Reasoning under Uncertainty

1. Reasoning under Uncertainty Eugene Fink LTI SeminarNovember 16, 2007

2. Challenges The available knowledgeabout the real world isinherently uncertain. We usually make decisionsbased on incomplete and partially inaccurate data.

3. Challenges • Representation of uncertainty • Fast reasoning based on uncertain knowledge • Elicitation of criticaladditional data • Learning of reasonabledefault assumptions • Contingency reasoning

4. RAPID (2007–2011) “Representation and Analysis of Probabilistic Intelligence Data” Analysis of uncertain military-intelligence data and planning of future data collection. Projects RADAR / Space-Time (2003–2008) “Reflective Agent with DistributedAdaptive Reasoning” Scheduling and resource allocation under uncertainty.

5. Outline • Representation of uncertainty • Reasoning based on uncertain knowledge • Elicitation of missing data • Future research challenges Representation of uncertainty

6. Probability distributions Weight: Phone location: 95% purse 2% home 2% office 1% car probabilitydensity 140 160 Alternative representations • Approximations • Mary’s weight is about 150. Mary’s cell phone is probably in her purse. • Ranges or sets of possible values • Mary’s weight is between 140 and 160. Mary’s cell phone may be in her purse, office, home, or car.

7. BUT… DEFAULT APPROACH • We assume that small input changes do not cause large output changes • We may need to modify standard algorithms to ensure that they do not violate this assumption WHICH MAY NOT WORK FOR SOME CASES Approximations Simple and intuitive approach, which usually does not require changes to standard algorithms.

8. amount ofmedication patient weight Approximations Example: Selecting an amount of medication. Since small input changes translate intosmall output changes, we can use anapproximate weight value.

9. chance ofoverloading 155 LB 140 LB load weight Approximations Example: Loading an elevator. We can adapt this procedure to the useof approximate weights by subtracting asafety margin from the weight limit.

10. If your weight isexactly 150 lb,you are a winner! prize player weight Approximations Example: Playing the “exact weight” game. If we use approximate weight values, we cannot determine the chances of winning.

11. BUT… We may lose the accuracy of computation, and we cannot evaluate the probabilities of different possible values. Ranges or sets of possible values • Explicit representation of a margin of error • Moderate changes to standard algorithms

12. amount ofmedication patient weight Ranges or sets of possible values Example: Selecting an amount of medication. We obtain a range that includes the correctamount of medication. If the range width is within the acceptable margin of error, we can use it to select an appropriate amount.

13. chance ofoverloading load weight Ranges or sets of possible values Example: Loading an elevator. We identify the danger of overloading, but we cannot determine its probability.

14. prize player weight Ranges or sets of possible values Example: Playing the “exact weight” game. We still cannot determine the chances of winning.

15. BUT… • Major changes to standard algorithms • Major increase of the running time Probability distributions Accurate analysis of possible values and their probabilities.

16. Probability distributions Example: Playing the “exact weight” game. prize player weight We can determine possible outcomes and evaluate their probabilities.

17. probabilitydensity 140 150 160 weight RADAR / RAPID approach to uncertainty representation ranges or sets of values ranges or setswith probabilities probability distributions We approximate a probability density function by a set of uniform distributions, and represent it as a set of ranges with probabilities. Weight: 0.1 chance: [140..145] 0.8 chance: [145..155] 0.1 chance: [155..160]

18. Uncertain data • Nominal values An uncertain nominal value is a set of possible values and their probabilities. Phone location: 0.95 chance: purse 0.02 chance: home 0.02 chance: office 0.01 chance: car

19. Uncertain data • Nominal values • Integers and reals An uncertain numeric value is a probability-density function represented by a set of uniform distributions. Weight: 0.1 chance: [140..145] 0.8 chance: [145..155] 0.1 chance: [155..160] probabilitydensity 140 150 160 weight

20. Uncertain data • Nominal values • Integers and reals • Strings An uncertain string is a regularexpression with probabilities.

21. Uncertain data • Nominal values • Integers and reals • Strings • Spatial regions An uncertain region is a set of rectangular regions and their probabilities. y 0.8 0.1 0.1 x

22. 0.2 chance 0.8 chance or a set of possible functions and their probabilities. Uncertain data • Nominal values • Integers and reals • Strings • Spatial regions • Functions An uncertain function is apiecewise-linear function with uncertain y-coordinates amount ofmedication patient weight

23. Outline • Representation of uncertainty • Reasoning based on uncertain knowledge • Elicitation of missing data • Future research challenges

24. Arithmetic operations + - x ≤ ≠ ¬ • Logical operations • Function application μσ • Analysis of distributions Uncertainty arithmetic We have developed a library of basic operations on uncertain data, which input and output uncertain values.

25. BUT… • Approximate and relatively slow • Assumes that all probability distributions are independent Uncertainty arithmetic • Allows extension of standard algorithms to reasoning with uncertain values • Supports the control of the trade-off between the speed and accuracy

26. RADAR application Scheduling and resource allocation based on uncertain knowledge of scheduling constraints, preferences, and available resources. • Uncertain room and event properties • Uncertain resource availability and prices • Uncertain utility functions We use an optimization algorithm that searches for a schedule with the greatest expected quality.

27. Manual and auto scheduling Search time ScheduleQuality ScheduleQuality 0.83 0.83 0.80 0.78 0.72 Auto Auto Auto 0.63 Manual 0.9 Manual Manual 0.8 0.7 0.6 4 1 3 9 2 5 6 7 8 10 13 rooms 84 events 5 rooms 32 events 9 rooms 62 events Time (seconds) 13 rooms 84 events problem size RADAR results Scheduling of conference events. without uncertainty with uncertainty

28. RAPID application Analysis of military intelligence, which usually includes uncertain and partially inaccurate data. • Relational database with uncertain data • Retrieval of approximate and probabilistic matches for given queries • Automated inferences, verification of given hypotheses, and search for novel patterns

29. Outline • Representation of uncertainty • Reasoning based on uncertain knowledge • Elicitation of missing data • Future research challenges

30. Elicitation challenge • Identification of critical missing data • Analysis of the trade-off between the cost of data acquisition and the expected performance improvements • Planning of effective data collection

31. RADAR / RAPID approach to elicitation of additional data • For each candidate question, estimate the probabilities of possible answers • For each possible answer, compute its cost, as well as its impact on the utility of reasoning or optimization • For each question, compute its expected impact on the overall utility, and select questions with best expected impacts

32. RADAR / RAPID approach to elicitation of additional data Top-Level Control modelutility andlimitations ModelConst-ruction QuestionSelection ModelEvalu-ation currentmodel Reasoning orOptimization answers questions DataCollection

33. RADAR application Elicitation of additional data about scheduling constraints, preferences, and available resources. The system identifies critical missing knowledge, sends related questions to the user, and improves the world model based on the user’s answers.

34. Parser Optimizer Info elicitor Updateresourceallocation Chooseand sendquestions Graphicaluser interface User RADAR application Elicitation of additional data about scheduling constraints, preferences, and available resources. Top-level control and learning Processnew info

35. Initial schedule: Posters Talk RADAR example: Initial schedule Available rooms: 2 1 3 • Assumptions: • Invited talk: – Needs a projector • Poster session: – Small room is OK – Needs no projector • Requests: • Invited talk, 9–10am: Needs a large room • Poster session, 9–11am: Needs a room • Missing info: • Invited talk: – Projector need • Poster session: – Room size – Projector need

36. Useless info: There are no large rooms w/o a projector × Useless info: There are no unoccupied larger rooms × √ Potentially useful info RADAR example: Choice of questions Initial schedule: 2 1 Posters 3 Talk • Candidate questions: • Invited talk: Needs a projector? • Poster session:Needs a larger room? Needs a projector? • Requests: • Invited talk, 9–10am: Needs a large room • Poster session, 9–11am: Needs a room

37. Initial schedule: 2 1 Posters 3 Talk New schedule: 2 1 3 Talk RADAR example: Improved schedule • Requests: • Invited talk, 9–10am: Needs a large room • Poster session, 9–11am: Needs a room Info elicitation: System: Does the poster sessionneed a projector? Posters User:A projector may be useful,but not really necessary.

38. Dependency of the qualityon the number of questions Manual and auto repair ScheduleQuality ScheduleQuality 0.72 0.68 0.72 0.61 Auto withElicitation 0.50 Auto w/oElicitation ManualRepair After Crisis 0.68 10 30 40 50 20 Number of Questions RADAR results Repairing a conference schedule after a “crisis” loss of rooms.

39. RAPID application Proactive collection ofmilitary intelligence. • Identification of critical uncertainties, based on given tasks and priorities • Planning of intelligence collection, based on the analysis of cost/benefit trade-offs and related risks

40. Analyst GUI Goals, queries, andhypotheses Uncertaininferencerules RAPID application Proactive collection ofmilitary intelligence. Knowledgeentry andediting Prioritized plans for proactivedata collection Learnedinferencerules RAPID Inference Engine RAPID Proactive Planner Criticaluncertainties Inferredfacts Uncertainfacts Evaluation ofhypotheses Querymatches

41. Outline • Representation of uncertainty • Reasoning based on uncertain knowledge • Elicitation of missing data • Future research challenges

42. Future work • Learning of defaults and “common-sense” rules • Contingency reasoning • Theory of proactive learning

43. Example assumptions: • Almost all people weigh less than 500 lb • Tall people usually weigh more than short people • For people under eighteen years old, the expected weight increases with age Defaults assumptions Learning to make reasonable common-sense assumptions in the absence of specific data.

44. Defaults assumptions Learning to make reasonable common-sense assumptions in the absence of specific data. • Representation of general uncertain assumptions, context-based assumptions, and uncertain dependencies • Passive and active learning of these assumptions and dependencies • Unsupervised learning of relevant contexts

45. Contingency reasoning Analysis of possible futuredevelopments and preparationto likely developments. • Identification of critical uncertainties and their discretization into specific scenarios • Compact representation of scenario spaces • Construction of related contingency plans

46. Proactive learning General theory of the development andanalysis of related learning techniques. • Integration of learning with follow-up reasoning Top-Level Control Integration of learning algorithms with reasoning engines that use the learned knowledge. QuestionSelection ModelConst-ruction ModelEvalu-ation modelutility andlimitations currentmodel Reasoning orOptimization answers questions DataCollection

47. Proactive learning General theory for the development andanalysis of related learning techniques. • Integration of learning with follow-up reasoning Top-Level Control • Automated selection of learning examples QuestionSelection ModelConst-ruction ModelEvalu-ation modelutility andlimitations currentmodel Active selection of examples based on the trade-off among their cost, expected accuracy, and impact on the learned-knowledge utility. Reasoning orOptimization answers questions DataCollection

48. Proactive learning General theory for the development andanalysis of related learning techniques. • Integration of learning with follow-up reasoning Top-Level Control • Automated selection of learning examples QuestionSelection ModelConst-ruction ModelEvalu-ation modelutility andlimitations currentmodel • Automated selection of high-level strategies Reasoning orOptimization answers questions Intelligent choice and guidance of learning strategies, with the purpose to reduce the cost and time of learning. DataCollection

49. Proactive learning General theory for the development andanalysis of related learning techniques. • Integration of learning with follow-up reasoning Top-Level Control • Automated selection of learning examples QuestionSelection ModelConst-ruction ModelEvalu-ation modelutility andlimitations currentmodel • Automated selection of high-level strategies Reasoning orOptimization answers questions • Proactive analysis of future needs DataCollection Automated evaluation of future needs for the learned knowledge, and adaptation of the learning process to both expected and sudden changes in these needs.

50. Reasoning under Uncertainty