Stat232A: Statistical Modeling and Learning in Vision and Cognition
Fall, 2018, Stat 232ACS266A, MW 12:301:45 pm, Boelter Hall 5436
This is the first of a series of graduate level courses (Stat232A, B and C) that introduce the principles, theories, and algorithms for modeling complex patterns in vision and cognition. Stat 232A is focused on models of images used in the lowmiddle level vision, as well as in machine learning (including deep generative learning). More specifically we study two classes of statistical models:
We start with one layer models to study the principles and models to gain indepth understanding, and then move to multilayered structures (compatible with Deep neural Networks) to scale up performances.
We will also study the interactions and integration of these models, and develop a general unified theory for pusuing statistical models over a series of probabilistic families. The course also teaches a common framework for conceptualizing stochastic patterns and for statistical knowledge representation. Although the lectures will mostly focus on visual patterns in images and videos, and the methodology should be generally applicable to a wide range of applications, such as biologic patterns, network traffic modeling, material science, artificial intelligence, cognitive modeling, and autonomous robots, etc.Prerequsites : Basic statistics, linear algebra, programming skills for a project. Knowledge and experience on images will be a plus.
Textbook [draft book pdf]
Instructor
Grading Plan
Two homework assignments 
20% 
Small projects and exercises

40% 
Final Exam: Thursday, December 13, 11:30 AM  2:30 PM, Boelter Hall 5436  40% 
List of Topics
Chapter 1 Introduction to Knowledge Representation, Modeling and Learning [Lecture_1.pdf] 1. Towards a unified representation of commonsense knowledge from pixels to minds 2. Modeling principles: Compositionality, reconfigurability, functionality and causality 3. Definition and Representation of concepts 4. Examples and demos: Regimes of models Chapter 2 Empirical Observations: Image Space and Natural Image Statistics [Lecture_2.pdf] 1. Empirical observation I: filtered responses 2. Empirical observation II: scaling properties 3. Empirical observation III: patch frequency (structural and textural patches). 4. Empirical observation IV: information scaling and regimes of statistical models. Chapter 3 Classical Markov and Gibbs Random Fields 1. Markov random field theory 2. Gibbs fields: Ising and Potts models 3. The equivalence of Gibbs and MRF (HammersleyClifford theorem) 4. Early Markov random field models for images 5, Maximum Entropy and Maximum Likelihood Eestimation 6, Variations of likelihood: pseodo, patch, partiallikelihood 7. From Gibbs distributions to PDEs in image processing Chapter 4 FRAME Model and Julesz Ensemble 1. FRAME model and texture modeling 2. Pythagorean theorem and information projection 3. Minimax entropy learning and feature pursuit 4. Julesz ensemble 5. Ensemble equivalence theorem 6. Ensembles in statistics mechanics 7. Other examples on general prior, shape, curves, Gestalt field etc Chapter 5 DeepFRAME Model 1. Posing hierarchical Convolutional Neural Net as a unfolded Generalized Linear Model 2. Defining DeepFRAME model 3. Sampling and Learning the DeepFRAME model 4. Examples on synthesizing images, videos and 3D shapes. Chapter 6 Classical Generative Models 1. Frame theory and wavelets 2. Design of frames: image pyramids 3. Overcomplete basis and matching pursuit 4. Markov tree and stochastic context free grammar Chapter 7 Sparse coding, Textons, and Active Basis Models 1. Learning sparse coding from natural images 2. Tangram models and hierarchical tiling 3. Textons and image dictionary 4. Sparse FRAME model 5. Active basis model 6. Examples Chapter 8 Hierarchical Generative Models 1. Factor analysis and autoencoder 2. Hierarchical Factor analysis with Convolutional Neural Nets 3. Alternating backpropagation for learning Chapter 9 Information Scaling, Scale Space and Imperceptibility 1. Image scaling, perceptual entropy, and imperceptibility 2. A continuous entropy spectrum and transition of model regimes 3. Perceptual scale space Chapter 10 Integrated Models: Descriptive + Generative 1. Primal sketch model as lowmiddle representations for generic images and video 2. 2.1D sketch or layeredrepresentation 3. 2.5D sketch representation Chapter 11 Discussion on advanced topics