ModelDriven Data Acquisition in Sensor Networks

1
Model-Driven Data Acquisition in Sensor Networks

• Amol Deshpande, Carlos Guestrin, Samuel R.
  Madden, Joseph M. Hellerstein, Wei Hong

Accepted by VLDB 2004
Presented by Chih-Chieh Hung 2004.9.29
2
Outline

• Introduction
• Overview of Approach
• Model-based Querying
• Choosing an observation plan
• Conclusion

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Introduction

• The metaphor that the sensornet is a database
  is problematic, because sensors dont
  exhaustively represent the data in the real
  world.
• In this paper, a probabilistic model of that
  reality is used to complement the readings.

4
Outline

• Introduction
• Overview of Approach
• Model-based Querying
• Choosing an observation plan
• Conclusion

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Architecture of Model-based Querying

• Using probability density function (pdf), p(X1,,
  Xn) to answer query, Xi where represents an
  attribute at a sensor.
• The model is used to estimate sensor readings in
  the current time period.
• The updating reading will help to refine
  estimates for which uncertainty is high.
• In BBQ, the specific model is based on
  time-varying multivariate Gaussians.

6
Architecture of Model-based Querying
1-d
e
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The reason of choosing different attributes in
observation plan

• Correlation in Value
• Cost Differential
• ex cost(read_volt) lt cost(read_temp)

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Support Queries

• Answering queries probabilistically based on a
  distribution is conceptually straightward.
• Using the pdf to compute the probability that Xi
  is within e from the mean,
  .
• Mean
• Choosing the reading to observe is an
  optimization problem. (NP-hard Problem)

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Outline

• Introduction
• Overview of Approach
• Model-based Querying
• Choosing an observation plan
• Conclusion

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Model-based querying

• Central element is the use of a probabilistic
  model to answer queries about the attributes in a
  sensornet.
• This section focuses on specific queries
• Range Predicates
• Attribute-value Estimates
• Standard Aggregate
• A probability density function(pdf) assigns a
  probability for each joint value x1, x2,, xn for
  the attributes X1, X2,, Xn.

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Probabilistic Queries Range Queries

• Range Queries
• ask if an attribute Xi is in the range ai, bi
  
• Probabilistic Model
• compute

YES
NO
NEED MORE DATA
100
0
1-d
d
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Probabilistic Queries Range Queries

• Two step to compute
• Step 1
• Marginalize the pdf to a density over only Xi
• Step 2
• Test if or
• for given confidence d

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Probabilistic Queries Range Queries

• Suppose that we observe the value of attribute Xj
  to be xj, we can obtain the conditional pdf
• We can then compute
• In general, we will make a set of observation o
  and obtain , the posterior
  probability of our set of attributes X given o.

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Probabilistic Queries Value Queries

• A user is interesting in the value of Xi, we can
  answer this query by the mean value of Xi, given
  the observations o
• Confidence
• for a given error bound egt0

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Probabilistic Queries AVERAGE aggregates

• We are interested in the average value of a set
  of attribute A.
• Define a random variable Y to present this
  average by
• The pdf of Y

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Dynamic Models

• The single static probability density function
  represents spatial correlation in sensornet
  deployment.
• However, many real-world system include
  attributes that evolve temporal and spatial
  correlations.
• A dynamic probabilistic model can represent
  temporal correlations.

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Dynamic Models (contd)

• Goal compute
• For simplicity, the model restrict to Markovian
  model.
• Markovian model

t
t-1
t-2
1
time

Independent to attributes in t
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Dynamic Models (contd)

• By the assumption, the dynamics are summarized by
  a pdf called the transition model
• Using this transition model, we can compute

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Outline

• Introduction
• Overview of Approach
• Model-based Querying
• Choosing an observation plan
• Conclusion

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Choosing an Observation Plan

• Cost of Observations
• Improvement in Confidence
• Optimization

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Cost of observations

• A set of observation
• Expected cost

Data transmission cost
The cost of observing attribute Xi
Acquisition cost
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Data Transmission Cost

• Transmission cost is dependent on the data
  collection mechanism and network topology.
• For simplicity
• Then the whole problem can be seen as TSP with
  weighted 1/ PijPji

j
i
Pij
j
i
Pji
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Improvement in Confidence

• Observation attributes O should improve the
  confidence of our posterior density.
• If we observe the specific value o, the benefit
  are
• Range Query
• Value and Average Query
• Expected Benefit

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Optimization

• We would like to pick the set of attribute O that
  meet the confidence 1-d at a minimum cost
• However, its a NP-hard problem.

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Solving the Optimization Problem

• Burst Force
• Need Exponential Time
• Greedy Incremental Heuristic
• O ? F
• At each iteration, for each Xi ,
• compute
• If
• then pick the lowest and return
  
• else

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Outline

• Introduction
• Overview of Approach
• Model-based Querying
• Choosing an observation plan
• Conclusion