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Graphical modelling and Bayesian structural learning
Published on Sep 01, 20161989 Views
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Chapter list
Graphical models and Bayesian structural learning00:00
Outline01:34
Conditional independence02:06
Conditional independence, probabilistically03:16
Markov random fields: the local Markov property03:55
Markov random fields = Gibbs distributions - 104:51
Markov random fields = Gibbs distributions - 205:15
The Hammersley–Clifford theorem - 105:38
Pairwise Markov property - 105:54
Pairwise Markov property - 206:26
The Hammersley–Clifford theorem - 206:57
Graphical models07:57
DAGs - 108:40
Markov properties of DAGs - 109:18
Markov properties of DAGs - 209:37
Roles for graphs in statistics10:23
Graphs driving algorithms10:58
Association and causality11:20
Structural learning of undirected graphs12:04
Contingency tables14:59
SNPs and gene expression15:49
S&P 500 equity data SPARSE16:15
Genetic epidemiology16:59
What is structural learning really supposed to deliver?17:47
Structural learning18:47
Decomposable graphical models20:11
Decomposability: junction trees21:32
Probabilistic significance of decomposability23:10
Computational significance of decomposability24:44
Statistical significance of decomposability25:00
How restrictive is decomposability?25:57
Does that matter?26:33
Bayesian model determination with non-decomposable graphs27:20
And assuming decomposability has tremendous advantages....28:56
Bayesian graphical model determination29:30
Priors on decomposable graphs30:40
Conjugate priors on decomposable graphs31:25
Byrne & Dawid’s structural Markov property - 131:50
Byrne & Dawid’s structural Markov property - 233:45
A new weak structural Markov property34:42
A weak structural Markov property35:47
Clique–separator factorisation graph laws36:32
Posterior using a prior with the weak structural Markov property36:56
Bayesian decomposable graphical model determination - 137:15
Bayesian decomposable graphical model determination - 237:49
Pre-tests for maintaining decomposability38:05
Using the junction tree as the state39:16
Sampling decomposable graphs for posterior simulation40:07
Updating parameters in decomposable graph models42:11
Learning decomposable graphs – beyond MCMC43:22
Non-decomposable graphs44:58
Bayesian model determination with non-decomposable graphs - 145:34
Bayesian model determination with non-decomposable graphs - 246:26
Stochastic shotgun search47:01
Examples of Stochastic shotgun search vs MCMC - 147:26
Examples of Stochastic shotgun search vs MCMC - 247:37
A sparse regression approach - 147:42
A sparse regression approach - 248:46
Other important contributions on non-decomposable graphs49:07
Trees49:17
Forest49:37
Trees and forests - 149:42
Trees and forests - 249:53
Trees and forests - 350:08
Perfect simulation for posterior on trees and forests50:22
DAGs - 251:10
DAGs - 351:28
Markov equivalence - 151:56
Markov equivalence - 253:15
MCMC on completed PDAGs53:35
Wrap-up53:50
Thank you!55:32