BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Sabre//Sabre VObject 4.5.8//EN
CALSCALE:GREGORIAN
BEGIN:VTIMEZONE
TZID:Europe/Zurich
X-LIC-LOCATION:Europe/Zurich
TZURL:http://tzurl.org/zoneinfo/Europe/Zurich
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19810329T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19961027T030000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:news2021@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20260408T174344
DTSTART;TZID=Europe/Zurich:20260429T150000
SUMMARY:Seminar Analysis and Mathematical Physics: Jose A. Carrillo  (Unive
 rsity of Oxford\, UK)
DESCRIPTION:The Stein Variational Gradient Descent method is a variatio
 nal inference method in statistics that has recently received a lot of at
 tention. The method provides a deterministic approximation of the target d
 istribution\, by introducing a nonlocal interaction with a kernel. Despite
  the significant interest\, the exponential rate of convergence for the co
 ntinuous method has remained an open problem\, due to the difficulty of es
 tablishing the related so-called Stein-log-Sobolev inequality. Here\, we 
 prove that the inequality is satisfied for each space dimension and every 
 kernel whose Fourier transform has a quadratic decay at infinity and is lo
 cally bounded away from zero and infinity. Moreover\, we construct weak so
 lutions to the related PDE satisfying exponential rate of decay towards th
 e equilibrium. The main novelty in our approach is to interpret the Stein
 -Fisher information\, also called the squared Stein discrepancy\, as a d
 uality pairing between H⁻¹(ℝⁿ) and H¹(ℝⁿ)\, which allows us to
  employ the Fourier transform. We also provide several examples of kernels
  for which the Stein-log-Sobolev inequality fails\, partially showing the
  necessity of our assumptions.
X-ALT-DESC:<p>The&nbsp\;Stein&nbsp\;Variational&nbsp\;Gradient Descent meth
 od is a&nbsp\;variational&nbsp\;inference method in statistics that has re
 cently received a lot of attention. The method provides a deterministic ap
 proximation of the target distribution\, by introducing a nonlocal interac
 tion with a kernel. Despite the significant interest\, the exponential rat
 e of convergence for the continuous method has remained an open problem\, 
 due to the difficulty of establishing the related so-called&nbsp\;Stein-lo
 g-Sobolev inequality. Here\, we prove that the inequality is satisfied for
  each space dimension and every kernel whose Fourier transform has a quadr
 atic decay at infinity and is locally bounded away from zero and infinity.
  Moreover\, we construct weak solutions to the related PDE satisfying expo
 nential rate of decay towards the equilibrium. The main novelty in our app
 roach is to interpret the&nbsp\;Stein-Fisher information\, also called the
  squared&nbsp\;Stein&nbsp\;discrepancy\, as a duality pairing between H⁻
 ¹(ℝⁿ) and H¹(ℝⁿ)\, which allows us to employ the Fourier transfo
 rm. We also provide several examples of kernels for which the&nbsp\;Stein-
 log-Sobolev inequality fails\, partially showing the necessity of our&nbsp
 \;assumptions.</p>
DTEND;TZID=Europe/Zurich:20260429T160000
END:VEVENT
END:VCALENDAR