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SUMMARY:Wei Biao Wu (University of Chicago)
DTSTART:20210324T160000Z
DTEND:20210324T170000Z
DTSTAMP:20260404T111244Z
UID:Heilbronn_VVP2021/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Heilb
 ronn_VVP2021/1/">Fast Algorithms for Estimating Covariance Matrices of Sto
 chastic Gradient Descent Solutions</a>\nby Wei Biao Wu (University of Chic
 ago) as part of Heilbronn Virtual Visiting Professors 2021\n\n\nAbstract\n
 Stochastic gradient descent (SGD)\, an important optimization method in ma
 chine learning\, is widely used for parameter estimation especially in onl
 ine setting where data comes in stream. While this recursive algorithm is 
 popular for the computation and memory efficiency\, it suffers from random
 ness of the solutions. In this talk we shall estimate the asymptotic covar
 iance matrices of the averaged SGD iterates (ASGD) in a fully online fashi
 on. Based on the recursive estimator and classic asymptotic normality resu
 lts of ASGD\, we can conduct online statistical inference of SGD estimator
 s and construct asymptotically valid confidence intervals for model parame
 ters. The algorithm for the recursive estimator is efficient and only uses
  SGD iterates: upon receiving new observations\, we update the confidence 
 intervals at the same time as updating the ASGD solutions without extra co
 mputational or memory cost. This approach fits in online setting even if t
 he total number of data is unknown and takes the full advantage of SGD: co
 mputation and memory efficiency. This work is joint with Wanrong Zhu and X
 i Chen.\n
LOCATION:https://stable.researchseminars.org/talk/Heilbronn_VVP2021/1/
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SUMMARY:Larry Guth (Massachusetts Institute of Technology)
DTSTART:20210426T150000Z
DTEND:20210426T160000Z
DTSTAMP:20260404T111244Z
UID:Heilbronn_VVP2021/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Heilb
 ronn_VVP2021/2/">Local smoothing for the wave equation</a>\nby Larry Guth 
 (Massachusetts Institute of Technology) as part of Heilbronn Virtual Visit
 ing Professors 2021\n\n\nAbstract\nThe local smoothing problem asks about 
 how much solutions to the wave equation can focus. It was formulated by Ch
 ris Sogge in the early 90s. Hong Wang\, Ruixiang Zhang\, and I recently pr
 oved the conjecture in two dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/Heilbronn_VVP2021/2/
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SUMMARY:Kaisa Matomäki (University of Turku\, Finland)
DTSTART:20210504T150000Z
DTEND:20210504T160000Z
DTSTAMP:20260404T111244Z
UID:Heilbronn_VVP2021/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Heilb
 ronn_VVP2021/3/">On primes and other interesting sequences in short interv
 als</a>\nby Kaisa Matomäki (University of Turku\, Finland) as part of Hei
 lbronn Virtual Visiting Professors 2021\n\n\nAbstract\nBy the prime number
  theorem\, 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\, t
 he interval $[x\, x+H]$ contains about $H/\\log x$ primes. I will discuss 
 what is known and what is not known about primes and almost primes (i.e. n
 umbers with only few prime factors) in short intervals. \n\nI will also ta
 lk about the Riemann zeta function and the Liouville function (defined\, f
 or an integer $n$\, to be $+1$ or $-1$ depending on whether $n$ has an eve
 n or odd number of prime factors)\, both of which are closely connected to
  the prime numbers.\n
LOCATION:https://stable.researchseminars.org/talk/Heilbronn_VVP2021/3/
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