Reasoning under Uncertainty

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Reasoning under Uncertainty
Eugene Fink LTI SeminarNovember 16, 2007
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Challenges
The available knowledgeabout the real world
isinherently uncertain.
We usually make decisionsbased on incomplete and
partially inaccurate data.
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Challenges

• Representation of uncertainty

• Fast reasoning based on uncertain knowledge

• Elicitation of criticaladditional data

• Learning of reasonabledefault assumptions

• Contingency reasoning

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Projects
RADAR / Space-Time (20032008)
Reflective Agent with DistributedAdaptive
Reasoning
Scheduling and resource allocation under
uncertainty.
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Outline

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

Representation of uncertainty
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Alternative representations

• Approximations
• Marys weight is about 150. Marys cell
  phone is probably in her purse.

• Ranges or sets of possible values
• Marys weight is between 140 and 160.
  Marys cell phone may be in her purse,
  office, home, or car.

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Approximations
Simple and intuitive approach, which usually does
not require changes to standard algorithms.
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Approximations
Example Selecting an amount of medication.
Since small input changes translate intosmall
output changes, we can use anapproximate weight
value.
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Approximations
Example Loading an elevator.
We can adapt this procedure to the useof
approximate weights by subtracting asafety
margin from the weight limit.
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Approximations
Example Playing the exact weight game.
If we use approximate weight values, we cannot
determine the chances of winning.
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Ranges or sets of possible values

• Explicit representation of a margin of error
• Moderate changes to standard algorithms

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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.
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Ranges or sets of possible values
Example Loading an elevator.
We identify the danger of overloading, but we
cannot determine its probability.
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Ranges or sets of possible values
Example Playing the exact weight game.
We still cannot determine the chances of winning.
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Probability distributions
Accurate analysis of possible values and their
probabilities.
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Probability distributions
Example Playing the exact weight game.
prize
player weight
We can determine possible outcomes and evaluate
their probabilities.
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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
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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
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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
160
150
weight
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Uncertain data

• Nominal values
• Integers and reals
• Strings

An uncertain string is a regularexpression with
probabilities.
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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
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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
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Outline

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

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Uncertainty arithmetic
We have developed a library of basic operations
on uncertain data, which input and output
uncertain values.
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Uncertainty arithmetic

• Allows extension of standard algorithms to
  reasoning with uncertain values
• Supports the control of the trade-off between
  the speed and accuracy

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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.
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RADAR results
Scheduling of conference events.
without uncertainty
with uncertainty
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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

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Outline

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

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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

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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

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RADAR / RAPID approach to elicitation of
additional data
Top-Level Control
modelutility andlimitations
ModelConst-ruction
ModelEvalu-ation
QuestionSelection
currentmodel
Reasoning orOptimization
questions
answers
DataCollection
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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 users
answers.
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RADAR application
Elicitation of additional data about scheduling
constraints, preferences, and available
resources.
Top-level control and learning
Processnew info
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RADAR example Initial schedule
Available rooms
2
Roomnum. Area(feet2) Proj-ector
123 2,0001,0001,000 YesNoYes
1
3

• Missing info
• Invited talk Projector need
• Poster session Room size Projector
  need

• Assumptions
• Invited talk Needs a projector
• Poster session Small room is OK
  Needs no projector

• Requests
• Invited talk, 910am Needs a large room
• Poster session, 911am Needs a room

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RADAR example Choice of questions
Initial schedule
2
1
Posters
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Talk

• Candidate questions
• Invited talk Needs a projector?
• Poster session Needs a larger room? Needs
  a projector?

• Requests
• Invited talk, 910am Needs a large room
• Poster session, 911am Needs a room

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RADAR example Improved schedule

• Requests
• Invited talk, 910am Needs a large room
• Poster session, 911am Needs a room

Info elicitation
System Does the poster sessionneed a projector?
Posters
UserA projector may be useful,but not really
necessary.
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RADAR results
Repairing a conference schedule after a crisis
loss of rooms.
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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

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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
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Outline

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

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Future work

• Learning of defaults and common-sense rules
• Contingency reasoning
• Theory of proactive learning

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Defaults assumptions
Learning to make reasonable common-sense
assumptions in the absence of specific data.
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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

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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

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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.
ModelConst-ruction
ModelEvalu-ation
QuestionSelection
modelutility andlimitations
currentmodel
Reasoning orOptimization
questions
answers
DataCollection
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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

ModelConst-ruction
ModelEvalu-ation
QuestionSelection
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
questions
answers
DataCollection
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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

ModelConst-ruction
ModelEvalu-ation
QuestionSelection
modelutility andlimitations
currentmodel

• Automated selection of high-level strategies

Reasoning orOptimization
questions
answers
Intelligent choice and guidance of learning
strategies, with the purpose to reduce the cost
and time of learning.
DataCollection
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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

ModelConst-ruction
ModelEvalu-ation
QuestionSelection
modelutility andlimitations
currentmodel

• Automated selection of high-level strategies

Reasoning orOptimization
questions
answers

• 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.
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Reasoning under
Uncertainty