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Bayesian Networks Lecture 1: Basics and Knowledge-Based Construction

Learn the basics of Bayesian networks, why we use them, how to build them by hand and from data, their applications, and their relationship to other models.

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Bayesian Networks Lecture 1: Basics and Knowledge-Based Construction

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  1. Bayesian Networks Lecture 1:Basics and Knowledge-Based Construction Lecture 1 is based on David Heckerman’s Tutorial slides. (Microsoft Research) Requirements: 50% home works; 50% Exam or a project

  2. What I hope you will get out ofthis course... • What are Bayesian networks? • Why do we use them? • How do we build them by hand? • How do we build them from data? • What are some applications? • What is their relationship to other models? • What are the properties of conditional independence that make these models appropriate? • Usage in genetic linkage analysis

  3. Applications of hand-built Bayes Nets • Answer Wizard 95, Office Assistant 97,2000 • Troubleshooters in Windows 98 • Lymph node pathology • Trauma care • NASA mission control Some Applications of learned Bayes Nets • Clustering users on the web (MSNBC) • Classifying Text (spam filtering)

  4. Some factors that support intelligence • Knowledge representation • Reasoning • Learning / adapting

  5. Artificial Intelligence

  6. Artificial Intelligence is better than none !

  7. Artificial Intelligence is better than ours!

  8. Outline for today • Basics • Knowledge-based construction • Probabilistic inference • Applications of hand-built BNs at Microsoft

  9. Bayesian Networks: History • 1920s: Wright -- analysis of crop failure • 1950s: I.J. Good -- causality • Early 1980s: Howard and Matheson, Pearl • Other names: • directed acyclic graphical (DAG) models • belief networks • causal networks • probabilistic networks • influence diagrams • knowledge maps

  10. Fuel Battery Fuel Gauge Engine Turns Over Start Bayesian Network p(f) p(b) p(g|f,b) p(t|b) p(s|f,t) Directed Acyclic Graph, annotated with prob distributions

  11. Fuel Battery p(f) p(b) Fuel Gauge p(g|f,b) Engine Turns Over p(t|b) Start p(s|f,t) BN structure: Definition Missing arcs encode independencies such that

  12. Independencies in a Bayes net Example: Many other independencies are entailed by (*): can be read from the graph using d-separation (Pearl)

  13. Fuel TurnOver Start Explaining Away and Induced Dependencies "explaining away" "induced dependencies"

  14. T F Fuel (empty, not) TurnOver (yes, no) S Start (yes, no) Local distributions Table: p(S=y|T=n,F=e) = 0.0 p(S=y|T=n,F=n) = 0.0 p(S=y|T=y,F=e) = 0.0 p(S=y|T=y,F=n) = 0.99

  15. T F Fuel (empty, not) TurnOver TurnOver (yes, no) S no yes Fuel Start (yes, no) p(start)=0 not empty empty p(start)=0 p(start)=0.99 Local distributions Tree:

  16. node parents Lots of possibilities for a local distribution... • y = discrete node: any probabilistic classifier • Decision tree • Neural net • y= continuous node: any probabilistic regression model • Linear regression with Gaussian noise • Neural net

  17. Class ... Input 1 Input 2 Input n Naïve Bayes Classifier discrete

  18. Hidden Markov Model discrete, hidden H1 H2 H3 H4 H5 ... ... X1 X2 X3 X4 X5 observations

  19. Feed-Forward Neural Network X1 X1 X1 inputs hidden layer sigmoid Y1 Y2 Y3 outputs (binary) sigmoid

  20. Outline • Basics • Knowledge-based construction • Probabilistic inference • Decision making • Applications of hand-built BNs at Microsoft

  21. Building a Bayes net by hand(ok, now we're starting to be Bayesian) • Define variables • Assess the structure • Assess the local probability distributions

  22. What is a variable? • Collectively exhaustive, mutually exclusive values Error Occured No Error

  23. Clarity Test: Is the variable knowable in principle • Is it raining? {Where, when, how many inches?} • Is it hot? {T  100F , T < 100F} • Is user’s personality dominant or submissive? {numerical result of standardized personality test}

  24. Assessing structure(one approach) • Choose an ordering for the variables • For each variable, identify parents Pai such that

  25. TurnOver Gauge Start Battery Example Fuel

  26. TurnOver Gauge Start Battery Example Fuel p(f)

  27. TurnOver Gauge Start Battery Example Fuel p(b|f)=p(b) p(f)

  28. TurnOver Gauge Start Battery Example Fuel p(b|f)=p(b) p(f) p(t|b,f)=p(t|b)

  29. TurnOver Gauge Start Battery Example Fuel p(b|f)=p(b) p(f) p(t|b,f)=p(t|b) p(g|f,b,t)=p(g|f,b)

  30. Fuel TurnOver Gauge Start Battery Example p(b|f)=p(b) p(f) p(t|b,f)=p(t|b) p(g|f,b,t)=p(g|f,b) p(s|f,b,t,g)=p(s|f,t) p(f,b,t,g,s) = p(f) p(b) p(t|b) p(g|f,b) p(s|f,t)

  31. Start Gauge Fuel Battery TurnOver Why is this the wrong way?Variable order can be critical

  32. Fuel Battery Gauge TurnOver Start A better way:Use causal knowledge

  33. Fuel TurnOver Gauge Start Battery Conditional Independence Simplifies Probabilistic Inference

  34. Online Troubleshooters

  35. Define Problem

  36. Gather Information

  37. Get Recommendations

  38. Portion of BN for print troubleshooting (see Breese & Heckerman, 1996)

  39. Office Assistant 97

  40. Lumière Project (see Horvitz, Breese, Heckerman, Hovel & Rommelse 1998) User’s Goals User’s Needs User Activity

  41. Studies with Human Subjects • “Wizard of OZ” experiments at MS Usability Labs User Actions Typed Advice Inexperienced user Expert Advisor

  42. Several classes of evidence Activities with Relevance to User’s Needs • Search: e.g., menu surfing • Introspection: e.g., sudden pause, slowing of command stream • Focus of attention: e.g, selected objects • Undesired effects: e.g., command/undo, dialogue opened and cancelled • Inefficient command sequences • Goal-specific sequences of actions .

  43. Summary so far Bayes nets are useful because... • They encode independence explicitly • more parsimonious models • efficient inference • They encode independence graphically • Easier explanation • Easier encoding • They sometimes correspond to causal models • Easier explanation • Easier encoding • Modularity leads to easier maintenance

  44. Teenage Bayes MICRONEWS 97: Microsoft Researchers Exchange Brainpower with Eighth-grader Teenager Designs Award-Winning Science Project .. For her science project, which she called "Dr. Sigmund Microchip," Tovar wanted to create a computer program to diagnose the probability of certain personality types. With only answers from a few questions, the program was able to accurately diagnose the correct personality type 90 percent of the time.

  45. Artificial Intelligence is a promising fieldalways was, always will be.

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