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BEGIN:VEVENT
SUMMARY:Yian Ma (UC San Diego)
DTSTART:20200428T230000Z
DTEND:20200429T001500Z
DTSTAMP:20260404T111111Z
UID:MADDD/1
DESCRIPTION:Title: Briding MCMC and Optimization\nby Yian Ma (UC San Diego) as part
of Mathematics of Data and Decisions @ Davis\n\nLecture held in ZOOM.\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MADDD/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roummel Marcia (UC Merced)
DTSTART:20200505T230000Z
DTEND:20200506T001500Z
DTSTAMP:20260404T111111Z
UID:MADDD/2
DESCRIPTION:Title: Optimization methods for machine learning\nby Roummel Marcia (UC
Merced) as part of Mathematics of Data and Decisions @ Davis\n\nLecture he
ld in ZOOM.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MADDD/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Venkat Chandrasekaran (Caltech)
DTSTART:20200512T230000Z
DTEND:20200513T001500Z
DTSTAMP:20260404T111111Z
UID:MADDD/3
DESCRIPTION:Title: Fitting convex sets to data\nby Venkat Chandrasekaran (Caltech) a
s part of Mathematics of Data and Decisions @ Davis\n\n\nAbstract\nA numbe
r of problems in signal processing may be viewed conceptually as fitting a
convex set to data. In vision and learning\, the task of identifying a c
ollection of features or atoms that provide a concise description of a dat
aset has been widely studied under the title of dictionary learning or spa
rse coding. In convex-geometric terms\, this problem entails learning a p
olytope with a desired facial structure from data. In computed tomography
\, reconstructing a shape from support measurements arises commonly in MRI
\, robotics\, and target reconstruction from radar data. This problem is
usually reformulated as one of estimating a polytope from a collection of
noisy halfspaces.\n\nIn this talk we describe new approaches to these prob
lems that leverage contemporary ideas from the optimization literature on
lift-and-project descriptions of convex sets. This perspective leads to n
atural semidefinite programming generalizations of previous techniques for
fitting polyhedral convex sets to data. We provide several stylized illu
strations in which these generalizations provide improved reconstructions.
On the algorithmic front our methods rely prominently on operator scalin
g\, while on the statistical side our analysis builds on links between lea
rning theory and semialgebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/MADDD/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Atzberger (UC Davis)
DTSTART:20200519T230000Z
DTEND:20200520T001500Z
DTSTAMP:20260404T111111Z
UID:MADDD/4
DESCRIPTION:Title: Geometric approaches for machine learning in the sciences and enginee
ring\nby Paul Atzberger (UC Davis) as part of Mathematics of Data and
Decisions @ Davis\n\n\nAbstract\nThere has been a lot of interest recently
in leveraging machine learning approaches for modeling and analysis in th
e sciences and engineering. This poses significant challenges and require
ments related to data efficiency\, interpretability\, and robustness. For
scientific problems there is often a lot of prior knowledge about general
underlying physical principles\, existence of low dimensional latent stru
ctures\, or groups of invariances or equivariances. We discuss approaches
for representing some of this knowledge to enhance learning methods by us
ing results on manifold embeddings\, stochastic processes within manifolds
\, and harmonic analysis. We show how the approaches can be used for high
-dimensional stochastic dynamical systems with slow-fast time-scale separa
tions to learn from observations\, slow variable representations and reduc
ed models for the dynamics. We also discuss a few other examples where ut
ilizing geometric structure has the potential to improve outcomes in scien
tific machine learning.\n
LOCATION:https://stable.researchseminars.org/talk/MADDD/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prem Devanbu (UC Santa Barbara)
DTSTART:20200526T230000Z
DTEND:20200527T001500Z
DTSTAMP:20260404T111111Z
UID:MADDD/5
DESCRIPTION:Title: Basic concepts and live tutorial on docker containers for novice user
s\nby Prem Devanbu (UC Santa Barbara) as part of Mathematics of Data a
nd Decisions @ Davis\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MADDD/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State University)
DTSTART:20200602T230000Z
DTEND:20200603T001500Z
DTSTAMP:20260404T111111Z
UID:MADDD/6
DESCRIPTION:Title: Applied topology: From global to local.\nby Henry Adams (Colorado
State University) as part of Mathematics of Data and Decisions @ Davis\n\
n\nAbstract\nThrough the use of examples\, I will explain one way in which
applied topology has evolved since the birth of persistent homology in th
e early 2000s. The first applications of topology to data emphasized the g
lobal shape of a dataset\, such as the three-circle model for 3 x 3 pixel
patches from natural images\, or the configuration space of the cyclo-octa
ne molecule\, which is a sphere with a Klein bottle attached via two circl
es of singularity. More recently\, persistent homology is being used to me
asure the local geometry of data. How do you vectorize geometry for use in
machine learning problems? Persistent homology\, and its vectorization te
chniques including persistence landscapes and persistence images\, provide
popular techniques for incorporating geometry in machine learning. I will
survey applications arising from machine learning tasks in agent-based mo
deling\, shape recognition\, archaeology\, materials science\, and biology
.\n
LOCATION:https://stable.researchseminars.org/talk/MADDD/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bartolomeo Stellato (MIT)
DTSTART:20200609T230000Z
DTEND:20200610T001500Z
DTSTAMP:20260404T111111Z
UID:MADDD/7
DESCRIPTION:Title: A machine learning approach to optimization\nby Bartolomeo Stella
to (MIT) as part of Mathematics of Data and Decisions @ Davis\n\n\nAbstrac
t\nMost applications in engineering\, operations research and finance rely
on solving the same optimization problem several times with varying param
eters. This method generates a large amount of data that is usually discar
ded. In this talk\, we describe how to use historical data to understand a
nd solve optimization problems. We present a machine learning approach to
predict the strategy behind the optimal solution of continuous and mixed-i
nteger convex optimization problems. Using interpretable algorithms such a
s optimal classification trees we gain insights on the relationship betwee
n the problem data and the optimal solution. In this way\, optimization is
no longer a black-box and practitioners can understand it. Moreover\, our
method is able to compute the optimal solutions at very high speed. This
applies also to non-interpretable machine learning predictors such as neur
al networks since they can be evaluated very efficiently. We benchmark our
approach on several examples obtaining accuracy above 90% and computation
times multiple orders of magnitude faster than state-of-the-art solvers.
Therefore\, our method provides on the one hand a novel insightful underst
anding of the optimal strategies to solve a broad class of continuous and
mixed-integer optimization problems and on the other hand a powerful compu
tational tool to solve online optimization at very high speed.\n
LOCATION:https://stable.researchseminars.org/talk/MADDD/7/
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