BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Asia/Kolkata X-WR-TIMEZONE:Asia/Kolkata BEGIN:VEVENT UID:49@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20240418T150000 DTEND;TZID=Asia/Kolkata:20240418T160000 DTSTAMP:20240410T073116Z URL:https://cds.iisc.ac.in/events/m-tech-research-thesis-defense-cds-18-ap ril-2024-an-importance-sampling-in-n-sphere-monte-carlo-and-its-performanc e-analysis-for-high-dimensional-integration/ SUMMARY:M.Tech Research: Thesis Defense: CDS: 18\, April 2024 "An importanc e sampling in N-Sphere Monte Carlo and its performance analysis for high d imensional integration" DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nM.Tech Research Oral Examination\n\n\n\nSpeaker : Mr. Jawlekar Abhijeet Rajendra\n\nS.R. N umber : 06-18-01-10-22-21-1-20128\n\nTitle : "An importance sampling in N- Sphere Monte Carlo and its performance analysis for high dimensional integ ration"\n\nThesis examiner  : Prof. Manohar C.\, Dept. of Civil Engine ering\, Indian Institute of Science.\nResearch Supervisor: Prof. Murugesan Venkatapathi\nDate &\; Time : April 18\, 2024 (Thursday) at 03:00 PM\n Venue : # 102 CDS Seminar Hall\n\n\n\nABSTRACT\n\nStatistical methods for estimating integrals are indispensable when the number of dimensions (para meters) become greater than ~ 10\, where numerical methods are unviable in general. Well-known statistical methods like Quasi-Monte Carlo converge q uickly only for problems with a small number of effective dimensions\, and Markov Chain Monte Carlo (MCMC) methods incur a sharply increasing comput ing effort with the number of dimensions 'n' that is bounded as O(n^5). Th is 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 integration). Note that the non-convexity and roughness of the boundar ies of the domain are factors that adversely affect the convergence of suc h methods based on a random walk in high dimensions.\n\nA different approa ch to high-D integration using (1D) line integrals along random directions coupled with a less-known volume transformation was suggested here at the Institute by Arun et. al. This method called as N-sphere Monte Carlo (NSM C) is agnostic to the shape and roughness of the boundary for any given di stribution of extents of the domain from a reference point. While the dime nsional scaling of computing in NSMC integration can be bound as O(n^3) fo r any distribution of relative extents (and not a particular convex shape) \, a similar bound does not exist for MCMC as any given extent distributio n can represent numerous geometries where it may not converge. It was show n earlier that when restricted to convex shapes where the extent density f unctions become increasingly heavy tailed as 'n' increases\, the naive NSM C may be more efficient than the multiphase MCMC only when n <\; ~100. T his thesis has three contributions. 1) It is analytically shown that\, unl ike MCMC\, the convergence of NSMC in the estimation of n-volume of a doma in is not a necessary condition for its convergence in any other integrati on over that domain. 2) A direct numerical comparison of the naive NSMC an d the multiphase MCMC was performed for estimating n-volumes and different types of integrands\, establishing this advantage in integration even ove r typical convex domains when n <\; ~ 100. 3) A method for importance sa mpling is suggested for NSMC with a demonstration of the improved performa nce in higher dimensions for domains with heavy tailed extent density func tions. In identifying and ensuring a local volume of interest is sampled a dequately\, this method employs efficient sampling in high-D cones with a target distribution.\n\n\n\nALL ARE WELCOME CATEGORIES:Events,Thesis Defense END:VEVENT BEGIN:VTIMEZONE TZID:Asia/Kolkata X-LIC-LOCATION:Asia/Kolkata BEGIN:STANDARD DTSTART:20230419T150000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR