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Advances in Approximate and Hybrid Reasoning for Decision Making Under Uncertainty Rina Dechter UC I

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and Hybrid Reasoning for. Decision Making ... Hybrid processing of beliefs and constraints. REES: Reasoning Engine Evaluation Shell. ... Hybrid (continued) ... – PowerPoint PPT presentation

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Title: Advances in Approximate and Hybrid Reasoning for Decision Making Under Uncertainty Rina Dechter UC I


1
Advances in Approximate and Hybrid Reasoning
for Decision Making Under UncertaintyRina
DechterUC- IrvineCollaboratorsKalev
Kask,Javier Larrosa,David Larkin,Robert
Mateescu
2
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)

3
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)

4
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

5
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.

6
Automated reasoning Tasks
7
A Reasoning problem Graph
A
  • Belief updating
  • ?y ?X-y ?j Pj
  • MPE
  • ?? maxX ?j Pj
  • CSP
  • ?? ?X ?j Cj
  • Max-CSP
  • ?? minX ?j Fj

C
B
F
D
G
8
Tree Decomposition
9
Cluster Tree Elimination(join-tree clustering)
10
Tree clustering Complexity
  • Time complexity
  • Exponential in the induced-width
  • O (N? dw1 )
  • Space complexity
  • Exponential in the separator
  • O ( N ?dsep)

11
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)

12
Idea of Mini-clustering
Split a cluster into mini-clusters gtbound
complexity
13
MC(3) algorithm - example
ABC
BC
2
BCDF
BF
3
BEF
EF
4
EFG
14
Tree-clustering vs Mini-clustering
15
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

16
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

17
Performance on CPCS54 w15
18
Noisy-OR Networks 1
N50, P2, w10
19
Random Networks 2
N50, P3, w16
20
Coding networks
N100, P4, w11
21
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)

22
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).

23
Example COP
Cij Xi ? Xj
Tree-width 3 sep(5,6) 1, 5
24
From Mini-bucket elimination to Mini-Bucket Tree
Elimination
25
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.

26
Accuracy of MCTE(z)
27
BBBT(z) vs BBMB(z), N50
BBBT(z) vs. BBMB(z)
28
BBBT(z) vs BBMB(z), N100
BBBT(z) vs. BBMB(z).
29
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).

30
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)

31
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

32
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.

33
Hybrid Processing Beliefs and Constraints
  • Hybrid deterministic and probabilistic
    Information
  • Complex queries
  • Complex evidence structure
  • All reduce to propositional queries over a
    Belief network.

34
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

35
A Hybrid Belief Network
Bucket G P(GF,D) Bucket F P(FB,C)
Bucket D P(DA,B) Bucket C
P(CA) Bucket B P(BA) Bucket A P(A)
Belief network P(g,f,d,c,b,a) P(gf,d)P(fc,b)P(d
b,a)P(ba)P(ca)P(a)
36
Variable elimination for a hybrid network
Bucket G P(GF,D) Bucket F P(FB,C)
Bucket D P(DA,B) Bucket C
P(CA) Bucket B P(BA) Bucket A P(A)
Bucket G P(GF,D) Bucket F P(FB,C)
Bucket D P(DA,B) Bucket C
P(CA) Bucket B P(BA) Bucket A P(A)
(b) Elim-CPE-D with clause extraction
(a) regular Elim-CPE
37
Empirical evaluation
  • Elim-CPE
  • Elim-Hidden
  • model clauses as CPT with hidden variables
  • Elim-CPE-D
  • extracts clauses from deterministic CPTs
  • Benchmarks
  • Insurance and Hailfinder networks
  • Random networks


38
Insurance Network
test instances of the insurance network with
query parameters lt 15, 5 gt
39
Elim-CPE vs. Elim-CPE-D
48 test instances with network parameters lt 80,
4, 75 gt and query parameters lt 0, 10 gt
40
Elim-CPE vs. Elim-Hidden
50 test instances, network parameters of lt 50, 5,
0 gt and query parameters lt 50, 15 gt
Averages over 35 test instances, network
parameters of lt 40, 5, 0 gt and query parameters
lt 60, 10 gt
41
Elim-CPE vs. Elim-D
Averages of 50 instances with network parameters
lt 80, 4, 75 gt and varied number of evidence.
42
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.

43
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)

44
REES Reasoning Engine Evaluation Shell
Created by Kyle Bolen and Kalev Kask
Under direction of Dr. Rina Dechter
  • 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

45
Interface Allows For
  • Easy parameter entry
  • Quick access to choices
  • Simple selection process

46
Customize To
  • Include only what you need
  • Output to a file
  • Run multiple instances
  • Run multiple algorithms

47
Understand The Results
  • Easily compare different algorithms
  • View only the output you want

48
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)

49
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)

50
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

51
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

52
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)
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