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Machine learning for cognitive science 2: Bayesian methods and statistical learning theory
Published on Jun 15, 20109663 Views
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Chapter list
Learning with Probabilities00:00
Statistical Learning Theory and Kernel Methods00:00
Outline - 100:02
Error Functoins to Probabilities00:45
Statistical Learning Theory01:48
Outline - 202:34
Probability Review 102:36
A Pictoral Definition of Probability04:51
Different Distributions04:57
Notational Details05:24
Normalization06:35
The Sum Rule07:26
The Product Rule07:52
Baye's Rule08:07
Expectations10:36
Distribution Representation11:52
Binomial Distribution12:18
Density14:10
Continuous Variables14:39
Gaussian PDF 115:12
The Gaussian Density - 117:07
The Gaussian Density - 217:49
Outline - 318:10
Sample Based Approximations 118:12
Sample Mean vs True Mean19:12
Outline - 419:14
Regression Revisited19:17
Noise Corrupted Mapping22:36
Gaussian Likelihood - 123:37
Gaussian Likelihood - 324:51
Gaussian Likelihood - 224:54
Gaussian Likelihood - 424:58
Gaussian Likelihood - 525:01
Gaussian Likelihood - 625:09
Gaussian Likelihood - 725:11
Gaussian Likelihood - 825:13
Gaussian Likelihood - 925:18
Gaussian Likelihood - 1025:31
Example26:47
Pattern Recognition26:48
Probabilistic Interpretation of the Error Function26:50
Convergence of Means to Expectations27:35
Consistency of Maximum Likelihood28:01
Consistency and Uniform Convergence28:52
Outline - 530:02
Bayesian Approach30:04
Note on the Term Bayesian31:07
The Importance of the Set of Functions31:43
Binomial Distribution Revisited - 132:26
Binomial Distribution Revisited - 232:38
Binomial Distribution Revisited - 332:51
Binomial Distribution Revisited - 432:54
Binomial Distribution Revisited - 533:03
Binomial Distribution Revisited - 633:26
Restricting the Class of Functions34:11
Simple Bayesian Inference34:30
Detailed Analysis34:35
Chernoff's Bound - 135:48
Example System: Robot Location36:43
Gaussian Noise - 138:32
Gaussian Noise - 238:42
Gaussian Noise - 339:19
Chernoff's Bound - 239:20
Uniform Convergence40:33
Expectation Propagation41:11
Probit Likelihood41:20
How to Prove a VC Bound41:46
Classification - 142:06
Classification - 242:12
Classification - 342:31
Classification - 443:12
The Case of Two Functions45:55
Ordinal Noise Model46:21
Ordinal Regression - 146:49
Ordinal Regression - 246:52
Ordinal Regression - 346:56
Ordinal Regression - 447:00
Outline - 647:04
Bayesian Linear Regression47:29
The Union Bound49:14
Marginal Likelihood49:17
Covariance Functions50:58
Covariance Samples - 151:58
Infinite Function Classes52:04
Covariance Samples - 252:36
Covariance Samples - 352:36
Covariance Samples - 452:37
Gaussian Process Regression - 153:07
Symmetrization53:20
Gaussian Process Regression - 253:26
Gaussian Process Regression - 353:32
Gaussian Process Regression - 453:33
Gaussian Process Regression - 553:34
Gaussian Process Regression - 654:12
Shattering Coefficient54:20
Gaussian Process Regression - 754:21
Gaussian Process Regression - 854:31
Learning Kernel Parametres - 154:48
Learning Kernel Parametres - 255:48
Learning Kernel Parametres - 356:09
Learning Kernel Parametres - 456:10
Learning Kernel Parametres - 556:10
Learning Kernel Parametres - 656:16
Learning Kernel Parametres - 756:17
Learning Kernel Parametres - 856:19
Learning Kernel Parametres - 956:43
Outline - 756:47
Outline - 856:49
Mixture of Gaussians 156:52
Putting Everything Together57:22
ctd.58:53
Confidence Intervals01:00:19
EM Algorithm - 101:00:34
EM Algorithm - 201:00:56
EM Algorithm - 301:01:38
EM Algorithm - 401:01:59