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UID:29@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20240112T160000
DTEND;TZID=Asia/Kolkata:20240112T170000
DTSTAMP:20240108T064154Z
URL:https://cds.iisc.ac.in/events/m-tech-research-thesis-colloquium-cds-an
 -importance-sampling-in-n-sphere-monte-carlo-nsmc-and-its-performance-anal
 ysis-for-high-dimensional-integration/
SUMMARY:M.Tech Research Thesis {Colloquium}: CDS : "An importance sampling 
 in N-Sphere Monte Carlo (NSMC) and its performance analysis for high dimen
 sional integration."
DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nM.Tech Research 
 Thesis Colloquium\n\n\n\nSpeaker : Mr. Jawlekar Abhijeet Rajendra\n\nS.R. 
 Number : 06-18-01-10-22-21-1-20128\n\nTitle :"An importance sampling in N-
 Sphere Monte Carlo (NSMC) and its performance analysis for high dimensiona
 l integration"\n\nResearch Supervisor: Prof. Murugesan Venkatapathi\n\nDat
 e &amp\; Time : January 12\, 2024 (Friday) at 04:00 PM\n\nVenue : # 102 CD
 S Seminar Hall\n\n\n\nABSTRACT\n\nStatistical methods for estimating integ
 rals are indispensable when the number of dimensions (parameters) become g
 reater than ~ 10\, where numerical methods are unviable in general.  Well
 -known statistical methods like Quasi-Monte Carlo converge quickly only fo
 r problems with a small number of effective dimensions\, and Markov Chain 
 Monte Carlo (MCMC) methods incur a sharply increasing computing effort wit
 h the number of dimensions 'n' that is bounded as O(n^5).  This bound on 
 the dimensional scaling of computing effort in multiphase MCMC is limited 
 to domains with a given convex shape (determined by the limits of integrat
 ion).  Note that the non-convexity and roughness of the boundaries of the
  domain are factors that adversely affect the convergence of such methods 
 based on a random walk\, as the n-volume concentrates near the boundary in
  high dimensions with increasing 'n'.\n\nA different approach to high-D in
 tegration using (1D) line integrals along random directions coupled with a
  less-known volume transformation was suggested here at the Institute by A
 run et. al. This method called as N-sphere Monte Carlo (NSMC) is agnostic 
 to the shape and roughness of the boundary for any given distribution of e
 xtents of the domain from a reference point. While the dimensional scaling
  of computing in NSMC integration can be bound as O(n^3) for any distribut
 ion of relative extents (and not a particular convex shape)\, a similar bo
 und does not exist for MCMC as any given extent distribution can represent
  numerous geometries where it may not converge.  It was shown earlier tha
 t when restricted to convex shapes where the extent density functions beco
 me increasingly heavy tailed as 'n' increases\, the naive NSMC may be more
  efficient than the multiphase MCMC only when n &lt\; ~100.  This thesis 
 has three contributions. 1) It is analytically shown that\, unlike MCMC\, 
 the convergence of NSMC in the estimation of n-volume of a domain is not a
  necessary condition for its convergence in any other integration over tha
 t domain. 2)  A direct numerical comparison of the naive NSMC and the mul
 tiphase MCMC was performed for estimating n-volumes and different types of
  integrands\, establishing this advantage in integration even over typical
  convex domains when n &lt\; ~ 100. 3) A method for importance sampling is
  suggested for NSMC with a demonstration of the improved performance in hi
 gher dimensions for domains with heavy tailed extent density functions. In
  identifying and ensuring a local volume of interest is sampled adequately
 \, this method employs efficient sampling in high-D cones with a target di
 stribution.\n\n\n\nALL ARE WELCOME
CATEGORIES:Events
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