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PAC-Bayesian Analysis: A Link Between Inference and Statistical Physics
Published on Oct 16, 20123952 Views
PAC-Bayesian analysis is a general tool for deriving generalization bounds for a wide class of inference rules. Interestingly, PAC-Bayesian generalization bounds take a form of a trade-off between the
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PAC-Bayesian Analysis: A Link Between Inference and Statistical Physics00:00
High Level Overview (1)00:13
High Level Overview (2)00:41
Outline (1)00:57
Outline (2)01:29
PAC (Probably Approximately Correct) Learning Framework01:35
Some Basic De nitions02:05
Randomized Classi fiers (1)03:04
Randomized Classi fiers (2)03:31
Randomized Classi fiers (3)03:52
PAC-Bayes-Hoeff ding Inequality04:01
Intuition Behind the Bound (1)04:49
Intuition Behind the Bound (2)05:25
Relation and Di fference with Bayesian Learning (1)07:03
Relation and Di fference with Bayesian Learning (2)07:21
Relation and Di fference with Bayesian Learning (3)07:39
Relation and Di fference with Bayesian Learning (4)08:04
Relation and Di fference with Bayesian Learning (5)08:21
Relation and Di fference with Bayesian Learning (6)08:51
Relation and Di erence with Vapnik-Chervonenkis (VC) (1)11:01
Relation and Di erence with Vapnik-Chervonenkis (VC) (2)11:19
Relation to Statistical Physics (1)11:51
Relation to Statistical Physics (2)12:30
Proof Idea: Basis (1)12:48
Proof Idea: Basis (2)13:06
Proof Idea: Some More Background (1)13:31
Proof Idea: Some More Background (2)13:38
Proof Idea (1)13:59
Proof Idea (2)14:05
Proof Idea (3)14:37
Proof Idea (4)15:11
Proof Idea (5)15:32
Proof Idea (6)15:36
Proof Idea (7)16:15
Proof Idea (8)16:20
Proof Idea (9)16:26
Outline (3)16:44
Multiarmed Bandits (1)16:55
Multiarmed Bandits (2)17:15
Applications18:06
Exploration-exploitation trade-o ff18:32
Multiarmed Bandits with Side Information19:12
Game Round19:58
Hierarchy of Reinforcement Learning Problems20:10
Goal (1)20:31
Goal (2)21:50
Goal (3)22:15
Supervised learning vs. Reinforcement learning22:46
Outline (4)24:06
Importance Weighted Sampling (1)24:18
Importance Weighted Sampling (2)24:32
Importance Weighted Sampling (3)25:02
Outline (5)25:24
Martingales25:49
Multiple Simultaneously Evolving and Interdependent Martingales26:16
Variance of the Martingales (1)27:13
Variance of the Martingales (2)27:30
PAC-Bayes-Bernstein Inequality for Martingales28:23
Outline (6)29:28
Hypothesis space for Multiarmed Bandits with Side Information29:36
PAC-Bayesian Regret Bounds (1)30:33
PAC-Bayesian Regret Bounds (2)31:29
PAC-Bayesian Regret Bounds (3)31:53
Playing Strategy (1)32:24
Playing Strategy (2)32:38
Playing Strategy (3)32:56
Playing Strategy (4)33:29
Experiments (1)34:00
Experiments (2)34:17
Experiments (3)34:25
Experiments - Regret Graph34:41
Experiments - Bound35:28
Experiments - Mutual Information35:29
Summary (1)35:44
Summary (2)36:02
Summary (3)36:09
References (1)36:26
Thank you36:28
References (2)36:33