ICS280 Presentation by Suraj Nagasrinivasa

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ICS280 Presentationby Suraj Nagasrinivasa

• (1) Evaluating Probabilistic Queries over
  Imprecise Data (SIGMOD 2003)
• by R Cheng, D Kalashnikov, S Prabhakar
• (2) Model-Driven Data Acquisition in Sensor
  Networks (VLDB 2004)
• by A Deshpande, C Guestrin, J Hellerstein, W
  Hong, S Madden
• Acknowledgements Dmitri Kalashnikov and Michal
  Kapalka

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In typical sensor applications...

• Sensors monitor external environment continuously
• Sensor readings are sent back to the application
• Decisions are often made based on these readings

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However, we face uncertainty

• Typically, DB/server collects sensor readings
• DB cannot store true sensor value at all points
  in time
• Scarce battery power
• Limited network bandwidth
• So, readings recorded at discrete time points
• Value of phenomenon continuously changing
• As a result, DB stored reading is mostly obsolete

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Scenario Answering Minimum Query with discrete
DB stored readings
Recorded Temperature
Current Temperature
x1
y0

• x0 lt y0 x is minimum
• y1 lt x1 y is minimum
• Wrong query result

x0
y1
x
y
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Scenario Answering Minimum Query with
error-bound readings I
Recorded Temperature
Bound for Current Temperature
y0

• x certainly gives the minimum temperature reading

x0
x
y
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Scenario Answering Minimum Query with
error-bound readings II
Recorded Temperature
Bound for Current Temperature
y0

• Both x and y have a chance of yielding the
  minimum value
• Which one has a higher probability?

x0
x
y
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Probabilistic Queries

• Based on variation characteristics of sensor
  value over time
• Bounds can be estimated for possible values
• Probability distribution of values defined within
  bounds
• Evaluate probability for query answers
• Probabilistic queries give a correct answer,
  instead of a potentially incorrect answer

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Rest of the paper

• Notation Uncertainty Model
• Classification of Probabilistic Queries
• Evaluating Probabilistic Queries
• Quality of Probabilistic Queries
• Object Refreshment Policies
• Experimental Results

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Notation

• T A set of DB objects (e.g. sensors)
• a Dynamic attribute (e.g. pressure)
• Ti ith object of T
• Ti.a(t) Value of a in Ti at time t

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Uncertainty Model
fi(x,t) uncertainty pdf
Ti.a(t)
li(t)
ui(t)
Uncertainty Interval Ui(t)

• Can be extended in n dimensions

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Classification of Probabilistic Queries

• Type of Result
• Value-based returns single value
• E.g. Minimum query (l,u, pdf)
• Entity-based returns set of objects
• E.g. Range query ((Ti, pi), pigt0)
• Aggregation
• Non-Aggregate query result for an object is
  independent of other objects
• E.g. Range query
• Aggregate query result computed from set of
  objects
• E.g. Nearest Neighbor query

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Classification of Probabilistic Queries
Value-based answer Entity-based answer
Non-aggregate VSingleQ What is the temperature of sensor x? ERQ Which sensor has temperature between 10F and 30F?
Aggregate VAvgQ, VSumQ, VMinQ, VMaxQ What is the average temperature of the sensors? ENNQ, EMinQ, EMaxQ Which sensor gives the highest temperature?

• Query evaluation algorithms and quality metrics
  are developed for each class

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ENNQ algorithmProjection, Pruning, Bounding
Evaluation
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ENNQ algorithm
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Quality of Probabilistic Result

• Introduce a notion of quality of answer
• Proposed metrics for different classes of queries

• regular range query
• "yes" or "no" with 100
• probabilistic query ERQ
• yes with pi 95 OK
• yes with pi 5 OK (95 it is not in l, u)
• yes with pi 50 NOT OK (not certain!)

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Quality for Entity-Aggregate Queries

• "Which sensor, among n, has the minimum reading?"
• Recall
• Result set R (Ti, pi)
• e.g. (T1, 30), (T2, 40), (T3, 30)
• B is interval, bounding all possible values
• e.g. minimum is somewhere in B 10,20
• Our metrics for aggregate queries Min, Max, NN
• objects cannot be treated independently as in ERQ
  metric
• uniform distribution (in result set) is the worst
  case
• metrics are based on entropy

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Quality for Entity-Aggregate Queries

• H(X) entropy of random variable X (X1 ,,Xn with
  p(X1) ,, p(Xn))
• entropy is smallest (i.e., 0) iff ? i p(Xi) 1
• entropy is largest (i.e., log2(n)) iff all Xi's
  are equally likely

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Improving Answer Quality

• Is important to pick right update policies that
  will help improve answer quality
• Global Choice
• Glb_RR (pick random)
• Local Choice
• Loc_RR (pick random)
• MaxUnc (heuristic chooses max. uncertainty
  interval )
• MinExpEntropy (heuristic choose object with
  minimum expected entropy)

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Experiments Simulation Set-up

• 1 server, 1000 sensors, limited network
  bandwidth, Min queries tested
• Queries arrival is a Poisson distribution
• Each query over a random set of 100 sensors

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Results
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Conclusions

• Probabilistic Querying for handling inherent
  uncertainty in sensor DBs
• Classification, Algorithms and Quality of Answer
  metrics for various query types
• Very general model of uncertainty which makes the
  algorithms not directly implement-able in any
  sensor network
• Besides, in order to achieve any reasonable
  energy-efficiency in sensor networks, application
  and network requirements that dictate sensor
  nodes to be awake have to be tightly coordinated.
  Especially in the case of multi-hop routing

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Outline for Model Driven Data Acquisition for
Sensor Networks

• Introduction
• Motivation for Model-Based Queries
• Framework Concept
• Model Example Multivariate Gaussian
• Algorithm
• Resolving Model-Based Queries
• Incorporating Dynamicity
• Observation Plan / Cost model
• Experiments
• BBQ System
• Results
• Conclusions

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Motivation for Model-Based Queries

• Declarative Queries adopted as key programming
  paradigm for large sensor nets
• However, interpreting sensor nets as databases
  results in two major problems
• Misinterpretation of Data
• Physically observable world is a set of
  continuous phenomenon in both time and space
• Sensor readings are UNLIKELY to be random samples
• Inefficient approximate queries
• If sensor readings are not true values, need
  for quantifying uncertainty to provide reliable
  answers

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Motivation for Model-Based Queries

• Paper Contribution To incorporate statistical
  models of real-world processes into sensor net
  query processing architecture
• Models help in
• Accounting for biases in spatial sampling
• Identifying sensors providing faulty data
• Extrapolating values for missing sensors

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Framework Concept

• Goal Given a query and model, to devise an
  efficient data acquisition plan to provide best
  possible answer
• Major dependencies
• Correlations between sensors captured by the
  statistical model
• Correlation between attributes for given sensor
• Correlation between sensors for given attribute
• Specific connectivity of the wireless network

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Framework ConceptObservation Plan parameters
Correlations in Value Cost Differential
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Framework Concept
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Model Example Multivariate Gaussian
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Resolving Model-Based Queries (Range Queries)
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Resolving Model-Based Queries(Value Queries)

• To compute value of Xi with maximum error e and
  confidence 1-delta
• Compute mean of Xi (where o observations)
• As in range queries, find probability

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Range Queries for Gaussian

• Projection for Gaussian is simple just drop
  unnecessary values from mean and variance matrix
• The integral
• has to be computed.

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Incorporating Dynamicity

• Use historical measurements to improve confidence
  of answers
• Given pdf in time t
• Compute pdf at time t1

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Incorporating Dynamicity

• Assumption Markovian Model
• Dynamicity summarized by transition model

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Observation Plan / Cost Model

• What is the cost of making o observations?
• C(o) acquisition cost transmission cost
• Acquisition cost constant for each attribute
• Transmission cost
• Network graph
• Edge weights (link quality)
• Paths taken could be sub-optimal

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Observation Plan / Cost Model

• A set of attributes (theta) to observe are
  determined by computing expected benefit
• And finding
• This, being similar to the traveling salesmans
  problem, is best dealt with heuristic algorithms

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BBQ System

• BBQ A Tiny-Model Query System
• Uses Multivariate Gaussians
• Has 24 transition models for different hour of
  day

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Results

• Experiment 11 sensors on a tree, 83000
  measurements, 2/3 used for training and 1/3 for
  tests
• Methodology
• BBQ builds a model based on training data
• One random query / hour taken possible
  observations and model is updated
• The answer is compared to the measured value
• Compare with two other methods
• TinyDB Each query broadcasted over sensor
  networks using an overlay tree
• Approximate-Caching Base station maintains a
  view of the sensor readings

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Results
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Results
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Conclusion

• Approximate queries can be well optimized, but
  model of physical phenomenon is needed
• Defining an appropriate model is a challenge
• The framework works well for fairly steady
  sensor data values
• Statistical model is largely static with
  refinements to the model based on incoming
  queries and observations made as a result