Download presentation

Presentation is loading. Please wait.

Published byStewart Dorsey Modified over 2 years ago

1
Learning Bayesian Networks

2
Dimensions of Learning ModelBayes netMarkov net DataCompleteIncomplete StructureKnownUnknown ObjectiveGenerativeDiscriminative

3
Bayes net(s) data X 1 true false true X21532X21532 X 3 0.7 -1.6 5.9 6.3........... Learning Bayes nets from data X1X1 X4X4 X9X9 X3X3 X2X2 X5X5 X6X6 X7X7 X8X8 Bayes-net learner + prior/expert information

4
From thumbtacks to Bayes nets Thumbtack problem can be viewed as learning the probability for a very simple BN: X heads/tails X1X1 X2X2 XNXN... toss 1 toss 2toss N

5
The next simplest Bayes net X heads/tails Y tails heads “heads”“tails”

6
The next simplest Bayes net X heads/tails Y XX X1X1 X2X2 XNXN YY Y1Y1 Y2Y2 YNYN case 1 case 2 case N ?

7
The next simplest Bayes net X heads/tails Y XX X1X1 X2X2 XNXN YY Y1Y1 Y2Y2 YNYN case 1 case 2 case N "parameter independence"

8
The next simplest Bayes net X heads/tails Y XX X1X1 X2X2 XNXN YY Y1Y1 Y2Y2 YNYN case 1 case 2 case N "parameter independence" two separate thumbtack-like learning problems

9
A bit more difficult... X heads/tails Y Three probabilities to learn: X=heads Y=heads|X=heads Y=heads|X=tails

10
A bit more difficult... X heads/tails Y XX X1X1 X2X2 Y|X=heads Y1Y1 Y2Y2 case 1 case 2 Y|X=tails heads tails

11
A bit more difficult... X heads/tails Y XX X1X1 X2X2 Y|X=heads Y1Y1 Y2Y2 case 1 case 2 Y|X=tails

12
A bit more difficult... X heads/tails Y XX X1X1 X2X2 Y|X=heads Y1Y1 Y2Y2 case 1 case 2 Y|X=tails ? ? ?

13
A bit more difficult... X heads/tails Y XX X1X1 X2X2 Y|X=heads Y1Y1 Y2Y2 case 1 case 2 Y|X=tails 3 separate thumbtack-like problems

14
In general … Learning probabilities in a Bayes net is straightforward if Complete data Local distributions from the exponential family (binomial, Poisson, gamma,...) Parameter independence Conjugate priors

15
Incomplete data makes parameters dependent X heads/tails Y XX X1X1 X2X2 Y|X=heads Y1Y1 Y2Y2 case 1 case 2 Y|X=tails

16
Solution: Use EM Initialize parameters ignoring missing data E step: Infer missing values using current parameters M step: Estimate parameters using completed data Can also use gradient descent

17
Learning Bayes-net structure Given data, which model is correct? XY model 1: XY model 2:

18
Bayesian approach Given data, which model is correct? more likely? XY model 1: XY model 2: Data d

19
Bayesian approach: Model averaging Given data, which model is correct? more likely? XY model 1: XY model 2: Data d average predictions

20
Bayesian approach: Model selection Given data, which model is correct? more likely? XY model 1: XY model 2: Data d Keep the best model: - Explanation - Understanding - Tractability

21
To score a model, use Bayes’ theorem Given data d: "marginal likelihood" model score likelihood

22
Thumbtack example conjugate prior X heads/tails

23
More complicated graphs X heads/tails Y 3 separate thumbtack-like learning problems X Y|X=heads Y|X=tails

24
Model score for a discrete Bayes net

25
Computation of marginal likelihood Efficient closed form if Local distributions from the exponential family (binomial, poisson, gamma,...) Parameter independence Conjugate priors No missing data (including no hidden variables)

26
Structure search Finding the BN structure with the highest score among those structures with at most k parents is NP hard for k>1 (Chickering, 1995) Heuristic methods –Greedy –Greedy with restarts –MCMC methods score all possible single changes any changes better? perform best change yes no return saved structure initialize structure

27
Structure priors 1. All possible structures equally likely 2. Partial ordering, required / prohibited arcs 3. Prior(m) Similarity(m, prior BN)

28
Parameter priors All uniform: Beta(1,1) Use a prior Bayes net

29
Parameter priors Recall the intuition behind the Beta prior for the thumbtack: The hyperparameters h and t can be thought of as imaginary counts from our prior experience, starting from "pure ignorance" Equivalent sample size = h + t The larger the equivalent sample size, the more confident we are about the long-run fraction

30
Parameter priors x1x1 x4x4 x9x9 x3x3 x2x2 x5x5 x6x6 x7x7 x8x8 + equivalent sample size imaginary count for any variable configuration parameter priors for any Bayes net structure for X 1 …X n parameter modularity

31
x1x1 x4x4 x9x9 x3x3 x2x2 x5x5 x6x6 x7x7 x8x8 prior network+equivalent sample size data improved network(s) x 1 true false true x 2 false true x 3 true false........... Combining knowledge & data x1x1 x4x4 x9x9 x3x3 x2x2 x5x5 x6x6 x7x7 x8x8

32
Example: College Plans Data (Heckerman et. Al 1997) Data on 5 variables that might influence high school students’ decision to attend college: –Sex: Male or Female –SES: Socio economic status (low, lower-middle, middle, upper- middle, high) –IQ: discritized into low, lower middle, upper middle, high –PE: Parental Encouragement (low or high) –CP: College plans (yes or no) 128 possible joint configurations Heckerman et. al. computed the exact posterior over all 29,281 possible 5 node DAGs –Except those in which Sex or SAS have parents and/or CP have children (prior knowledge)

Similar presentations

OK

CS 478 - Bayesian Learning1 Bayesian Learning. CS 478 - Bayesian Learning2 States, causes, hypotheses. Observations, effect, data. We need to reconcile.

CS 478 - Bayesian Learning1 Bayesian Learning. CS 478 - Bayesian Learning2 States, causes, hypotheses. Observations, effect, data. We need to reconcile.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on road accidents in pakistan Ppt on 60 years of indian parliament news Marketing mix ppt on nokia pc Ppt on public health administration in india Seminar ppt on 3d password Ieee papers ppt on sustainable buildings Convert pdf ppt to ppt online reader Ppt on hotel management career Ppt on structure in c language Ppt on thermal power plant working