NATO Advanced Study Institute on Mining Massive Data Sets for Security

Foundations of Statistical Learning Theory : Empirical Infe-rence in high-dimention spaces

author: Léon Bottou, NEC Research
coauthor: Vladimir Vapnik, University of London

Categories

Top: Computer Science: Machine Learning: Statistical Learning

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*Slides*
0:00	EMPIRICAL INFERENCE SCIENCE
0:46	SUMMARY (1)
3:10	SUMMARY (2)
3:13	CONTENTS
4:24	I. INDUCTIVE INFERENCES
4:26	PATTERN RECOGNITION PROBLEM
5:05	COMPLEXITY CONCEPT
6:05	OCCAM’S RAZOR IN PHYSICAL SCIENCE
7:32	THE MAIN THEOREM OF VC THEORY
8:45	CAPACITY CONCEPTS: THE VC ENTROPY AND THE GROWTH FUNCTION
10:11	THE STRUCTURE OF THE GROWTH FUNCTION: THE VC DIMENSION
11:01	THE MAIN RESULTS OF THE VC THEORY
12:10	CONCEPT OF FALSIFIABILITY
13:28	VC DIMENSION AND POPPER DIMENSION
14:31	VC AND POPPER DIMENSION: ILLUSTRATION
16:01	VC BOUNDS AND SRM PRINCIPLE
17:57	THE OCCAM’S RAZOR PRINCIPLE AND THE SRM PRINCIPLE
18:46	THE CRUCIAL POINT
18:54	EXAMPLE 1: The VC dimension is equal to the number of entities (parameters)
19:12	EXAMPLE 2: The VC dimension is larger than the number of entities (parameters)
19:50	EXAMPLE 3: The VC dimensions is less than the number of entities (parameters)
20:48	THE IDEA OF SUPPORT VECTOR MACHINES
21:17	EXAMPLE 3: The VC dimensions is less than the number of entities (parameters)
21:31	ILLUSTRATION
22:29	TECHNICAL DETAILS
22:42	MORE TECHNICAL DETAILS
22:58	II. TRANSDUCTIVE INFERENCES
23:30	INDUCTIVE AND TRANSDUCTIVE INFERENCES
24:13	WHAT IS THE TRANSDUCTION PROBLEM
25:52	EQUIVALENCE CLASSES
27:09	PREDICTION OF MOLECULAR BIOACTIVITY (1)
27:36	PREDICTION OF MOLECULAR BIOACTIVITY (2)
28:22	SELECTIVE INFERENCE
30:22	THE IMPERATIVE FOR THE COMPLEX WORLD
41:05	III. PROBLEMS OF NON-INDUCTIVE INFERENCES
41:28	WHAT IS WRONG WITH LARGE MARGIN?
44:12	BACK TO VC ENTROPY: THE CONCEPT OF CONTRADICTION
46:04	IDEA OF UNIVERSUM
47:09	INFERENCE BASED ON THE NUMBER OF CONTRADICTIONS ON UNIVERSUM
47:15	EXPERIMENTS WITH DIGIT RECOGNITION
51:02	FURTHER CAPACITY CONTROL: SVM+
51:19	INFERENCE BASED ON THE NUMBER OF CONTRADICTIONS ON UNIVERSUM
70:22	FURTHER CAPACITY CONTROL: SVM+
72:18	SVM+: FORMULATION
72:41	SVM+: DUAL SPACE SOLUTION
72:54	ONE STEP MORE: LEARNING HIDDEN INFORMATION
74:40	MASTER-CLASS LEARNING
77:13	ORIGINAL DIGITS
77:19	CORRUPTED DIGITS
77:28	MASTER-CLASS DIGIT RECOGNITION LEARNING: TECHNICAL SPACE
77:31	MASTER-CLASS DIGIT RECOGNITION LEARNING: HOLISTIC SPACE (1)
78:06	MASTER-CLASS DIGIT RECOGNITION LEARNING: HOLISTIC SPACE (2)
78:11	CODES FOR HOLISTIC DESCRIPTION (1)
78:31	CODES FOR HOLISTIC DESCRIPTION (2)
79:27	BIG PICTURE
79:30	CODES FOR HOLISTIC DESCRIPTION (2)
79:48	BIG PICTURE
81:53	MACHINE LEARNING AND EMPIRICAL INFERENCE SCIENCE
82:58	CONCLUSION: TWO METAPHORS FOR A SIMPLE WORLD
83:35	CONCLUSION: TWO METAPHORS FOR A COMPLEX WORLD
84:32	WHAT IS EMPIRICAL INFERENCE SCIENCE ABOUT?
86:05	- Questions
86:22	- Questions

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