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### CS 504 Computational Modeling

### Overview

### Class Meetings

### Thursday 1/24 - Introduction

### Thursday 1/31 - An overview of models

### Thursday 2/7: Continuous simulation

### Thursday 2/14: Discrete simulation

### Thursday 2/21 - Simulation of light

### Thursday 2/28 - Discrete models and inference

### Thursday 3/7 - Continuous models and inference

### Thursday 3/14

### Thursday 3/21

### Thursday 3/28 - Overview: Sampling for probabilistic inference

### Thursday 4/4 - Understanding Sampling - Continuous domains

### Thursday 4/11 - Understanding Sampling - Discrete domains

### Thursday 4/18 - Mixing discrete and continuous: Clustering

### Thursday 4/25 - Applications in Vision, I

### Thursday 5/2 - Applications in Vision, II

- Slides
- Matlab transcript and spring files: Euler, midpoint and exact
- Homework 2

- Slides for cellular automata
- Description of elementary cellular automata from Wolfram mathworld and Matlab implementation using dense matrices
- Interactive simulation of Conway's life
- Cleve Moler's tutorial on implementing life in Matlab with sparse matrices with summary matlab script, interactive matlab simulation and data file of examples. See also Experiments with Matlab
- Slides for agent simulations
- Craig Reynold's 1987 SIGGRAPH paper on agent simulations

- Slides on constraints in vision
- Constraint satisfaction: Moler on solving Sudoku in matlab with Matlab visual solver and sample puzzles. C. Nalwa, Line Drawing Interpretation (Chapter 4 from A Guided Tour of Computer Vision, Addison Wesley, 1993)
- Understanding visual inference as constraint satisfaction: Edward H. Adelson. Lightness Perception and Lightness Illusions. In The New Cognitive Neurosciences, 2nd ed., M. Gazzaniga, ed. Cambridge, MA: MIT Press, pp. 339-351, (2000).

- Slides
- Matlab demo of statistical inference
- Worked example of Kalman filter with Matlab sources
- Maybeck's introduction to the Kalman filter

- Slides
- Classic paper on particle filters for estimation (Condensation): PDF Dellaert, Burgard, Fox and Thrun, Using the CONDENSATION algorithm for robust, vision-based mobile robot localization. CVPR 1999.
- Another useful application of particle filters PDF De Freitas, Rao-Blackwellised particle filtering for fault diagnosis. IEEE Aerospace Conference, 2002.
- Tarball of de Freitas's matlab demo code for particle filtering. Originally here.

- Overview of MCMC: PDF D. J. C. MacKay. Introduction to Monte Carlo Methods. Proceedings of the NATO Advanced Study Institute on Learning in graphical models, Kluwer 1999, Pages 175 - 204.
- Source: Steyvers, chapter 1. Mark Steyvers, Computational Statistics in Matlab. Course notes, available here.
- simple MH sampler for Bayesian data analysis and how to run it, based on Lab notes from Andersson's MCMC computer exercises from Stockholm University.

- Sampling from orderings, the Mallows Model
- Source: Steyvers, chapter 2. Mark Steyvers, Computational Statistics in Matlab. Course notes, available here.
- Matlab code

- Processing image data: PCA
- Expectation maximization clustering: mixtures of Gaussians: tutorial reading and Matlab code from here. (Tutorial is Theory and Use of the EM Algorithm, by Maya R. Gupta and Yihua Chen, Foundations and Trends in Signal Processing Vol. 4, No. 3 (2010) 223–296.)
- Matlab code to cluster image pixels with a mixture of Gaussian model and Expectation Maximization.
- Bayesian Clustering with the Chinese Restaurant Process. application paper and Matlab code from Frank Wood. Paper is Wood and Black, A Nonparametric Bayesian Alternative to Spike Sorting, Journal of Neuroscience Methods, 173:1-12, 2008.
- Matlab code to cluster image pixels with a Dirichlet Process Mixture Model and Gibbs Sampling.

- Matlab code to organize feature points to explain image data, using a subroutine that partitions pixels in an image according to a triangulation and computes statistics over the clusters. It works in an interesting way on a simple synthetic image but is a disaster on a complex real image.
- Doug and my paper on "Visual Explanations" which gives some programmatic background about this way of representing the interpretations of visual imagery.
- David Lowe's 1999 ICCV paper that introduced the scale-invariant feature transform, one of the important current methods for detecting interesting points in imagery.
- Charles Bouman's 1995 Tutorial on Markov Random Fields from the IEEE International Conference on Image Processing.

- Jacob Feldman, Manish Singh and Vicky Froyen's new overview paper on Bayesian approaches to perceptual grouping.
- Vicky Froyen, Jacob Feldman and Manish Singh's 2010 NIPS paper with a more technical and brief presentation of perceptual grouping as Bayesian inference.
- Project 3