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CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20221003T155006Z
DTSTART:20221005T140000Z
DTEND:20221005T150000Z
SUMMARY:Jonas Latz - Gradient flows and randomised thresholding: sparse i
nversion and classification
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}v9k-l84a9d6
d-lgn06w
DESCRIPTION:Join us for this research seminar\, part of the SQUIDS (Stati
stics\, quantification of uncertainty\, inverse problems and data scienc
e) seminar series.\n\nAbstract: Sparse inversion and classification prob
lems are ubiquitous in modern data science and imaging. They are often f
ormulated as non-smooth minimisation problems. In sparse inversion\, we
minimise\, e.g.\, the sum of a data fidelity term and an L1/LASSO regula
riser. In classification\, we consider\, e.g.\, the sum of a data fideli
ty term and a non-smooth Ginzburg--Landau energy. Standard (sub)gradient
descent methods have shown to be inefficient when approaching such prob
lems. Splitting techniques are much more useful: here\, the target funct
ion is partitioned into a sum of two subtarget functions -- each of whic
h can be efficiently optimised. Splitting proceeds by performing optimis
ation steps alternately with respect to each of the two subtarget functi
ons. \nIn this work\, we study splitting from a stochastic continuous-ti
me perspective. Indeed\, we define a differential inclusion that follows
one of the two subtarget function's negative subdifferential at each po
int in time. The choice of the subtarget function is controlled by a bin
ary continuous-time Markov process. The resulting dynamical system is a
stochastic approximation of the underlying subgradient flow. We investig
ate this stochastic approximation for an L1-regularised sparse inversion
flow and for a discrete Allen-Cahn equation minimising a Ginzburg--Land
au energy. In both cases\, we study the longtime behaviour of the stocha
stic dynamical system and its ability to approximate the underlying subg
radient flow at any accuracy. We illustrate our theoretical findings in
a simple sparse estimation problem and also in low- and high-dimensional
classification problems.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:G.108\, Alan Turing Building\, Manchester
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