Statistical Modeling and Learning
in Vision and Cognition
Stat 232A-CS266A, MW 2:00-3:15 pm, January-March, 2017, WGYoung 1044 [syllabus.pdf]
This graduate level course introduces the principles, theories, and algorithms for modeling complex patterns in very high dimensional spaces, learning these statistical models from large data sets, and verifying them through stochastic sampling (synthesis). More specifically we study two classes of statistical models:
The visual patterns that we will study include:
We will study an information projection principle for learning these patterns and models in an unsupervised or weakly supervised way, as well as some theories of learning in the space of and-or graphs (AOG).
Prerequsites : Basic statistics, linear algebra, programming skills for a project. Knowledge and experience on images will be a plus.
Textbook [draft book pdf]
Two homework assignments
Small projects and exercises
List of Topics
Chapter 1 Introduction to Knowledge Representation, Modeling and Learning 1. Towards a unified representation of commonsense knowledge 2. Compositionality, reconfigurability, functionality and causality 3. Representation of concepts 4. Examples and demos: Regimes of models Chapter 2 Empirical Observations: Image Space and Natural Image Statistics 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 Descriptive Models I : Classical Markov 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 Descriptive Models II : FRAME Model and Julesz Ensemble 1. Pythagorean theorem and information projection 2. Minimax entropy learning and feature pursuit 3. Julesz ensemble 4. Ensemble equivalence theorem 5. Ensembles in statistics mechanics 6. Examples on general prior, shape, curves, Gestalt field etc Chapter 5 Descriptive Models III : Hierarchical FRAME Model 1. Posing hierarchical Convolutional Neural Net as a unfolded Generalized Linear Model 2. Defining hierarchical FRAME model 3. Synthesis and reconstruction with hierarchical FRAME model Chapter 6 Generative Models I: Classical 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 Generative Models II: Sparse codeing, 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 representation of faces 5. Active basis model Chapter 8 Generative Models III: Hierarchical Factor Analysis 1. Factor analysis and auto-encoder 2. Hierarchical Factor analysis with Convolutional Neural Nets 3. Alternating back-propagation Chapter 9 Information Scaling, Scale Space and Imperceptibility 1. Image scaling and perceptual entropy 2. A continuous entropy spectrum 3. Perceptual scale space Chapter 10 Integrated Models: Descriptive + Generative 1. Primal sketch model as low-middle representations for generic images and video 2, Hybrid image templates for objects and scenes 3. An integrated language model(SCFG + bigram) 4. And-Or graphs for context sensitive graph grammars Chapter 11 Learning Compositional Models 1. Unsupervised learning of And-Or graph: Block pursuit and bi-clustering. 2. Learning temporal And-or graph (event grammar) for actions and events. 3. Learning causal and-or graph for perceptual causality. Chapter 12 Discussion on Advanced Topics in Cognition and Robotics 1. Attribute AOG for human attributes 2. Attribute AOG for single view 3D scene parsing 3. Spatial, Temporal and Causal reasoning: using objects as tools 3. Utility: loss and cost in human behaviors