Haystax bayesian networks
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The document discusses automated construction of Bayesian networks from qualitative knowledge. It outlines challenges in generating conditional probability tables (CPTs) from expert knowledge and proposes representing common patterns like concepts, indicators, summaries, and mitigations through qualitative assessments to derive default parameter values for CPTs. Examples demonstrate how qualitative statements can be used to automatically generate a Bayesian network for chest X-ray diagnosis to model relationships between hypotheses of interest and indicating evidence with uncertainty.
![COMPANY PROPRIETARY INFORMATION
Haystax Advanced Analytics Lab
CPT Generation - NoisyOR (Other Functions are possible, i.e. NoisyAnd)
• NoisyOR for CPT
• Need strength(s) and Leak
• Default leak = 0.1
• Can be overridden
• Strength
• Strength of evidence - Use ratios
• Strong = 8:1
• Medium = 4:1
• Weak = 2:1
• Absolute = inf
• Polarity. If negative polarity, swap the parent
state for the CPT calculation
• Absolute strength: replace the row where the
absolute parent is false with [0, 1.0]
E is the child node
C is the set of parent nodes
True ( C ) is the set of parents whose
state is true for the CPT element
being calculated
pi is the causal strength
p0 is the leak
Noisy-Or, -And, -Max and -Sum Nodes in Netica
2008-02-08
© 2000-2008 Norsys Software Corp.](https://image.slidesharecdn.com/haystaxbayesiannetworks-140606090229-phpapp02/85/Haystax-bayesian-networks-10-320.jpg)
![COMPANY PROPRIETARY INFORMATION
Haystax Advanced Analytics Lab
Example - Chest X-Ray Qualitative statements
Tuberculosis is a medium positive indicator of VisitToAsia
LungCancer is a strong positive indicator of Smoking
Bronchitis is a weak positive indicator of smoking
XRay is a strong positive indicator of
TuberculosisOrCancer
Dyspnea is a strong positive indicator of Bronchitis
Dyspnea is a strong positive indicator of
TuberculosisOrCancer
TuberculosisOrCancer is an OR summary of [Tuberculosis,
LungCancer]
VisitToAsia prior: 0.01
Smoking prior: 0.5
Tuberculosis targetBelief: 0.01
LungCancer leak: 0.01
Bronchitis leak: 0.30
XRay leak 0.05
Tuberculosis
present
absent
1.04
99.0
Tuberculosis or Cancer
true
false
6.48
93.5
XRay
abnormal
normal
11.0
89.0
Lung Cancer
present
absent
5.50
94.5
Dyspnea
present
absent
43.6
56.4
Bronchitis
present
absent
45.0
55.0
Smoking
smoker
nonsmoker
50.0
50.0
Visit to Asia
Visited Asia within the last 3 y...
no visit
1.00
99.0
Original model: Based on Lauritzen & Spiegelhalter
1988. Distributed by Norsys Software Corp.](https://image.slidesharecdn.com/haystaxbayesiannetworks-140606090229-phpapp02/85/Haystax-bayesian-networks-16-320.jpg)
Haystax bayesian networks
- 1. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Automated Construction of Bayesian Networks from Qualitative Knowledge • Dr. Ed Wright • Dr. Bob Schrag Haystax Advanced Threat Analytics
- 2. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Outline • Intro • Fusion, situation assessment • Bayesian Networks • Challenges – where do all the numbers come from? • Qualitative representation of Common Patterns • Concepts, Indicators, Summary, Mitigation and Relevance • Qualitative representation: default values => parameters for the CPTs • Some implementation issues • Examples • BN - Chest Xray • Complex Model • Implementation • Future enhancements • Conclusion
- 3. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Information Fusion - Situation Assessment • Making inferences from heterogeneous, incomplete, contradictory information • Intelligence data fusion, Political forecasts, Medical diagnosis, Marketing, … • Characteristics • Hypotheses of Interest – that can not be directly observed • Indicating hypotheses – that are likely true (or false) if a Hypothesis of Interest is true • Evidence / information related to one or more of the hypotheses • Incomplete knowledge and Uncertainty
- 4. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Information Fusion - Example Hypotheses of Interest Will the Blue insurgency succeed in country Orange? Indicating hypotheses Blue is popular Blue has the military capacity to succeed Blue has adequate military communications Blue has adequate weapons Blue has operational success Blue has operational failure Blue leadership is adequate Orange is Popular Evidence Intel reports, radio intercepts, news reports, blogs, twitter, … Incomplete knowledge and Uncertainty Blue Insurgency Succeeds Blue is Popular Blue has Military Capability Blue has Adequate Leadership Orange is Vulnerable Blue has military Comms Blue has Adequate Weapons Blue has Operational Success Blue has Operational Failure radio intercept News Report News Report Intel. Report Twitter Sentiment News Report News Report
- 5. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Bayesian Networks for Information Fusion • Probabilistic Model • Executable model • Uncertainty representation is built in • Explicit / Efficient representation • Makes assumptions explicit • Facilitates communication between analysts • Support for learning, and for encoding prior knowledge • Inference propagates in all directions • Computational model • ‘What if’ analysis • Sensitivity analysis Hypothesis Indicator1 true false 0.1 0.9 true false true 0.8 0.2 false 0.1 0.9 Indicator2 Hypothesis Indicator1 true false T T 0.96 0.04 T F 0.8 0.2 F T 0.8 0.2 F F 0.1 0.9
- 6. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Challenges – Where do all of the numbers come from? • Each node requires a local probability table • No parents - > Prior distribution • Node with Parents – Conditional Probability Table (CPT) • One row in the table for each combination of the states of the parent • Where do the numbers come from? • Learning • Expert knowledge from Subject Matter Experts • Combination Knowledge + Learning • DARPA Program Manager: ‘It is a humongous knowledge engineering challenge!’ Parent1 t/f Parent2 t/f Parent3 t/f Parent4 t/f Child t/f Parent1 Parent2 Parent3 Parent4 true false T T T T T T T F T T F T T T F F T F T T T F T F T F F T T F F F F T T T F T T F F T F T F T F F F F T T F F T F F F F T F F F F
- 7. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Patterns • Concepts – Hypotheses • Indicator • Evidence for or against one or more hypotheses • Also a hypothesis • We need a CPT function -> NoisyOR • Mitigation, Relevance • Also a hypothesis • Summary • Also a Hypothesis Hypotheses Indicator Hypotheses Indicator Mitigation Indicator Summary IndicatorIndicator
- 8. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Qualitative assessment: Default Parameter Values • Strength • Setting an evidence node true => same as applying likelihood to the hypothesis • Strength of evidence: • Use ratios • Strong = 8:1 • Medium = 4:1 • Weak = 2:1 • Absolute = • Polarity. If negative polarity, swap the parent state for the CPT calculation Hypothesis Indicator Hypothesis true false 12.0 88.0 Indicator true false 18.4 81.6 Hypothesis true false 100 0 Absolute Indicator true false 100 0 Hypothesis true false 0 100 Absolute Neg Indicator true false 100 0 Hypothesis true false 52.2 47.8 Strong Indicator true false 100 0 Hypothesis true false 1.68 98.3 Strong Neg Indicator true false 100 0 Hypothesis true false 35.3 64.7 Medium Indicator true false 100 0 Hypothesis true false 3.30 96.7 Medium Neg Indicator true false 100 0 Hypothesis true false 21.4 78.6 Weak Indicator true false 100 0 Hypothesis true false 6.38 93.6 Weak Neg Indicator true false 100 0
- 9. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab CPT Generation - Indicators for Multiple Hypotheses Need a function: F(a set of states of the parent nodes ) => one row of the CPT Using Strength and polarity strong, positive medium, positive weak, positive strong, negative Hypothesis1 true false 32.8 67.2 Hypothesis2 true false 9.32 90.7 Hypothesis3 true false 11.3 88.7 Hypothesis4 true false 59.1 40.9 ind2no true false 100 0 Hypothesis1 true false 12.0 88.0 Hypothesis2 true false 5.00 95.0 Hypothesis3 true false 8.00 92.0 Hypothesis4 true false 85.0 15.0 ind2no true false 31.0 69.0
- 10. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab CPT Generation - NoisyOR (Other Functions are possible, i.e. NoisyAnd) • NoisyOR for CPT • Need strength(s) and Leak • Default leak = 0.1 • Can be overridden • Strength • Strength of evidence - Use ratios • Strong = 8:1 • Medium = 4:1 • Weak = 2:1 • Absolute = inf • Polarity. If negative polarity, swap the parent state for the CPT calculation • Absolute strength: replace the row where the absolute parent is false with [0, 1.0] E is the child node C is the set of parent nodes True ( C ) is the set of parents whose state is true for the CPT element being calculated pi is the causal strength p0 is the leak Noisy-Or, -And, -Max and -Sum Nodes in Netica 2008-02-08 © 2000-2008 Norsys Software Corp.
- 11. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab CPT Generation: Relevance and Mitigation Mitigation true false 12.0 88.0 Indicator with Mitigation true false 22.2 77.8 Hypothesis true false 12.0 88.0 Hypothesis Indicator with Mitigation Mitigation Evidence for or against Mitigation Evidence for Mitigation true false 18.4 81.6 Mitigation true false 0 100 Indicator with Mitigation true false 100 0 Hypothesis true false 52.2 47.8 Evidence for Mitigation true false 10.0 90.0 Mitigation true false 100 0 Indicator with Mitigation true false 100 0 Hypothesis true false 12.0 88.0 Evidence for Mitigation true false 80.0 20.0 Indicator with Mitigation true false 100 0 Hypothesis true false 22.1 77.9 Mitigation true false 74.8 25.2 Hypothesis Relevance Indicator with Relevance Evidence for or Evidence for Mitigation true 100
- 12. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab CPT Generation: Relevance and Mitigation • Desired(?): applying evidence does not change the mitigation Indicator with Mitigation true false 1.62 98.4 Evidence in Mitigation true false 0 100 Mitigation true false 2.94 97.1 Hypothesis true false 0.50 99.5 Indicator with Mitigation true false 100 0 Evidence in Mitigation true false 0 100 Mitigation true false 91.0 9.01 Hypothesis true false 9.46 90.5 Indicator with Mitigation true false 100 0 Evidence in Mitigation true false 0 100 Mitigation true false 2.94 97.1 Hypothesis true false 97.1 2.93 Need to do the algebra, figure out what numbers will result in no change to the mitigation when evidence is applied. Note: when evidence is applied elsewhere in the network, mitigation will change.
- 13. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Patterns - Extras • Copy of / opposite of • Rare event • Over ride the default Leak • Target beliefs Hypothesis OppositeSynonym Deterministic Relationship Hypotheses Indicator Hypotheses Indicator Mitigation Indicator Summary IndicatorIndicatorPrior P(t) is too small or too large TgtBelCnstrnt Calculate CPT for artificial evidence, when applied, brings P(t) to desired value
- 14. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Patterns - Extras If a node is a parent to a summary node, the effect of mitigation or relevance on that node gets ignored • Hypothesis Copy The construction software automatically detects this, and introduces a Hypothesis copy as the parent of the original hypothesis, and of the summary HypothesesHypotheses Mitigation Indicator Summary Hypotheses Hypotheses Mitigation Indicator Summary Hyp Copy Indicator Indicator Deterministic Relationship
- 15. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Visualization Positive Influence Negative Influence Absolute Influence Strong Influence Moderate Influence Weak Influence Absolute, Positive Absolute, Negative Weak, Negative Strong, Positive Moderate, Positive Strong, Positive Strong, Positive Absolute , Negative Moderate, Positive
- 16. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Example - Chest X-Ray Qualitative statements Tuberculosis is a medium positive indicator of VisitToAsia LungCancer is a strong positive indicator of Smoking Bronchitis is a weak positive indicator of smoking XRay is a strong positive indicator of TuberculosisOrCancer Dyspnea is a strong positive indicator of Bronchitis Dyspnea is a strong positive indicator of TuberculosisOrCancer TuberculosisOrCancer is an OR summary of [Tuberculosis, LungCancer] VisitToAsia prior: 0.01 Smoking prior: 0.5 Tuberculosis targetBelief: 0.01 LungCancer leak: 0.01 Bronchitis leak: 0.30 XRay leak 0.05 Tuberculosis present absent 1.04 99.0 Tuberculosis or Cancer true false 6.48 93.5 XRay abnormal normal 11.0 89.0 Lung Cancer present absent 5.50 94.5 Dyspnea present absent 43.6 56.4 Bronchitis present absent 45.0 55.0 Smoking smoker nonsmoker 50.0 50.0 Visit to Asia Visited Asia within the last 3 y... no visit 1.00 99.0 Original model: Based on Lauritzen & Spiegelhalter 1988. Distributed by Norsys Software Corp.
- 17. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Example - Chest Xray Tuberculosis present absent 1.04 99.0 Tuberculosis or Cancer true false 6.48 93.5 XRay abnormal normal 11.0 89.0 Lung Cancer present absent 5.50 94.5 Dyspnea present absent 43.6 56.4 Bronchitis present absent 45.0 55.0 Smoking smoker nonsmoker 50.0 50.0 Visit to Asia Visited Asia within the last 3 y... no visit 1.00 99.0 Original model: Based on Lauritzen & Spiegelhalter 1988. Distributed by Norsys Software Corp. VisitToAsia true false 0.64 99.4 Smoking true false 50.0 50.0 XRay true false 7.25 92.8 Dyspnea true false 48.8 51.2 TuberculosisOrCancer true false 5.91 94.1 TgtBelCnstForTuberculosis true false 100 0 Tuberculosis true false 1.0 99.0 LungCancer true false 4.96 95.0 Bronchitis true false 51.0 49.0 Automatically constructed from qualitative representation.
- 18. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Example – Complex Model • Bayesian Network representing concepts and relationships defined in a set of source documents • 700(+) concepts • The Government Customer: “for the first time, we have a computational model of the concepts in this document!”
- 19. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab 1. Extract key concept nodes. 2. Extract influence arcs, specifying… 3. Create master influence graph. 4. Compile into standard Bayesian network (BN). 5. Exploit, improve the model. • Strength: Absolute, strong, moderate, weak, … • Polarity: Positive, negative • Assemble graph from extracted arcs. • Review extracted concepts, influences. • Normalize extracted concept names, definitions. • Insert missing concepts, influences. • Add missing logical structure: AND, OR, Opposite. • Collect concepts’ parent nodes, build conditional probability tables (CPTs) per influence spec’s. • Insert pattern-required nodes for mitigation, relevance. • Run the model against test cases. • Review model inferences with SMEs. • Revise as appropriate. Model Development Process
- 20. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Master Influence Graph (defparameter *Influences* '((VisitToAsia (:IndicatedBy (:Moderately (Tuberculosis)))) (Smoking (:IndicatedBy (:Strongly (LungCancer)) (:Weakly (Bronchitis (:IndicatedBy (:Strongly (Dyspnea))))))) (TuberculosisOrCancer (:ImpliedByDisjunction (Tuberculosis) (LungCancer)) (:IndicatedBy (:Strongly (XRay) (Dyspnea)))))) Tuberculosis present absent 1.04 99.0 Tuberculosis or Cancer true false 6.48 93.5 XRay abnormal normal 11.0 89.0 Lung Cancer present absent 5.50 94.5 Dyspnea present absent 43.6 56.4 Bronchitis present absent 45.0 55.0 Smoking smoker nonsmoker 50.0 50.0 Visit to Asia Visited Asia within the last 3 y... no visit 1.00 99.0
- 21. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Implementation • Netica, NeticaJ API • Jython • Integrate with Java/NeticaJ • Higher level tools on top of NeticaJ • GraphViz • Netica does not do graph layout • Build the BN in Netica (all the nodes are on top of each other) • Extract nodes and links • Use GraphViz to layout • Update each Node in Netica with new coordinates • Franz Lisp / AllegroGraph – Netica API • Master Influence Graph • Ingesting data and applying evidence to the network
- 22. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Limitations & Future Enhancements • Limitations • Binary Nodes • Limited (but extendable) set of patterns • Future Enhancements • Strength of mitigation / relevance • Richer set of qualitative statements • Additional CPT models (NoisyAnd, …) • Global / local mitigation • Visual editor
- 23. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Conclusion For a large set of information fusion problems, it is possible to shortcut the ‘humongous knowledge engineering challenge’, by automatically generating a usable Bayesian Network from English like qualitative statements (and a few numbers). The resulting Bayesian Network is immediately useful, and can be a start point for further knowledge refinement.
- 24. COMPANY PROPRIETARY INFORMATION Haystax Advanced Analytics Lab Thank You Contact us: info@haystax.com Visit us: www.haystax.com 8251 Greensboro Drive, Suite 1111 McLean, VA 22012