PPT-Sampling from Gaussian Graphical Models via Spectral Sparsi

Richard Peng MIT Joint work with Dehua Cheng Yu Cheng Yan Liu and Shanghua Teng USC Outline Gaussian sampling linear systems matrixroots Sparse factorizations of L p. Marti Blad PhD PE. EPA Definitions. Dispersion Models. : Estimate pollutants at ground level receptors. Photochemical Models. : Estimate regional air quality, predicts chemical reactions. Receptor Models. Graphical Model Inference. View observed data and unobserved properties as . random variables. Graphical Models: compact graph-based encoding of probability distributions (high dimensional, with complex dependencies). Richard Peng. M.I.T.. Joint work with . Dehua. Cheng, Yu Cheng, Yan Liu and . Shanghua. . Teng. (U.S.C.). Outline. Gaussian sampling, linear systems, matrix-roots. Sparse factorizations of . L. p. Jongmin Baek and David E. Jacobs. Stanford University. . Motivation. Input. Gaussian. Filter. Spatially. Varying. Gaussian. Filter. Accelerating Spatially Varying. . Gaussian Filters . Accelerating. By. Dr. Rajeev Srivastava. Principle Sources of Noise. Noise Model Assumptions. When the Fourier Spectrum of noise is constant the noise is called White Noise. The terminology comes from the fact that the white light contains nearly all frequencies in the visible spectrum in equal proportions . Tamara L Berg. CSE 595 Words & Pictures. Announcements. HW3 . online tonight. Start thinking about project ideas . Project . proposals in class Oct 30 . . Come to office hours . Oct. 23-25 . to discuss . Generalized covariance matrices and their inverses. Menglong Li. Ph.d. of Industrial Engineering. Dec 1. st. 2016. Outline. Recap: Gaussian graphical model. Extend to general graphical model. Model setting. . A . Brief . Introduction. Image from Univ. of Waterloo Environmental Sciences. Marti Blad. 2. Transport of Air Pollution. Plumes tell story. Ambient . vs. DALR. Models predict air pollution concentrations . EPA Definitions. Dispersion Models. : Estimate pollutants at ground level receptors. Photochemical Models. : Estimate regional air quality, predicts chemical reactions. Receptor Models. : Estimate contribution of multiple sources to receptor location based on multiple measurements at receptor. Mikhail . Belkin. Dept. of Computer Science and Engineering, . Dept. of Statistics . Ohio State . University / ISTA. Joint work with . Kaushik. . Sinha. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . Smokey Bear. Lincoln National Forest. U.S. Forest Service Mascot. Revised: 2014.12.30. Why Re-Engineer?. New technologies in the last decade. Better databases. Improved programming languages and tools. Comparison of Strategies for Scalable Causal Discovery of Latent Variable Models from Mixed Data Vineet Raghu , Joseph D. Ramsey, Alison Morris, Dimitrios V. Manatakis, Peter Spirtes, Panos K. Chrysanthis, Clark Glymour, and Panayiotis V. Benos Geological models – “Mineral Systems”. after Kelley et al., 2006 . Supergene : regolith processes. Hypogene : source, pathway, depositional site, outflow. Contrasting physicochemical conditions. Part 1: Overview and Applications . Outline. Motivation for Probabilistic Graphical Models. Applications of Probabilistic Graphical Models. Graphical Model Representation. Probabilistic Modeling. 1. when trying to solve a real-world problem using mathematics, it is common to define a mathematical model of the world, e.g..