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CATEGORIES:ML@CL Seminar Series
SUMMARY:Uncertainty-Aware Numerical Solutions of ODEs by B
ayesian Filtering - Hans Kersting\, INRIA Paris
DTSTART;TZID=Europe/London:20210216T150000
DTEND;TZID=Europe/London:20210216T160000
UID:TALK157396AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/157396
DESCRIPTION:Numerical approximations can be regarded as statis
tical inference\, if one interprets the solution o
f the numerical problem as a parameter in a statis
tical model whose likelihood links it to the infor
mation (`data') available from evaluating function
s. This view is advocated by the field of Probabil
istic Numerics and has already yielded two success
es: Bayesian Optimization and Bayesian Quadrature.
In an analogous manner\, we construct a Bayesian
probabilistic-numerical method for ODEs. To this e
nd\, we construct a probabilistic state space mode
l for ODEs which enables us to borrow the machiner
y of Bayesian filtering. This unlocks the applicat
ion of all Bayesian filters from signal processing
to ODEs\, which we name ODE filters. We theoretic
ally analyse the convergence rates of the most ele
mentary one\, the Kalman ODE filter and discuss it
s uncertainty quantification. Lastly\, we demonstr
ate how employing these ODE filters as forward sim
ulators engenders new ODE inverse problem solvers
that outperform its classical 'likelihood-free' co
unterparts.
LOCATION:https://us02web.zoom.us/j/86046826779?pwd=RUZCVGxz
dDMrRDN2bDJEUkk1NUVyUT09
CONTACT:
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