker-Planck
equation. In today’s talk\, I will contrast this classical approach wit
h a deterministic particle method corresponding to the porous medium equat
ion. This method corresponds exactly to the mean-field dynamics of trainin
g a two layer neural network for a radial basis function activation functi
on. We prove that\, as the number of samples increases and the variance of
the radial basis function goes to zero\, the particle method converges to
a bounded entropy solution of the porous medium equation. As a consequenc
e\, we obtain both a novel method for sampling probability distributions a
s well as insight into the training dynamics of two layer neural networks
in the mean field regime. This is joint work with Karthik Elamvazhuthi (UC
LA)\, Matt Haberland (Cal Poly)\, and Olga Turanova (Michigan State).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5120/22/
END:VEVENT
END:VCALENDAR