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UID:calendar.124412.field_date.0@www.tse-fr.eu
DTSTAMP:20210620T001652Z
CREATED:20210211T161001Z
DESCRIPTION:Yohann De Castro (Ecole Central de Lyon)\, “Supermix Sparse Reg
ularization for Mixtures”\, MAD-Stat. Seminar\, Toulouse: TSE\, April 15\,
2021\, 11:00–12:15\, Zoom.\n\nThis paper investigates the statistical est
imation of a discrete mixing measure µº involved in a kernel mixture model
. Using some recent advances in l1-regularization over the space of measur
es\,\nwe introduce a “data fitting and regularization” convex program for
estimating µº in a grid-less manner from a sample of mixture law\, this me
thod is referred to as Beurling-LASSO.\nOur contribution is two-fold: we d
erive a lower bound on the bandwidth of our data fitting term depending on
ly on the support of µº and its so-called “minimum separation” to ensure q
uantitative support\nlocalization error bounds\; and under a so-called “no
n-degenerate source condition” we derive a non-asymptotic support stabilit
y property. This latter shows that for a sufficiently large sample size n\
,\nour estimator has exactly as many weighted Dirac masses as the target µ
º\, converging in amplitude and localization towards the true ones. Finall
y\, we also introduce some tractable algorithms for solving\nthis convex p
rogram based on “Sliding Frank-Wolfe” or “Conic Particle Gradient Descent”
. Statistical performances of this estimator are investigated designing a
so-called “dual certificate”\, which is appropriate to our setting.\nSome
classical situations\, as e.g. mixtures of super-smooth distributions (e.g
. Gaussian distributions) or ordinary-smooth distributions (e.g. Laplace d
istributions)\, are discussed at the end of the paper.
DTSTART;TZID=Europe/Paris:20210415T120000
DTEND;TZID=Europe/Paris:20210415T131500
LAST-MODIFIED:20210216T011001Z
LOCATION:Toulouse: TSE\, April 15\, 2021\, 11:00–12:15\, Zoom
SUMMARY:MAD-Stat. Seminar
URL;TYPE=URI:https://www.tse-fr.eu/seminars/2021-supermix-sparse-regulariza
tion-mixtures
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