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What cannot be learned with Bethe Approximations
Published on Jan 16, 20133671 Views
We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. H
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Chapter list
What cannot be learned with belief propagation00:00
Multivariate Signals00:07
Modeling Multivariate Distributions00:23
Pairwise Graphical Models00:50
The Learning Problem (1)01:15
The Learning Problem (2)02:03
The Learning Problem (3)02:12
The Learning Problem (4)02:15
The Learning Problem (5)02:21
Approximate Learning02:48
Results04:17
Maximum Likelihood (1)05:02
Maximum Likelihood (2)05:36
Maximum Likelihood (3)05:55
Maximum Likelihood (4)06:05
Moment Matching (1)06:27
Moment Matching (2)06:42
Moment Matching (3)06:53
Moment Matching (4)07:04
Moment Matching (5)07:14
Moment Matching (6)07:18
Moment Matching (7)07:25
Moment Matching (8)07:26
Approximate Learning (1)08:39
Approximate Learning (2)08:53
Approximate Learning (3)08:57
Approximate ML (1)09:02
Approximate ML (2)09:43
Approximate ML (3)09:45
Approximate ML (4)09:52
Variational view of Z (1)09:57
Variational view of Z (2)10:00
Variational view of Z (3)10:12
Variational view of Z (4)10:19
Variational view of Z (5)10:24
Variational view of Z (6)10:29
Variational view of Z (7)10:35
Variational view of Z (8)10:47
Variational view of Z (9)10:57
Variational view of Z (10)11:01
Bethe approximations (1)11:03
Bethe approximations (2)11:10
Bethe approximations (3)11:13
Bethe approximations (4)11:16
Bethe approximations (5)11:41
Bethe approximations (6)11:47
Bethe approximations (7)11:53
Bethe approximations (8)12:03
Bethe approximations (9)12:04
Bethe approximations (10)12:06
Loopy BP (1)12:32
Loopy BP (2)12:33
Loopy BP (3)12:37
Loopy BP (4)12:47
Loopy BP (5)12:58
Loopy BP (6)13:00
Loopy BP (7)13:00
Loopy BP (8)13:32
Loopy BP (9)13:36
Bethe ML14:49
Bethe Inference15:52
Approximate Learning (4)16:33
Approximate Learning (5)16:49
Approximate Learning (6)16:54
Approximate Learning (7)16:56
Approximate Learning (8)16:58
Approximate Learning (9)16:58
Optimality in Bethe ML (1)17:06
Optimality in Bethe ML (2)17:31
Optimality in Bethe ML (3)17:39
Optimality in Bethe ML (4)17:41
Optimality in Bethe ML (5)17:43
Optimality in Bethe ML (6)17:52
Optimality in Bethe ML (7)17:56
Optimality in Bethe ML (8)18:19
Optimality in Bethe ML (9)18:27
Optimality in Bethe ML (10)18:28
Optimality in Bethe ML (11)18:29
Optimality in Bethe ML (12)18:30
Optimality in Bethe ML (13)18:31
Optimality in Bethe ML (14)18:32
Optimality in Bethe ML (15)18:33
Optimality in Bethe ML (16)18:34
Optimality in Bethe ML (17)18:40
Optimality in Bethe ML (18)19:29
Optimality in Bethe ML (19)19:41
A two maxima case20:18
Bethe Learnable Marginals (1)21:10
Bethe Learnable Marginals (2)21:51
Bethe Learnable Marginals (3)21:55
Bethe Learnable Marginals (4)22:10
Bethe Learnable Marginals (5)22:18
Bethe Learnable Marginals (6)22:21
Bethe Learnable Marginals (7)22:23
Bethe Learnable Marginals (8)22:25
Bethe Learnable Marginals (9)22:26
Bethe Learnable Marginals (10)22:28
Bethe Learnable Marginals (11)22:44
Canonical Parameters (1)23:25
Canonical Parameters (2)24:22
Canonical Parameters (3)24:31
Canonical Parameters (4)24:33
Canonical Parameters (5)24:34
Stationary point invariance (1)25:02
Stationary point invariance (2)25:26
Stationary point invariance (3)25:34
Stationary point invariance (4)25:46
Message I26:20
Outer Bound I (1)26:42
Outer Bound I (2)26:46
Outer Bound I (3)26:47
Outer Bound I (4)26:49
Outer Bound I (5)26:53
Outer Bound I (6)26:54
Outer Bound I (7)26:56
Outer Bound I (8)26:58
Outer Bound I (9)27:01
Outer Bound I (10)27:09
Outer Bound I (11)27:37
Outer Bound I (12)27:39
Outer Bound I (13)27:54
Outer Bound I (14)27:55
Outer Bound I (15)28:10
Outer Bound I (16)28:11
Outer Bound I (17)28:14
Outer Bound II (1)28:19
Outer Bound II (2)28:33
Outer Bound II (3)29:12
Outer Bound II (4)29:29
Outer Bound II (5)29:37
Outer Bound II (6)30:51
Outer Bound II (7)30:53
Outer Bound II (8)30:59
Message II31:14
Outer Bound II31:17
Homogenous Binary Case (1)32:25
Homogenous Binary Case (2)33:05
Inner Bounds (1)34:28
Inner Bounds (2)34:32
Inner Bounds (3)34:32
Inner Bounds (4)34:33
Inner Bounds (5)34:34
Inner Bounds (6)34:37
Inner Bounds (8)34:53
Inner Bounds (9)34:54
Inner Bounds (10)35:07
Inner Bounds (11)35:09
Inner Bounds (12)35:11
Experiments (1)35:35
Inner Bounds (7)35:59
Experiments (2)36:34
3x3 Grid (1)36:50
3x3 Grid (2)37:46
Bipartite 8x837:50
Learnability and Performance (1)38:46
Learnability and Performance (2)39:46
Learnability and Performance (3)40:07
Learnability and Performance (4)40:27
Learnability and Performance (5)40:49
Take Home Messages41:08
Future Work41:48