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Eiman Elnahrawy WSNA’03 Cleaning and Querying Noisy Sensors Eiman Elnahrawy and Badri Nath Rutgers University WSNA September 2003 This work was supported in part by NSF grant ANI-0240383 and DARPA under contract number N-666001-00-1-8953

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Eiman Elnahrawy WSNA’03 I can’t rely on this sensor data anymore. It has too many problems!!? -N-Noise -B-Bias -M-Missing information -Hmm, is this a malicious sensor -Something strange or sensor gone bad

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Outline Motivation General Framework Cleaning Noise Querying Noisy Sensors Statistically Preliminary Evaluations Challenges and Future Work Conclusion

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Eiman Elnahrawy WSNA’03 Motivation “Measurements” subject to many sources of error Systematic errors->Bias (Calibration) [Bychkovskiy03] Random errors (Noise) : external, uncontrollable environmental, HW, inaccuracies/imprecision Current technology: cheap noisy sensors, vary in tolerance, precision/accuracy Focus of industry is even cheaper sensors -> noisier, noise varies with the cost of the sensor

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Eiman Elnahrawy WSNA’03 So What? Uncertainty Interest is generally queries over a set of noisy sensors –Predicate/ range queries –Aggregates SUM, MIN –Other Accumulation: seriously affects decision-making/triggers False +ve/-ve Misleading answers May cost you money h t

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Eiman Elnahrawy WSNA’03 Problem Definition Research focused on homogeneous sensors, in-network aggregation, query languages, optimization The primitives are now working fairly fine, why don’t we move on to more complex data quality problems If the collected data/query result is erroneous/misleading, why would we need such nets? Given any query and some user-defined confidence metrics, how do we answer this query “efficiently” given noisy sensors? What is the effect of noise on queries?

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Eiman Elnahrawy WSNA’03 Is this a new problem? Traditional databases –Data entry, transactional activity –Clean data: no noise –Supervised off-line cleaning Sensors –Stream –Decision-making in real time –Online cleaning and query processing –Many resource constraints

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Eiman Elnahrawy WSNA’03 General Framework Two Steps Online cleaning –Inputs: noisy data + error models + prior knowledge –Output: uncertainty models (clean data) Queries evaluated on clean data (uncertainty models) Cleaning Module Query Processing Module Uncertainty Models (Posteriors) Query Answer Noisy Observations from Sensors Error Models Prior Knowledge User Query

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Eiman Elnahrawy WSNA’03 Observation: noisy reading from the sensor Prior Knowledge: r.v., distribution of the true reading –Facts, learning, using less noisy as priors for noisier, experts, dynamic (parametric model) Error Model: r.v., noise characteristic –Any appropriate distribution, e.g., Gaussian –Heterogeneity -> model for each type or even each individual sensor Uncertainty Model (true unknown): r.v., with a distribution, we would like to estimate Cleaning Module Noisy Observations from Sensors Error Models Prior Knowledge Uncertainty Models (Posteriors)

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Eiman Elnahrawy WSNA’03 Cleaning Single Sensor Fusion using Bayes’ rule Posterior = (likelihood x prior) / (evidence) Single attribute sensors Example: Gaussian prior ( μ s, σ 2 s ), Gaussian error ( 0,δ 2 ) yield Gaussian posterior (uncertainty model)

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Eiman Elnahrawy WSNA’03 Cleaning Multi-attributes sensors Example: Gaussian prior ( μ s, Σ s ), Gaussian error ( 0, Σ 2 ) yield Gaussian posterior (uncertainty model) The terms Σ s [Σ s + Σ] -1, Σ T will be computed off-line

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Eiman Elnahrawy WSNA’03 Classification of Queries –What is the reading(s) of sensor x ? Single Source Queries (SSQ) –Which sensors have at least c% chance of satisfying a given predicate? Set Non-Aggregate Queries (SNAQ) –On those sensors which have at least c% chance of satisfying a given predicate, what is the value of a given aggregate? Summary Aggregate Queries (SUM, AVG, COUNT) SAQ Exemplary Aggregate Queries (MIN, MAX, etc.) EAQ Query Processing Module Uncertainty Models (Posteriors) Query Answer User Query

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Eiman Elnahrawy WSNA’03 Single Source Queries Approach 1: output expected value of the probability distribution Approach 2: output p% confidence interval using Chebychev’s inequality [μ s - ε, μ s + ε] –“p” is user-defined with a default value, e.g., 95% Multi-attribute: first compute the marginal pdf of each attribute then proceed as above

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Eiman Elnahrawy WSNA’03 Set Non-Aggregate Queries Output sensor id, confidence ( p i ) Confidence = probability of satisfying the given predicate (range R ) >= user defined confidence p i = ∫ R p si (t) dt {s i } = S R, eligible set If the readings are required compute it using the SSQ’s algorithms Multi-attribute: compute S R over a region rather than a single interval

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Eiman Elnahrawy WSNA’03 Summary Aggregate Queries SUM: compute sum of independent continuous r.vs. Z = sum(s 1, s 2,…, s m ) Perform convolution on two sensors and then add one sensor repeatedly from the eligible set ( S R ) Output expected value or p% confidence interval of overall sum

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Eiman Elnahrawy WSNA’03 Summary Aggregate Queries COUNT: output |S R | over the given predicate AVG: output SUM/COUNT Multi-attribute: compute S R, marginalize over the aggregated attribute, then proceed as above

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Eiman Elnahrawy WSNA’03 Exemplary Aggregate Queries Min: compute min of independent continuous r.vs. Z = min(s 1, s 2,…, s m ) Output expected value or p% confidence interval Other order statistics Max, Top-K, Min-K, and median in a similar manner Multi-attribute: analogous

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Eiman Elnahrawy WSNA’03 Tradeoffs “Sensors” Vs. “Database” Sensor Level –Storage cost –Communication cost “sending priors” –Processing cost “compute posteriors” –Adv: point estimate, in-network aggregation with error bounds Database Level –0 cost assuming free processing, storage –Communication cost saved –Exact query answer –Disadv: no distributed query processing

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Eiman Elnahrawy WSNA’03 Evaluations Synthetic data “Unknown” true readings –1000 sensors, random from 5 clusters –Gaussian, μ = 1000, 2000, 3000, 4000, 5000, δ 2 = 100 Noisy data (Raw data) –Added random noise, Gaussian, μ = 0, different noise levels Posteriors (Bayesian data) –Prior: distribution of the cluster generated the reading Predicates: 500 random range queries at each noise level, averaged the error

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Eiman Elnahrawy WSNA’03 Single source queries –Metric is MSE –Reduces uncertainty, yields far less errors –Error scaled down by a factor of δ p 2 /(δ p 2 + δ n 2)

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Eiman Elnahrawy WSNA’03 Set non-aggregate queries: prior δ = 10 –Metrics are Precision and Recall –Recall: fraction of relevant objects that are retrieved –Precision: fraction of retrieved objects that are relevant –High Recall, Precision (low false –ve, +ve, res.) better –Maintained high Recall, Precision at different confidence levels –95 % versus 70 % for noisy readings

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Eiman Elnahrawy WSNA’03 Summary aggregate queries: prior δ = 10 –Metric is Absolute error –More accurate priors yield smaller error –SUM: noisy readings caused four times the error –COUNT: 2 versus 14 for noisy data

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Eiman Elnahrawy WSNA’03 Challenges and Future Work Prototype and more evaluations on real data Just scratched the surface! –Other estimation techniques –Other uncertainty problems: outliers, missing data, etc. –Other queries –Effect of noise on queries “Efficient” distributed query processing

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Eiman Elnahrawy WSNA’03 Challenges and Future Work Given a query and specific quality requirements (confidence, number of false +/-) what to do if can’t satisfy confidence? –Sensors are not homogeneous –Change sampling method at running time –Turn on “specific” sensors at running time –Routing –Up-to-date metadata about sensors’ resources/characteristics –Cost and query optimization

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Eiman Elnahrawy WSNA’03 Conclusion Taking noise into consideration is important Single sensor fusion Statistical queries Works well Many open problems and future work directions

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Eiman Elnahrawy WSNA’03 Thank You

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