PPT-Sampling and Volume Computation in High Dimension

Santosh Vempala Georgia Tech A really old p roblem Given set K in ndimensional space estimate its volume Eg Pyramids wine barrels Polytopes Intersection of a polytope with ellipsoids . High-dimensional Data Analysis. Jong Youl Choi, . Seung-Hee. . Bae. , Judy . Qiu. , . and Geoffrey Fox. School of Informatics and Computing. Pervasive Technology Institute. Indiana University. S. A. Santosh . Vempala. Tutorial outline. Intro to high dimension and convexity. Volume distribution, . logconcavity. Ellipsoids. Lower bounds. Algorithms. Rounding. Volume/Integration. Optimization. Sampling. Alex Andoni. (. Microsoft Research . SVC). Prism of nearest neighbor search (NNS). 2. H. igh dimensional . geometry. dimension reduction. space partitions. embeddings. …. NNS. ???. Nearest Neighbor Search (NNS). and. purge techniques. Acquiring . a . representative sample. Your Resources:. ISO Standards (5667). GNS National Protocol. What are we trying to achieve?. 3. Why is this so important?. A REPRESENTATIVE SAMPLE!. Sublinear. Algorithms:. Euclidean space: . dimension reduction and NNS. Alex Andoni. (MSR SVC). A Sketching Problem. 2. Sketching:. :objects . short bit-strings. given . . and . . should be able to deduce if . Latin. . Hypercube . and . Orthogonal. . sampling. Emine Şule Yazıcı . Koç University. Joint. . work. . with. :Kevin, Pamela Burrage, Diane Donovan,. Thomas A McCourt. ,. Bevan Thompson. Population. Metamodeling. Techniques for High-Dimensional IC Design Estimation Problems. Andrew B. Kahng, Bill Lin and Siddhartha . Nath. VLSI CAD LABORATORY, . UC. San Diego. Presented by: . SeokHyeong. Kang. Metamodeling. Techniques for High-Dimensional IC Design Estimation Problems. Andrew B. Kahng, Bill Lin and Siddhartha . Nath. VLSI CAD LABORATORY, . UC. San Diego. Presented by: . SeokHyeong. Kang. Latin. . Hypercube . and . Orthogonal. . sampling. Emine Şule Yazıcı . Koç University. Joint. . work. . with. :Kevin, Pamela Burrage, Diane Donovan,. Thomas A McCourt. ,. Bevan Thompson. Population. Santosh . Vempala. Tutorial outline. Intro to high dimension and convexity. Volume distribution, . logconcavity. Ellipsoids. Lower bounds. Algorithms. Rounding. Volume/Integration. Optimization. Sampling. EUS 210. Types of Dielectric. Mineral Oil . Polychlorinated biphenyls (PCBs). Silicone-based or Fluorinated Hydrocarbons. Natural and Synthetic Esters. Air. Why Do We Sample the oil. In-Service Electric Transformer:. High-dimensional Data Analysis. Jong Youl Choi, . Seung-Hee. . Bae. , Judy . Qiu. , . and Geoffrey Fox. School of Informatics and Computing. Pervasive Technology Institute. Indiana University. S. A. Basic Terminology . Understanding the terms used in volume computation and how they relate to different methods . Gaps and Incomplete Coverage. How do gaps in data affect the result of volume computation quantities. A. Wagner; S. Hilgert; R. T. Kishi; S. Drummond; L. Kiemle; . J.P. Nickel; K. Sotiri . and. S. Fuchs . EGU - 11. th. of April 2019. Large Volume Sampler. 11 April 2019. 2. 11 April 2019. 3. Kraichbach .