Post on 15-Jan-2016
MURI Progress Report, June 2001
Advances in Approximate and Hybrid Reasoning for Decision Making Under Uncertainty
Rina DechterUC- Irvine
Collaborators:Kalev Kask,Javier Larrosa,David Larkin,Robert Mateescu
MURI Progress Report, June 2001
Summary of Results
Mini-clustering: a universal anytime approximation scheme. Applied to probabilistic inference and to Optimization, decision making tasks
Hybrid processing of beliefs and constraints
REES: Reasoning Engine Evaluation Shell.
Online algorithms (S. Irani)
MURI Progress Report, June 2001
Outline
Mini-clustering approximation; approximation by partitioning, a universal anytime scheme Applied to probabilistic inference Applied to Decision Optimization tasks
Hybrid processing of beliefs and constraints
REES: Reasoning Engine Evaluation Shell. Online algorithms (S. Irani)
MURI Progress Report, June 2001
Mini-Clustering :Approximation by partitioning
Past work: Mini-bucket approximation for variable elimination Applied to optimization Used for static heuristic generation for search Experiments with coding tasks, medical diagnosis
Progress this year Mini-clustering approximation of tree-clustering Applied to Belief updating Applied to optimization and search
MURI Progress Report, June 2001
Motivation
Decision-making algorithms are all too complex (NP-Hard).
The main bottleneck is probabilistic inference: determining the posterior beliefs given evidence to help forming the right decision.
Consequently, approximate, anytime methods are essential to assist in advise-giving for decision making.
MURI Progress Report, June 2001
Automated reasoning Tasks
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MURI Progress Report, June 2001
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MURI Progress Report, June 2001
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MURI Progress Report, June 2001
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MURI Progress Report, June 2001
Time complexity: Exponential in the induced-width
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Space complexity: Exponential in the separator O ( N dsep)
Tree clustering Complexity
MURI Progress Report, June 2001
Idea of Mini-clustering
Reduce the exponent (i.e. size of the cluster); partition into mini-clusters.
Accuracy-control parameter z = maximum number of variables in a mini-cluster
The idea was explored for variable elimination (Mini-Bucket)
MURI Progress Report, June 2001
Idea of Mini-clustering
Split a cluster into mini-clusters =>bound complexity
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MURI Progress Report, June 2001
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MURI Progress Report, June 2001
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Tree-clustering vs Mini-clustering
MURI Progress Report, June 2001
Properties of MC(z)
MC(z) computes a bound on the joint probability P(X,e) of each variable and each of its values.
Time & space complexity: O(n hw* exp(z))
Lower, Upper bounds and Mean approximations
Approximation improves with z but takes more time
MURI Progress Report, June 2001
Experiments Algorithms:
Exact IBP Gibbs sampling (GS) Mini-Clustering (MC(z))
Networks: Probabilistic Decoding networks Medical diagnosis: CPCS 54 Random noisy-OR networks Random networks
MURI Progress Report, June 2001
0|e|=10 max mean max mean max mean max mean
20
0.01852 0.00032 0.00064 2.450IBP 0.15727 0.03307 0.07349 2.191
0.20765 0.05934 0.14202 1.5610.49444 0.07797 0.18034 17.247
GS 0.51409 0.09002 0.21298 17.2080.48706 0.10608 0.26853 17.335
0.16667 0.07407 0.02722 0.01221 0.05648 0.02520 0.154 0.153MC(2) 0.11636 0.07636 0.02623 0.01843 0.05581 0.03943 0.096 0.095
0.10529 0.07941 0.02876 0.02196 0.06357 0.04878 0.067 0.0670.18519 0.09259 0.02488 0.01183 0.05128 0.02454 0.157 0.155
MC(5) 0.10727 0.07682 0.02464 0.01703 0.05239 0.03628 0.112 0.1120.08059 0.05941 0.02174 0.01705 0.04790 0.03778 0.090 0.0870.12963 0.07407 0.01487 0.00619 0.03047 0.01273 0.438 0.446
MC(8) 0.06591 0.05000 0.01590 0.01040 0.03394 0.02227 0.369 0.3700.03235 0.02588 0.00977 0.00770 0.02165 0.01707 0.292 0.2940.11111 0.07407 0.01133 0.00688 0.02369 0.01434 2.038 2.032
MC(11) 0.02818 0.01500 0.00600 0.00398 0.01295 0.00869 1.567 1.5710.00353 0.00353 0.00124 0.00101 0.00285 0.00236 0.867 0.869
NHD Absolute Error Relative Error Time
Performance on CPCS54 w*=15
MURI Progress Report, June 2001
0|e|=10 max mean max mean max mean max mean
20
0 9.0E-09 1.1E-05 0.102IBP 0 3.4E-04 4.2E-01 0.081
0 9.6E-04 1.2E+00 0.0620.51 5.0E-01 5.9E+02 12.976
GS 0.52 5.0E-01 5.9E+02 13.1600.51 5.0E-01 6.0E+02 12.976
0 0 1.6E-03 1.1E-03 1.9E+00 1.3E+00 0.056 0.057MC(2) 0 0 1.1E-03 8.4E-04 1.4E+00 1.0E+00 0.048 0.049
0 0 5.7E-04 4.8E-04 7.1E-01 5.9E-01 0.039 0.0390 0 1.1E-03 9.4E-04 1.4E+00 1.2E+00 0.070 0.072
MC(5) 0 0 7.7E-04 6.9E-04 9.3E-01 8.4E-01 0.063 0.0660 0 2.8E-04 2.7E-04 3.5E-01 3.3E-01 0.058 0.0570 0 3.6E-04 3.2E-04 4.4E-01 3.9E-01 0.214 0.221
MC(8) 0 0 1.7E-04 1.5E-04 2.0E-01 1.9E-01 0.184 0.1900 0 3.5E-05 3.5E-05 4.3E-02 4.3E-02 0.123 0.127
NHD Absolute Error Relative Error Time
N=50, P=2, w*=10
Noisy-OR Networks 1
MURI Progress Report, June 2001
0|e|=10 max mean max mean max mean max mean
20
0.03652 0.00907 0.01894 0.298IBP 0.25200 0.08319 0.22335 0.240
0.34000 0.13995 0.91671 0.1830.17304 0.04377 0.09395 0.140
MC(2) 0.17600 0.11600 0.05930 0.04558 0.14706 0.11034 0.100 0.1030.15067 0.14000 0.07658 0.06683 0.23155 0.19538 0.075 0.0780.15652 0.04380 0.09398 0.158
MC(5) 0.15600 0.11800 0.05665 0.04320 0.13484 0.10221 0.124 0.1290.09467 0.09467 0.05545 0.05049 0.15000 0.13706 0.105 0.1070.16783 0.04166 0.08904 0.602
MC(8) 0.09800 0.08100 0.04051 0.03254 0.09923 0.07942 0.481 0.4910.05467 0.04533 0.02939 0.02691 0.07865 0.07237 0.385 0.3930.12087 0.03076 0.06550 2.986
MC(11) 0.05500 0.04700 0.02425 0.01946 0.05644 0.04533 2.307 2.3450.00800 0.00533 0.00483 0.00431 0.01307 0.01156 1.564 1.5850.06348 0.01910 0.04071 14.910
MC(14) 0.01400 0.01200 0.00542 0.00434 0.01350 0.01108 8.548 8.5780.00000 0.00000 0.00089 0.00089 0.00212 0.00211 3.656 3.676
NHD Absolute Error Relative Error Time
N=50, P=3, w*=16
Random Networks 2
MURI Progress Report, June 2001
Outline
Mini-clustering approximation; approximation by partitioning, a universal anytime scheme Applied to probabilistic inference Applied to Optimization and decision-making
tasks Hybrid processing of beliefs and constraints REES: Reasoning Engine Evaluation Shell. Online algorithms (S. Irani)
MURI Progress Report, June 2001
Constraint Optimization for Decision-making (COP)
Global optimization: Find the best cost assignment subject
to constraints
Singleton optimality: Find the best cost-extension for every
singleton variable-value assignment (X,a).
MURI Progress Report, June 2001
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MURI Progress Report, June 2001
From Mini-bucket elimination to Mini-Bucket Tree Elimination
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MURI Progress Report, June 2001
Branch and Bound with lower bound Heuristics
BBMB(z), the earlier algorithm: Heuristic, computed by MB(z), is static,
variable ordering fixed.
BBBT(z), the new algorithm: Lower bound is computed at each node of
the search by MC(z). Used for dynamic variable and value
ordering.
MURI Progress Report, June 2001
BBBT(z) vs. BBMB(z)
BBBT(z) vs BBMB(z), N=50
MURI Progress Report, June 2001
BBBT(z) vs. BBMB(z).
BBBT(z) vs BBMB(z), N=100
MURI Progress Report, June 2001
Conclusion
Mini-clustering, MC(z) extends partition-based approximation from mini-buckets to tree decompositions.
For Probabilistic inference:
For Optimization and decision-making tasks
Empirical evaluation demonstrates its effectiveness and superiority (for certain types of problems).
MURI Progress Report, June 2001
Outline
Mini-clustering approximation; approximation by partitioning, a universal anytime scheme Applied to probabilistic inference Applied to Optimization and decision tasks
Processing beliefs and constraints REES: Reasoning Engine Evaluation
Shell. Online algorithms (S. Irani)
MURI Progress Report, June 2001
Task A: Representation and Integration of Uncertain Information
Challenges: Coherent and efficient extension of Bayesian networks to accommodate diverse types of information.
Subtasks: Constraint-based information Temporal information Incomplete information
MURI Progress Report, June 2001
Motivation
Complex queries for war scenarios:
What is the probability that either plan1 or plan2 hit the target, when plan2 or plan 3 can divert enemy fire, under bad weather or poor communication.
Observing that the enemy fire is coming either from direction 1 or direction 2, when direction 1 implies ground fire, what is the likelihood of being hit.
MURI Progress Report, June 2001
Hybrid Processing Beliefs and Constraints
Hybrid deterministic and probabilistic Information
Complex queries:
Complex evidence structure
All reduce to propositional queries over a Belief network.
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MURI Progress Report, June 2001
Hybrid (continued)
Deterministic queries and information can be handled as Conditional Probability Tables (CPTs)
Drawbacks: computational properties such as constraint propagation and unit resolution are not exploited.
Target: to exploit constraint processing whenever possible
MURI Progress Report, June 2001
A Hybrid Belief Network
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MURI Progress Report, June 2001
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MURI Progress Report, June 2001
Empirical evaluation
Elim-CPE
Elim-Hidden model clauses as CPT with hidden variables
Elim-CPE-D extracts clauses from deterministic CPT’s
Benchmarks: Insurance and Hailfinder networks Random networks
MURI Progress Report, June 2001
test instances of the insurance network with query parameters < 15, 5 >
Insurance Network
MURI Progress Report, June 2001
48 test instances with network parameters < 80, 4, 75 > and query parameters < 0, 10 >
Elim-CPE vs. Elim-CPE-D
MURI Progress Report, June 2001
50 test instances, network parameters of < 50, 5, 0 > and query parameters < 50, 15 >
Averages over 35 test instances, network parameters of < 40, 5, 0 > and query parameters < 60, 10 >
Elim-CPE vs. Elim-Hidden
MURI Progress Report, June 2001
Conclusion
Elim-CPE: an extended variable elimination algorithm exploiting both constraints and probabilities
Empirical evaluation demonstrate Elim-CPE highly more effective than regular algorithms (Elim-Hidden)
Elim-CPE-D, extracting deterministic information from BN, improves performance and becomes more significant as deterministic information grows.
MURI Progress Report, June 2001
Outline
Mini-clustering approximation; approximation by partitioning, a universal anytime scheme Applied to probabilistic inference Applied to Optimization and decision tasks
Processing beliefs and constraints REES: Reasoning Engine Evaluation
Shell. Online algorithms (S. Irani)
MURI Progress Report, June 2001
REES: Reasoning Engine Evaluation Shell
Generalizable and Customizable: Consistent handling of reasoning tasks Handles manually and randomly generated
problems with same user interface Add your own network types Use your own calculating engine Not limited by present AI problem types
Created by Kyle Bolen and Kalev KaskUnder direction of Dr. Rina Dechter
MURI Progress Report, June 2001
Interface Allows For:
Easy parameter entry
Quick access to choices
Simple selection process
MURI Progress Report, June 2001
Customize To:
Include only what you need
Output to a file Run multiple
instances Run multiple
algorithms
MURI Progress Report, June 2001
Understand The Results
Easily compare different algorithms
View only the output you want
MURI Progress Report, June 2001
Outline
Mini-clustering approximation; approximation by partitioning, a universal anytime scheme Applied to probabilistic inference Applied to Optimization and decision tasks
Processing beliefs and constraints REES: Reasoning Engine Evaluation
Shell. Online algorithms (S. Irani)
MURI Progress Report, June 2001
Online Load Balancing with Multiple Resources, S. Irani
Tasks arrive in time and must be assigned to a server/agent as they arrive Each task requires a known amount of each
resource. Goal is to make assignments so that all
resources are evenly balanced among agents Results
Online algorithm whose performance within 2r of optimal. (r = number of resources)
MURI Progress Report, June 2001
Dynamic Vehicle Routing
Requests for service arrive at specific locations over a given area.
Each request has a deadline A single server travels between location
servicing requests Plan route of vehicle to maximize
number of requests satisfied by deadline.
Progress report for Sandy Irani
MURI Progress Report, June 2001
Dynamic Vehicle Routing
Results: Two different online algorithms developed
whose performance is provably close to optimal. (Which is better depends on parameters of the system)
Lower bounds showing algorithms within a constant of best online algorithms.
Progress report for Sandy Irani
MURI Progress Report, June 2001
Summary
Mini-clustering approximation; approximation by partitioning, a universal anytime scheme Applied to probabilistic inference Applied to Optimization and decision tasks
Processing beliefs and constraints REES: Reasoning Engine Evaluation
Shell. Online algorithms (S. Irani)