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SUMMARY:Wei Biao Wu (University of Chicago)
DTSTART:20210324T160000Z
DTEND:20210324T170000Z
DTSTAMP:20260422T225921Z
UID:Heilbronn_VVP2021/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Heilbronn_VV
 P2021/1/">Fast Algorithms for Estimating Covariance Matrices of Stochastic
  Gradient Descent Solutions</a>\nby Wei Biao Wu (University of Chicago) as
  part of Heilbronn Virtual Visiting Professors 2021\n\n\nAbstract\nStochas
 tic gradient descent (SGD)\, an important optimization method in machine l
 earning\, is widely used for parameter estimation especially in online set
 ting where data comes in stream. While this recursive algorithm is popular
  for the computation and memory efficiency\, it suffers from randomness of
  the solutions. In this talk we shall estimate the asymptotic covariance m
 atrices of the averaged SGD iterates (ASGD) in a fully online fashion. Bas
 ed on the recursive estimator and classic asymptotic normality results of 
 ASGD\, we can conduct online statistical inference of SGD estimators and c
 onstruct asymptotically valid confidence intervals for model parameters. T
 he algorithm for the recursive estimator is efficient and only uses SGD it
 erates: upon receiving new observations\, we update the confidence interva
 ls at the same time as updating the ASGD solutions without extra computati
 onal or memory cost. This approach fits in online setting even if the tota
 l number of data is unknown and takes the full advantage of SGD: computati
 on and memory efficiency. This work is joint with Wanrong Zhu and Xi Chen.
 \n
LOCATION:https://researchseminars.org/talk/Heilbronn_VVP2021/1/
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SUMMARY:Larry Guth (Massachusetts Institute of Technology)
DTSTART:20210426T150000Z
DTEND:20210426T160000Z
DTSTAMP:20260422T225921Z
UID:Heilbronn_VVP2021/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Heilbronn_VV
 P2021/2/">Local smoothing for the wave equation</a>\nby Larry Guth (Massac
 husetts Institute of Technology) as part of Heilbronn Virtual Visiting Pro
 fessors 2021\n\n\nAbstract\nThe local smoothing problem asks about how muc
 h solutions to the wave equation can focus. It was formulated by Chris Sog
 ge in the early 90s. Hong Wang\, Ruixiang Zhang\, and I recently proved th
 e conjecture in two dimensions.\n
LOCATION:https://researchseminars.org/talk/Heilbronn_VVP2021/2/
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SUMMARY:Kaisa Matomäki (University of Turku\, Finland)
DTSTART:20210504T150000Z
DTEND:20210504T160000Z
DTSTAMP:20260422T225921Z
UID:Heilbronn_VVP2021/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Heilbronn_VV
 P2021/3/">On primes and other interesting sequences in short intervals</a>
 \nby Kaisa Matomäki (University of Turku\, Finland) as part of Heilbronn 
 Virtual Visiting Professors 2021\n\n\nAbstract\nBy the prime number theore
 m\, the number of primes up to $x$ is known to be asymptotically $x/\\log 
 x$. This suggests that whenever $H \\leq x$ is reasonably large\, the inte
 rval $[x\, x+H]$ contains about $H/\\log x$ primes. I will discuss what is
  known and what is not known about primes and almost primes (i.e. numbers 
 with only few prime factors) in short intervals. \n\nI will also talk abou
 t the Riemann zeta function and the Liouville function (defined\, for an i
 nteger $n$\, to be $+1$ or $-1$ depending on whether $n$ has an even or od
 d number of prime factors)\, both of which are closely connected to the pr
 ime numbers.\n
LOCATION:https://researchseminars.org/talk/Heilbronn_VVP2021/3/
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