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SUMMARY:Step size control for Newton type MCMC samplers   Jonathan Goodman
  - Jonathan Goodman ()
DTSTART:20191120T150500Z
DTEND:20191120T153500Z
UID:TALK135031@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:ABSTRACT: MCMC sampling can use ideas from the optimization co
 mmunity. &nbsp\;Optimization via Newton&rsquo\;s method can fail without l
 ine search\, even for smooth strictly convex problems. &nbsp\;Affine invar
 iant Newton based MCMC sampling uses a Gaussian proposal based on a quadra
 tic model of the potential using the local gradient and Hessian. &nbsp\;Th
 is can fail (conjecture: give a transient Markov chain) even for smooth st
 rictly convex potentials. &nbsp\;We describe a criterion that allows a seq
 uence of proposal distributions from X_n with decreasing &ldquo\;step size
 s&rdquo\; until (with probability 1) a proposal is accepted. &nbsp\;&ldquo
 \;Very detailed balance&rdquo\; allows the whole process to preserve the t
 arget distribution. &nbsp\;The method works in experiments but the theory 
 is missing.  <br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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