PPT-Algebraic-Geometric Methods for Learning Gaussian Mixture Models

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 . edu Ming Yuan mingyuanisyegatechedu School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta GA 30332 USA Hui Zou hzoustatumnedu School of Statistics University of Minnesota Minneapolis MN 55455 USA Finite gaussian mixture Raghu . Meka. (IAS & DIMACS). “. When you have eliminated the impossible, whatever remains, . however improbable, must be the truth. ” . . Union Bound. Popularized by . Erdos. Probabilistic Method 101. 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. 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.: . Alan Ritter. Latent Variable Models. Previously: learning parameters with fully observed data. Alternate approach: hidden (latent) variables. Latent Cause. Q: how do we learn parameters?. Unsupervised Learning. Mixture Models and Expectation Maximization. Machine Learning. Last Time. Review of Supervised Learning. Clustering. K-means. Soft K-means. Today. Gaussian Mixture Models. Expectation Maximization. The Problem. Machine . Learning . 10-601. , Fall . 2014. Bhavana. . Dalvi. Mishra. PhD student LTI, CMU. Slides are based . on materials . from . Prof. . Eric Xing, Prof. . . William Cohen and Prof. Andrew Ng. 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 . Machine Learning. April 13, 2010. Last Time. Review of Supervised Learning. Clustering. K-means. Soft K-means. Today. A brief look at Homework 2. Gaussian Mixture Models. Expectation Maximization. The Problem. . Revisted. Isabel K. Darcy. Mathematics Department. Applied Math and Computational Sciences. University of Iowa. Fig from . knotplot.com. A. . is diagonalizable if there exists an invertible. . m. 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. AP Statistics B. Overview of Chapter 17. Two new models: Geometric model, and the Binomial model. Yes, the binomial model involves Pascal’s triangles that (I hope) you learned about in Algebra 2. Use the geometric model whenever you want to find how many events you have to have before a “success”. the . EM Algorithm. CSE . 6363 – Machine Learning. Vassilis. . Athitsos. Computer Science and Engineering Department. University of Texas at . Arlington. 1. Gaussians. A popular way to estimate . probability density . – . 2. Introduction. Many linear inverse problems are solved using a Bayesian approach assuming Gaussian distribution of the model.. We show the analytical solution of the Bayesian linear inverse problem in the Gaussian mixture case..