BEGIN:VCALENDAR
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PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Yu Bai (Salesforce Research)
DTSTART;VALUE=DATE-TIME:20201028T170000Z
DTEND;VALUE=DATE-TIME:20201028T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/2
DESCRIPTION:Title: How Important is the Train-Validation Split in Meta-Learning?\nby Y
u Bai (Salesforce Research) as part of One World Seminar Series on the Ma
thematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Murray (NC State University)
DTSTART;VALUE=DATE-TIME:20201021T160000Z
DTEND;VALUE=DATE-TIME:20201021T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/3
DESCRIPTION:Title: Consistency of Cheeger cuts: Total Variation\, Isoperimetry\, and Clust
ering\nby Ryan Murray (NC State University) as part of One World Semin
ar Series on the Mathematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Latz (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20201104T170000Z
DTEND;VALUE=DATE-TIME:20201104T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/4
DESCRIPTION:Title: Analysis of Stochastic Gradient Descent in Continuous Time\nby Jona
s Latz (University of Cambridge) as part of One World Seminar Series on th
e Mathematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengdao Chen (New York University)
DTSTART;VALUE=DATE-TIME:20201111T170000Z
DTEND;VALUE=DATE-TIME:20201111T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/5
DESCRIPTION:Title: A Dynamical Central Limit Theorem for Shallow Neural Networks\nby Z
hengdao Chen (New York University) as part of One World Seminar Series on
the Mathematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bamdad Hosseini (Caltech)
DTSTART;VALUE=DATE-TIME:20201118T170000Z
DTEND;VALUE=DATE-TIME:20201118T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/6
DESCRIPTION:Title: Conditional Sampling with Monotone GANs: Modifying Generative Models to
Solve Inverse Problems\nby Bamdad Hosseini (Caltech) as part of One W
orld Seminar Series on the Mathematics of Machine Learning\n\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Voigtlaender (University of Vienna)
DTSTART;VALUE=DATE-TIME:20201125T170000Z
DTEND;VALUE=DATE-TIME:20201125T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/7
DESCRIPTION:Title: Neural network performance for classification problems with boundaries
of Barron class\nby Felix Voigtlaender (University of Vienna) as part
of One World Seminar Series on the Mathematics of Machine Learning\n\n\nA
bstract\nWe study classification problems in which the distances between t
he different classes are not necessarily positive\, but for which the boun
daries between the classes are well-behaved. More precisely\, we assume th
ese boundaries to be locally described by graphs of functions of Barron-cl
ass. ReLU neural networks can approximate and estimate classification func
tions of this type with rates independent of the ambient dimension. More f
ormally\, three-layer networks with $N$ neurons can approximate such funct
ions with $L^1$-error bounded by $O(N^{-1/2})$. Furthermore\, given $m$ tr
aining samples from such a function\, and using ReLU networks of a suitabl
e architecture as the hypothesis space\, any empirical risk minimizer has
generalization error bounded by $O(m^{-1/4})$. All implied constants depen
d only polynomially on the input dimension. We also discuss the optimality
of these rates. Our results mostly rely on the "Fourier-analytic" Barron
spaces that consist of functions with finite first Fourier moment. But sin
ce several different function spaces have been dubbed "Barron spaces'' in
the recent literature\, we discuss how these spaces relate to each other.
We will see that they differ more than the existing literature suggests.\n
LOCATION:https://researchseminars.org/talk/OneWorldML/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadia Drenska (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20201209T170000Z
DTEND;VALUE=DATE-TIME:20201209T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/8
DESCRIPTION:Title: A PDE Interpretation of Prediction with Expert Advice\nby Nadia Dre
nska (University of Minnesota) as part of One World Seminar Series on the
Mathematics of Machine Learning\n\n\nAbstract\nWe study the problem of pr
ediction of binary sequences with expert advice in the online setting\, wh
ich is a classic example of online machine learning. We interpret the bina
ry sequence as the price history of a stock\, and view the predictor as an
investor\, which converts the problem into a stock prediction problem. In
this framework\, an investor\, who predicts the daily movements of a stoc
k\, and an adversarial market\, who controls the stock\, play against each
other over N turns. The investor combines the predictions of n ≥ 2 expe
rts in order to make a decision about how much to invest at each turn\, an
d aims to minimize their regret with respect to the best-performing expert
at the end of the game. We consider the problem with history-dependent ex
perts\, in which each expert uses the previous d days of history of the ma
rket in making their predictions. The prediction problem is played (in par
t) over a discrete graph called the d dimensional de Bruijn graph.\n\nWe f
ocus on an appropriate continuum limit and using methods from optimal cont
rol\, graph theory\, and partial differential equations\, we discuss strat
egies for the investor and the adversarial market. We prove that the value
function for this game\, rescaled appropriately\, converges as N → ∞
at a rate of O(N−1/2) (for C4 payoff functions) to the viscosity soluti
on of a nonlinear degenerate parabolic PDE. It can be understood as the Ha
milton-Jacobi-Issacs equation for the two-person game. As a result\, we ar
e able to deduce asymptotically optimal strategies for the investor. \n\nT
his is joint work with Robert Kohn and Jeff Calder.\n
LOCATION:https://researchseminars.org/talk/OneWorldML/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziwei Ji (University of Illinois)
DTSTART;VALUE=DATE-TIME:20201216T170000Z
DTEND;VALUE=DATE-TIME:20201216T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/9
DESCRIPTION:Title: The dual of the margin: improved analyses and rates for gradient descen
t’s implicit bias\nby Ziwei Ji (University of Illinois) as part of O
ne World Seminar Series on the Mathematics of Machine Learning\n\nAbstrac
t: TBA\n\nThe implicit bias of gradient descent\, and specifically its mar
gin maximization properties\, have arisen as a promising explanation for t
he good generalization of deep networks. The purpose of this talk is to de
monstrate the effectiveness of a dual problem to smoothed margin maximizat
ion. Concretely\, this talk will develop this dual\, as well as a variety
of consequences in linear and nonlinear settings.\n\nIn the linear case\,
this dual perspective firstly will yield fast 1/t rates for margin maximiz
ation and implicit bias. This is faster than any prior first-order hard-ma
rgin SVM solver\, which achieves 1/sqrt{t} at best.\n\nSecondly\, the dual
analysis also allows a characterization of the implicit bias\, even outsi
de the standard setting of exponentially-tailed losses\; in this sense\, i
t is gradient descent\, and not a particular loss structure which leads to
implicit bias.\n\nIn the nonlinear case\, duality will enable the proof o
f a gradient alignment property: asymptotically\, the parameters and their
gradients become colinear. Although abstract\, this property in turn impl
ies various existing and new margin maximization results.\n\nJoint work wi
th Matus Telgarsky.\n
LOCATION:https://researchseminars.org/talk/OneWorldML/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carola Bibiane Schönlieb (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20210113T170000Z
DTEND;VALUE=DATE-TIME:20210113T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/10
DESCRIPTION:Title: Machine Learned Regularization for Solving Inverse Problems\nby Ca
rola Bibiane Schönlieb (University of Cambridge) as part of One World Sem
inar Series on the Mathematics of Machine Learning\n\n\nAbstract\nInverse
problems are about the reconstruction of an unknown physical quantity fro
m indirect measurements. Most inverse problems of interest are ill-posed a
nd require appropriate mathematical treatment for recovering meaningful so
lutions. Regularization is one of the main mechanisms to turn inverse prob
lems into well-posed ones by adding prior information about the unknown qu
antity to the problem\, often in the form of assumed regularity of solutio
ns. Classically\, such regularization approaches are handcrafted. Examples
include Tikhonov regularization\, the total variation and several sparsit
y-promoting regularizers such as the L1 norm of Wavelet coefficients of th
e solution. While such handcrafted approaches deliver mathematically and c
omputationally robust solutions to inverse problems\, providing a universa
l approach to their solution\, they are also limited by our ability to mod
el solution properties and to realise these regularization approaches comp
utationally.\n\n\n\nRecently\, a new paradigm has been introduced to the r
egularization of inverse problems\, which derives regularization approache
s for inverse problems in a data driven way. Here\, regularization is not
mathematically modelled in the classical sense\, but modelled by highly ov
er-parametrised models\, typically deep neural networks\, that are adapted
to the inverse problems at hand by appropriately selected (and usually pl
enty of) training data.\n\n\n\nIn this talk\, I will review some machine l
earning based regularization techniques\, present some work on unsupervise
d and deeply learned convex regularisers and their application to image re
construction from tomographic and blurred measurements\, and finish by dis
cussing some open mathematical problems.\n
LOCATION:https://researchseminars.org/talk/OneWorldML/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Weber (Princeton University)
DTSTART;VALUE=DATE-TIME:20210120T170000Z
DTEND;VALUE=DATE-TIME:20210120T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/11
DESCRIPTION:Title: Geometric Methods for Machine Learning and Optimization\nby Melani
e Weber (Princeton University) as part of One World Seminar Series on the
Mathematics of Machine Learning\n\n\nAbstract\nMany machine learning appl
ications involve non-Euclidean data\, such as graphs\, strings or matrices
. In such cases\, exploiting Riemannian geometry can deliver algorithms th
at are computationally superior to standard (Euclidean) nonlinear programm
ing approaches. This observation has resulted in an increasing interest in
Riemannian methods in the optimization and machine learning community.\n\
nIn the first part of the talk\, we consider the task of learning a robust
classifier in hyperbolic space. Such spaces have received a surge of inte
rest for representing large-scale\, hierarchical data\, due to the fact th
at they achieve better representation accuracy with lower dimensions. We p
resent the first theoretical guarantees for the (robust) large-margin lear
ning problem in hyperbolic space and discuss conditions under which hyperb
olic methods are guaranteed to surpass the performance of their Euclidean
counterparts. In the second part\, we introduce Riemannian Frank-Wolfe (RF
W) methods for constraint optimization on manifolds. Here\, the goal of th
e theoretical analysis is two-fold: We first show that RFW converges at a
nonasymptotic sublinear rate\, recovering the best-known guarantees for it
s Euclidean counterpart. Secondly\, we discuss how to implement the method
efficiently on matrix manifolds. Finally\, we consider applications of RF
W to the computation of Riemannian centroids and Wasserstein barycenters\,
which are crucial subroutines in many machine learning methods.\n\nBased
on joint work with Suvrit Sra (MIT) and Manzil Zaheer\, Ankit Singh Rawat\
, Aditya Menon and Sanjiv Kumar (all Google Research).\n
LOCATION:https://researchseminars.org/talk/OneWorldML/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathaniel Trask
DTSTART;VALUE=DATE-TIME:20210127T170000Z
DTEND;VALUE=DATE-TIME:20210127T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/12
DESCRIPTION:Title: Structure preservation and convergence in scientific machine learning<
/a>\nby Nathaniel Trask as part of One World Seminar Series on the Mathem
atics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Bertozzi
DTSTART;VALUE=DATE-TIME:20210203T170000Z
DTEND;VALUE=DATE-TIME:20210203T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/13
DESCRIPTION:by Andrea Bertozzi as part of One World Seminar Series on the
Mathematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Agazzi (Duke University)
DTSTART;VALUE=DATE-TIME:20210210T170000Z
DTEND;VALUE=DATE-TIME:20210210T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/14
DESCRIPTION:Title: Convergence and optimality of single-layer neural networks for reinfor
cement learning\nby Andrea Agazzi (Duke University) as part of One Wor
ld Seminar Series on the Mathematics of Machine Learning\n\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/OneWorldML/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederic Koehler
DTSTART;VALUE=DATE-TIME:20210217T170000Z
DTEND;VALUE=DATE-TIME:20210217T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/15
DESCRIPTION:by Frederic Koehler as part of One World Seminar Series on the
Mathematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bubacarr Bah
DTSTART;VALUE=DATE-TIME:20210224T170000Z
DTEND;VALUE=DATE-TIME:20210224T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/16
DESCRIPTION:by Bubacarr Bah as part of One World Seminar Series on the Ma
thematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathaniel Trask
DTSTART;VALUE=DATE-TIME:20210303T170000Z
DTEND;VALUE=DATE-TIME:20210303T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/17
DESCRIPTION:Title: Structure preservation and convergence in scientific machine learning<
/a>\nby Nathaniel Trask as part of One World Seminar Series on the Mathem
atics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Hanin
DTSTART;VALUE=DATE-TIME:20210310T170000Z
DTEND;VALUE=DATE-TIME:20210310T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/18
DESCRIPTION:by Boris Hanin as part of One World Seminar Series on the Mat
hematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Ward
DTSTART;VALUE=DATE-TIME:20210317T170000Z
DTEND;VALUE=DATE-TIME:20210317T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/19
DESCRIPTION:by Rachel Ward as part of One World Seminar Series on the Mat
hematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Calder
DTSTART;VALUE=DATE-TIME:20210324T170000Z
DTEND;VALUE=DATE-TIME:20210324T180000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/20
DESCRIPTION:by Jeff Calder as part of One World Seminar Series on the Mat
hematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Garcia Trillos (Wisconsin Madison)
DTSTART;VALUE=DATE-TIME:20210505T160000Z
DTEND;VALUE=DATE-TIME:20210505T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T191749Z
UID:OneWorldML/21
DESCRIPTION:Title: Adversarial Classification\, Optimal Transport\, and Geometric Flows\nby Nicolas Garcia Trillos (Wisconsin Madison) as part of One World Sem
inar Series on the Mathematics of Machine Learning\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OneWorldML/21/
END:VEVENT
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