93 Views

Download Presentation
##### Belief Nets

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Belief Nets**Notes 6: CDS**Bayesian Networks**• Closely related ideas • Belief nets • Influence ets • Networks of concepts linked with conditional probabilities • Now easy to calculate for large, moderately complex nets • Connectivity - maximum number of connected nodes • Size - total number of nodes**p(LosesLvs |Dry,Sick)=0.95p(NotLosesLvs|Dry,Sick)=0.05**p(Losesvs |Dry, NotSick)=0.85p(NotLosesLvs|Dry, NotSick)=0.15 etc. A Simple Bayesian Network p(Dry) = 0.1 p(NotDry) =0.9 p(Sick) = 0.1 p(NotSick)=0.9**Probability of ‘Looses Leaves’ set to 100%**Probability of Dry and Sick about equal**Probability of Dry set to 0**Probability of ‘Sick’ now much higher**Initialise the Network**No information really on Leaves: Just the ‘prior probability on everything**Now Set LosesLeaves to True**Probability of Dry and Sick both go up, but Dry goes up much more.**Now set GrassBrown to ‘yes’**Probability of Dry jumps to 97.95%but look also at probability of NearbyTree**Say there is also a nearby tree**Unsurprisingly, the probability of Dry is nearly certain The probability of Sick drops 10% or so**Even Consider there is no tree**The evidence of the brown grass is enough to favour ‘Dry’ over ‘Sick’ by over 4:1**Evidence that is ‘Explained away’ is not evidence:**consider...**Losing Leaves, no nearby tree**Sick vs Dry roughly 50:50(as before)**Add that the grass is brown**Odds in favour of Dry over Sick rise to 4:1(84:22)**Now say that weedkiller was applied**The evidence from GrassBrown is explained awayOdds go back to 50:50**Diagnosis from Evidence and Diagnosis by Exclusion**• Previous examples were diagnosis from evidence • Normally evidence is a manifestation of the problem • Dryness causes brown grass • Sometimes we also reason from known causes, e.g. Nearby trees can add to dryness • Diagnosis of Exclusion • If there is evidence against all other causes, then the probability of what is left must rise • Consider the next example...**Initialise the Network**No information really on Leaves: Just the ‘prior probability on everything**Now Set LosesLeaves to True**Probability of Dry and Sick both go up, but Dry goes up much more.**Now say there is no nearby tree**Probability of Sick goes up to 50:50Probability of Dry falls to 50:50**Now add that the grass is not brown**Probability of Dry falls to under 10%Probability of Sick rises to 75%‘Diagnosis of Exclusion’**Bayesian Nets: Summary so far**• Probabilities propagate • Probability must go someplace • The good news: Diagnoses of exclusion • The bad news: spurious conclusions**IF fungus THEN Black Mould**• if P then Q = not both P and not Q • P Q ¬(P & ¬Q) • Equivalent to p(P&¬Q) 0 • If Black Mould then Fungus • There is never black mould without fungus • No fungus implies no black mould**A More Complex Network Initialised**Sick to Dry roughly 50:50Note Normal Rainfall**Set Black Mould**Sick goes to nearly 100% (because of Fungus)Note that Normal Rain=yes risesIs this sensible?**Now also set BrownGrass to yes**Dry goes up to 68%Normal rain = yes falls to 73% from 89% Two things can both be wrong at once!**Note: Black Mould is indirect evidence for ‘Sick’: It is**evidence for a mutual cause**Summary of Bayesian Nets**• Formalism is strictly based on probability • Normal practice is to use an ‘influence diagram’ and for arrows in the direction of causation: p(E|H) • Require lots and lots of numbers • But there are many ways of approximating them • Allow reasoning • From cause to effect • From effect to cause • By exclusion • But beware of “residual diagnoses” • PQ shown by negation (probability 0) • equivalences: ¬Q¬P ¬(P&¬Q)**Tools**• Several sets of free tools • Hugin-Lite (used for this handout) • www.hugin.com • Excellent tutorials and documentation on Web • Belief net site • http://bayes.stat.washington.edu/almond/belief.html • GeNIe and SMILE • http://www2.sis.pitt.edu/~genie • C++ and graphics packages • Good project materal