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Bayesian Interpretations of RKHS Embedding Methods
Published on Jan 16, 20134577 Views
We give a simple interpretation of mean embeddings as expectations under a Gaussian process prior. Methods such as kernel two-sample tests, the Hilbert-Schmidt Independence Criterion, and kernel herdi
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Chapter list
Bayesian Interpretations of RKHS Embedding Methods00:00
Outline (1)00:01
The Quadrature Problem00:30
Sampling Methods (1)00:53
Sampling Methods (2)01:06
Sampling Methods (3)01:22
Sampling Methods (4)01:24
Sampling Methods (5)01:34
Kernel Herding [Welling et. al., 2009, Chen et. al., 2010] (1)01:50
Kernel Herding [Welling et. al., 2009, Chen et. al., 2010] (2)02:05
Kernel Herding [Welling et. al., 2009, Chen et. al., 2010] (3)02:21
Kernel Herding Objective (1)02:55
Kernel Herding Objective (2)03:33
Kernel Herding (1)03:54
Kernel Herding (2)04:05
Kernel Herding in Action (1)04:24
Kernel Herding in Action (2)04:46
Kernel Herding in Action (3)04:54
Kernel Herding in Action (4)04:58
Kernel Herding in Action (5)05:03
Kernel Herding in Action (6)05:03
Kernel Herding in Action (7)05:04
Kernel Herding in Action (8)05:05
Kernel Herding in Action (9)05:05
Kernel Herding in Action (10)05:06
Kernel Herding in Action (11)05:07
Kernel Herding in Action (12)05:07
Kernel Herding in Action (13)05:08
Kernel Herding in Action (14)05:09
Kernel Herding in Action (15)05:10
Kernel Herding in Action (16)05:11
Kernel Herding in Action (17)05:11
Kernel Herding in Action (18)05:12
Kernel Herding in Action (19)05:13
Kernel Herding in Action (20)05:14
Kernel Herding Summary (1)05:22
Kernel Herding Summary (2)05:40
Kernel Herding Summary (3)05:43
Kernel Herding Summary (4)05:52
Bayesian Quadrature (a.k.a. Bayesian Monte Carlo) - 105:57
Bayesian Quadrature (a.k.a. Bayesian Monte Carlo) - 206:10
Bayesian Quadrature (a.k.a. Bayesian Monte Carlo) - 306:16
Bayesian Quadrature (a.k.a. Bayesian Monte Carlo) - 406:24
Bayesian Quadrature (a.k.a. Bayesian Monte Carlo) - 506:42
Bayesian Quadrature (a.k.a. Bayesian Monte Carlo) - 606:45
Bayesian Quadrature (a.k.a. Bayesian Monte Carlo) - 706:47
Bayesian Quadrature (a.k.a. Bayesian Monte Carlo) - 806:54
Bayesian Quadrature Estimator (1)07:00
Bayesian Quadrature Estimator (2)07:17
How to select samples? (1)07:35
How to select samples? (2)07:43
How to select samples? (3)07:52
How to select samples? (4)08:13
How to select samples? (5)08:28
Relating Objectives (1)08:33
Relating Objectives (2)08:50
Relating Objectives (3)09:09
Performance (1)09:15
Performance (2)09:27
Performance (3)09:31
Performance (4)09:47
Rates of Convergence (1)10:03
Rates of Convergence (2)10:26
Rates of Convergence (3)10:36
Rates of Convergence (4)10:53
Rates of Convergence (5)11:04
Rates of Convergence (6)11:16
Summary (1)11:41
Summary (2)11:56
Summary (3)12:00
Summary (4)12:05
Summary (5)12:08
Outline (2)12:10
GPs vs Log-GPs for Inference (1)12:41
GPs vs Log-GPs for Inference (2)13:23
GPs vs Log-GPs for Inference (3)13:45
GPs vs Log-GPs for Inference (4)13:48
GPs vs Log-GPs for Inference (5)13:57
GPs vs Log-GPs for Inference (6)14:05
Mean Embedding Interpretation (1)14:34
Mean Embedding Interpretation (2)14:50
Mean Embedding Interpretation (3)15:03
Kernel two-sample test (1)15:26
Kernel two-sample test (2)15:36
Kernel two-sample test (3)15:47
Kernel two-sample test (4)16:20
Hilbert-Schmidt Independence Criterion (1)16:58
Hilbert-Schmidt Independence Criterion (2)17:13
Hilbert-Schmidt Independence Criterion (3)17:26
Hilbert-Schmidt Independence Criterion (4)17:35
Determinantal Point Processes (1)18:08
Determinantal Point Processes (2)18:19
Determinantal Point Processes (3)18:29
Determinantal Point Processes (4)18:45
Determinantal Point Processes (5)19:25
Determinantal Point Processes (6)19:38
Summary of Connections (1)19:45
Summary of Connections (2)19:58
Summary of Connections (3)20:03
Summary of Connections (4)20:08
Summary of Connections (5)20:15
Summary of Connections (6)20:49
Thanks!22:12