Copyright ©2004 Carlos Guestrin guestrin VLDB 2004 Efficient Data Acquisition in Sensor Networks...

Copyright ©2004 Carlos Guestrin www.cs.cmu.edu/~guestrin VLDB 2004

Efficient Data Acquisition in Sensor

Networks

Presented ByKedar Bellare

(Slides adapted from Carlos Guestrin)


Papers A. Deshpande, C. Guestrin, S. Madden, J.

Hellerstein, W.Hong. "Model-Driven Data Acquisition in Sensor Networks," In the 30th International Conference on Very Large Data Bases (VLDB 2004), Toronto, Canada, August 2004.

A. Deshpande, C. Guestrin, W. Hong, S. Madden. "Exploiting Correlated Attributes in Acquisitional Query Processing" In the 21st International Conference on Data Engineering (ICDE 2005), Tokyo, Japan, April 2005.

http://www-2.cs.cmu.edu/%7Eguestrin/Publications/VLDB04/vldb04.pdf

http://www-2.cs.cmu.edu/%7Eguestrin/Publications/VLDB04/vldb04.pdf

http://www-2.cs.cmu.edu/%7Eguestrin/Publications/ICDE05/icde05.pdf




Model-driven Data Acquisition in Sensor

Networks

Amol Deshpande1,4 Carlos Guestrin4,2 Sam Madden4,3

Joe Hellerstein1,4 Wei Hong4

1UC Berkeley 2Carnegie Mellon University 3MIT 4Intel Research - Berkeley


Every time step

Analogy:Sensor net as a database

TinyDBQuery

Distributequery

Collectquery answer

or data

SQL-stylequery

Declarative interface: Sensor nets are not just for PhDs Decrease deployment time

Data aggregation: Can reduce communication


Every time step

Limitations of existing approach

TinyDBQuery

Distributequery

Collectdata

New QuerySQL-style

query

Redoprocesseverytimequery

changes

Query distribution: Every node must receive query (even when approximate answer needed)

Data collection: Every node must wake up at every time step Data loss ignored No quality guarantees Data inefficient – ignoring correlations


Sensor net data is correlated

Spatial-temporal correlation

Inter-attributed correlation

Data is not i.i.d. shouldn’t ignore missing data

Observing one sensor information about other sensors (and future values)

Observing one attribute information about other attributes


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t

SQL-style query

with desired confidence

Model-driven data acquisition: overview

Probabilistic Model

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Query

Data gathering

plan

Conditionon new

observations

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New Query

posterior belief

Strengths of model-based data acquisition Observe fewer attributes Exploit correlations Reuse information between queries Directly deal with missing data Answer more complex (probabilistic) queries


Benefits of Statistical Models

More robust interpretation of sensor net readings Account for biases in spatial sampling Identify faulty sensors Extrapolate missing values of sensors

More efficient data acquisition Lesser number of attributes to observe Reuse of information between queries Exploit correlations – acquire data when model not able

to answer query with acceptable confidence More complex queries

Probabilistic queries


Issues introduced by Models

Optimization problem Given query and model, choose data acquisition

plan to best refine answer Two dependencies – statistical benefit of

acquiring reading AND system costs Any non-trivial statistical model can capture

first dependency Improving model-driven estimates for nearby

nodes Connectivity of wireless sensnet affects

second dependency


Probabilistic models and queries

User’s perspective:QuerySELECT nodeId, temp ± 0.5°C, conf(.95) FROM sensorsWHERE nodeId in {1..8}

System selects and observes subset of nodesObserved nodes: {3,6,8}

Query result

Node 1 2 3 4 5 6 7 8

Temp. 17.3

18.1 17.4 16.1 19.2 21.3 17.5 16.3

Conf. 98%

95% 100% 99% 95% 100% 98% 100%


Probabilistic models - Illustration

Node 0 – Interfacebetween user and sensor net

No need to query entire network

Model chooses to observevoltage even though queryis temperature


Probabilistic models (Contd.)

Why did model choose to observe voltage instead of temperature?

Correlation in Value

Cost differential


Probabilistic models and queries

Joint distribution P(X1,…,Xn)

Probabilistic queryExample:

Value of X2± with prob. > 1- Prob. below 1-?

Observe attributes

Example: Observe X1=18

P(X2|X1=18)

Higher prob.,could answer query

Learn from historical data


Dynamic models: filteringJoint distribution

at time t Condition onobservations

t

Fewer obs. infuture queries

Example: Kalman filter Learn from historical data


Kalman Filtering Transition model maintained for each hour of

the day – mod(t,24)

Evolution of system over time from to

Compute using simple marginalization

Next obtain posterior distribution for observations including that at (t+1)

)|,,( 11

ttn

t oXXp )|,,( 111

1tt

nt oXXp

),,|,,( 111

1tn

ttn

t XXXXp

tn

tttn

ttn

ttn

tttn

t dxdxoXXpXXXXpoXXp 1

111

111

1111 )|,,(),,|,,()|,,(


Kalman Filtering (Contd.) Transition model is learned by first computing

joint density

Then use conditioning rule to compute the transition model

),,,,,( 111

1tn

ttn

t XXXXp


Supported queries Value query

Xi ± with prob. at least 1-

SELECT and Range query Xi[a,b] with prob. at least 1- which sensors have temperature greater than 25°C ?

Aggregation average ± of subset of attribs. with prob. > 1- combine aggregation and selection probability > 10 sensors have temperature greater than

25°C ? Queries require solution to integrals

Many queries computed in closed-form Some require numerical integration/sampling


Probabilistic queries Range queries –

First marginalize multivariate gaussian – Done by dropping entries being marginalized

Compute confidence of query using error function If confidence is less, make observation to improve

confidence Conditioning a gaussian on value of some attributes

gives another gaussian

),( iii baXP

oYYoY1

|

YYYYoYY 1

||


Probabilistic queries (Contd.)

Value Query

Easy to estimate Also determine confidence interval for given error

bound and observe attributes if needed Posterior mean can be obtained directly from mean

vector conditioned on observed o

iiii dxoxpxx )|(_


Probabilistic queries (Contd.)

Average aggregates If we are interested in average over attributes A Define random variable The pdf of Y is given by:

where 1[:] is the indicator function Once P(Y=y|o) is defined simply define a value query for

random variable Y Other complex aggregate queries can be similarly answered

by constructing new random variables PDF of sum of gaussians is a gaussian where:

expected mean is the mean of expected values variance is weighted sum of variances Xi plus covariances of

Xi and Xj

nAi

in dxdxyAxoxxpoyYp 11 /1)|,,()|(

AXYAi

i /


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SQL-style query


Model-driven data acquisition: overview

Probabilistic Model

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Query

Data gathering

plan

Conditionon new

observations

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posterior beliefWhat sensors do we observe ?How do we collect observations?


Acquisition costs Attributes have

different acquisition costs

Exploit correlation through probabilistic model

Must consider networking cost1

2

63

4 5

cheaper?


Network model and plan format

Assume known (quasi-static) network topology Define traversal using (1.5-approximate) TSP Ct(S ) is expected cost of TSP (lossy communication)

12

63

4 5

7 8

129

10 11

Cost of collecting subset S of sensor values:

C(S )= Ca(S )+ Ct(S )

Goal:Find subset S that is sufficient to answer query at minimum cost C(S )


Choosing observation plan

Is a subset S sufficient? Xi2[a,b] with prob. > 1-

If we observe S =s :Ri(s ) = max{ P(Xi2[a,b] | s ), 1-P(Xi2[a,b] | s )}

Value of S is unknown:Ri(S ) = P(s ) Ri(s ) dsOptimization problem:


Observation Plan General optimization problem is NP-hard Two algorithms

Exhaustive search – exponential Greedy search

Begin with empty observation plan Compute benefit R and cost C for added attribute If confidence reached, choose attribute with minimum

cost Else add the attribute which has maximum

benefit/cost ratio Repeat until you reach desired confidence


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SQL-style query


BBQ system

Probabilistic Model

10 20 300

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Query

Data gathering

plan

Conditionon new

observations

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posterior belief

ValueRangeAverage

Multivariate GaussiansLearn from historical data

Equivalent to Kalman filterSimple matrix operations

Simple matrix operations

Exhaustive or greedy searchFactor 1.5 TSP approximation


Exploiting correlated attributes

Extension of single plan to conditional plan Useful when cost of acquisition non-negligible Correlations exist between one or more attributes

Queries of the form multi-predicate range queries

Query evaluation can become cheaper by observing additional attributes

If additional attributes are low-cost Reject tuple with high confidence without

expensive acquisition – substantial performance gains


Conditional Plans


Conditional Plans (Contd.) Simple binary decision trees Each interior node n_j specifies binary

conditioning predicate (depends on only single attribute value)

Choose conditional plan with minimum expected cost


Cost of Conditional Plans Optimal plan

Traversal cost

Expected plan cost


Issues in Conditional Plans

Need to estimate P(Tj|t) Naïve method is to scan historical data for each

computation – expensive Cost model

Only acquisition cost taken into account Transmission cost Size of plan to fit in RAM Add into the cost model

Authors only focus on limiting plan sizes


Architecture


Optimal Conditional Plan Problem is hard

Even if we are given conditional probabilities (by oracle) complexity is #P-hard – reduction from 3-SAT

Even if we try to optimize our plan with respect to set of d tuples D problem is NP-complete – reduction from complexity of binary decision trees

Exhaustive search Depth first search With caching and Pruning

Also heuristic solutions using greedy


SERVER

LAB

KITCHEN

COPYELEC

PHONEQUIET

STORAGE

CONFERENCE

OFFICEOFFICE

Example: Intel Berkeley Lab deployment

SERVER

LAB

KITCHEN

COPYELEC

PHONEQUIET

STORAGE

CONFERENCE

OFFICEOFFICE50

51

52 53

54

46

48

49

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42 41

3739

38 36

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3

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1516

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2021

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242526283032

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3540


Experimental results

Redwood trees and Intel Lab datasets Learned models from data

Static model Dynamic model – Kalman filter, time-indexed

transition probabilities Evaluated on a wide range of queries

SERVER

LAB

KITCHEN

COPYELEC

PHONEQUIET

STORAGE

CONFERENCE

OFFICEOFFICE50

51

52 53

54

46

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Cost versus Confidence level


Obtaining approximate values

Query: True temperature value ± epsilon with confidence 95%


Approximate range queries

Query: Temperature in [T1,T2] with confidence 95%


Comparison to other methods


Intel Lab traversals


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SQL-style query


BBQ system

Probabilistic Model

10 20 300

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Query

Data gathering

plan

Conditionon new

observations

10 20 300

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posterior belief

ValueRangeAverage

Multivariate GaussiansLearn from historical data

Equivalent to Kalman filterSimple matrix operations

Simple matrix operations

Exhaustive or greedy searchFactor 1.5 TSP approximationExtensions

More complex queries Other probabilistic models More advanced planning Outlier detection Dynamic networks Continuous queries …


Conclusions Model-driven data acquisition

Observe fewer attributes Exploit correlations Reuse information between queries Directly deal with missing data Answer more complex (probabilistic)

queries

Basis for future sensor network systems


Discussion Questions What other models apart from multivariate

gaussian can be used? If other models are used will their solution be in closed form?

Model-driven techniques are suitable only if test data is same as training data. Will solution be adaptable if test region is different from training region?

Optimization problem is hard and expensive to compute even with heuristics. Will it work for real-time data analysis?

Outlier detection is not supported for model-driven acquisition. Is there any way to do it for model-based sensor networks?

If in general your needed confidence on the query is low then some nodes may not be queried at all?

Copyright ©2004 Carlos Guestrin guestrin VLDB 2004 Efficient Data Acquisition in Sensor Networks...

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