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Sensitivity Analysis, Modeling, Inference And More SamIam

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**1. **Sensitivity Analysis, Modeling, Inference And More (SamIam)

**3. **When do numbers really matter? Hei Chan and Adnan Darwiche, UAI-01
Approximating MAP using stochastic local search James Park and Adnan Darwiche, UAI-01
Using recursive decomposition to compute elimination orders, jointrees and dtrees Adnan Darwiche and Mark Hopkins, ECSQARU-01
Recursive conditioning Adnan Darwiche, Journal of Artificial Intelligence, 01

**6. **Current Users/Evaluators HRL Labs (Diagnosis)
TRW IIT (reasoning about adversary intentions)
Bizrate.com (e-commerce)
UCLA Human Perception Lab

**7. **SamIam Features JAVA-based
Implements:
Differential approach
Sensitivity analysis
MAP computations
Innovative decomposition algorithms**
Will integrate:
Anyspace algorithms
Approximate algorithms
Causal reasoning algorithms

**8. **Sensitivity Analysis

**9. **Tuning network parameters Evidence = {report, ~smoke}
Currently, Pr(tampering | e) = 0.5. We want Pr(tampering | e) to 0.65.
SamIam recommends:
Increase Pr(tampering) from 0.02 to 0.036, or
decrease Pr(report | ~leaving) from 0.01 to 0.005.

**10. **Tuning network parameters SamIam calculates minimal changes for each network parameter to enforce the following constraints:
DIFFERENCE: Pr(y|e) – Pr(z|e) ³ e.
RATIO: Pr(y|e) / Pr(z|e) ³ e.

**11. **How we do it… Difference: Pr(y|e) – Pr(z|e) ³ e

**12. **The sensitivity of probabilistic queries to parameter changes We want to understand the sensitivity of a query Pr(y|e) to changes in a meta parameter tx|u.
A bound of the partial derivative:

**13. **Plot of the bound of the partial derivative

**14. **Some observations… An example where the bound of the derivative is tight.
An example network in which the derivative tends to infinity.
An example where an infinitesimal absolute change in a parameter can induce a non-infinitesimal absolute change in some query.
An example where the relative change in query is not bounded by the relative parameter change

**15. **Effects of infinitesimal parameter changes Assume that tx|u £ 0.5. We apply an infinitesimal change Dtx|u to the meta parameter tx|u, leading to a change of D Pr(y|e).
The relative change in the query Pr(y|e) is bounded by:

**16. **Effects of arbitrary parameter changes Odds of x|u: O(x|u) = Pr(x|u) / (1-Pr(x|u))
Odds of y|e: O(y|e) = Pr(y|e) / (1-Pr(y|e))
O’(x|u) and O’(y|e) are the new odds after having applied an arbitrary change to the meta parameter tx|u.

**17. **Effects of arbitrary parameter changes If the change in tx|u is positive, then:
If the change in tx|u is negative, then:
Combining both results, we have:

**18. **Applications Given a parameter Pr(x|u) and an applied change, we can calculate the upper bounds of the change in query Pr(y|e).
Given a query Pr(y|e) and a desired change, we can calculate the lower bounds of the change in Pr(x|u) that we need.
This can be done in constant time and serve as a preliminary recommendation.

**19. **Applications Bring the COA’s probability of success to >= .90
Bring the enemy’s COA probability of failure to >= .99
Reliability…
What are the most influential “sensors” in predicting the probability of intention X

**20. **“Minimal” change The same relative odds change in different network parameters give us the same possible effects of the network queries.
Therefore, the relative odds change can be adopted as a measure of a “minimal” change, instead of the absolute or relative change. We can use it to choose between different recommendations of parameter changes.

**21. **Changes that (don’t) matter Pr(y|e) = 0.6

**23. **Elimination orders, jointrees and dtrees

**24. **Elimination orders, jointrees and dtrees

**26. **Hypergraph partitioning

**27. **An algorithm using hypergraph partitioning to construct dtrees

**29. **Statistics for ISCAS ’85 Benchmark Circuits

**30. **Results for Suite of Belief Networks

**31. **Conclusions Theoretically, we have shown how methods for recursively decomposing DAGs can be used to construct elimination orders, dtrees, and jointrees.
Practically, we have proposed and evaluated the use of a state-of-the-art system for hypergraph partitioning to recursively decompose DAGs and, hence, to construct elimination orders, dtrees, and jointrees.
Currently, looking into other methods for constructing dtrees: graph aggregation! Dtree of undirected graphs.

**33. **Possible elimination orders for MPE, Pr(e) Orders width
ABC 2
ACB 2
BAC 1
BCA 1
CAB 1
CBA 1

**34. **Possible elimination orders for MAP of B,C Orders width
ABC 2
ACB 2
BAC 1
BCA 1
CAB 1
CBA 1

**35. **Unconstrained vs Constrained Width

**36. **Local Search Local search works as follows:
Start from an initial guess
Iteratively try to improve the estimate by moving to a neighbor which is better.
It requires the ability to efficiently compute the score of each neighbor.

**37. **Local Search for MPE State space consists of all complete network instantiations.
Neighbors of w are all instantiations w-X,x where x isn’t in w.
The score for state w is Pr(w,e).
The score for each neighbor can be computed locally in constant time.

**38. **Local Search for MAP State space consists of all instantiations of the MAP variables.
Neighbors of w are all instantiations w-X,x where x isn’t in w.
The score for state w is Pr(w,e).
To be useful, requires an efficient method to compute Pr(w-X,x,e) for all X in W.

**39. **Computing Neighbor Scores Efficiently Pr(w-X,x,e) can be computed for all neighbors in the same time complexity as computing P(w,e).
Can be done using differential inference.
Can be done using fast retraction in jointrees.

**40. **Methods Search Strategies
Hill climbing with random restart
Taboo search
Initialization Strategies
Random
MPE
Individual maximum likelihood (ML)
Sequential

**41. **Solution Quality

**42. **Evaluations Required

**44. **When do numbers really matter? Hei Chan and Adnan Darwiche, UAI-01
Approximating MAP using stochastic local search James Park and Adnan Darwiche, UAI-01
Using recursive decomposition to compute elimination orders, jointrees and dtrees Adnan Darwiche and Mark Hopkins, ECSQARU-01
Recursive conditioning Adnan Darwiche, Journal of Artificial Intelligence, 01