Stat232A: Statistical Modeling and Learning in Vision and Cognition

Fall, 2018, Stat 232A-CS266A, MW 12:30-1:45 pm, Boelter Hall 5436


Course Description

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 low-middle level vision, as well as in machine learning (including deep generative learning). More specifically we study two classes of statistical models:

  1. Descriptive models (Markov random fields, Gibbs distributions); and
  2. Generative models (sparse coding, auto-encoding) .

We start with one layer models to study the principles and models to gain in-depth understanding, and then move to multi-layered 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]


Grading Plan

Two homework assignments
HW1 [10 %] -- HW2 [10% ]


Small projects and exercises

  • 1. Natural image statistics, scale invariance and image completion by PDE [10%]
  • 2. Sampling the Julesz texture ensemble [10%]
  • 3. Multi-grid sampling of DeepFRAME model [10%]
  • 4. Alternative back-propagation for hierarchical models [10%]
Final Exam: Thursday, December 13, 11:30 AM - 2:30 PM, Boelter Hall 5436


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 (Hammersley-Clifford theorem)
   4. Early Markov random field models for images
   5, Maximum Entropy and Maximum Likelihood Eestimation
   6, Variations of likelihood: pseodo-, patch-, partial-likelihood
   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. Over-complete 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 auto-encoder
   2. Hierarchical Factor analysis with Convolutional Neural Nets
   3. Alternating back-propagation 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 low-middle representations for generic images and video                                  
   2. 2.1D sketch or layered-representation
   3. 2.5D sketch representation

  Chapter 11 Discussion on advanced topics