Coordinated Statistical Modeling and Optimization for Ensuring Data Integrity and Attack-Resiliency in Networked- Embedded Systems Farinaz Koushanfar, ECE Dept. Rice University Statistics Colloquium Oct 9, 2006

2 outline Sensor Networks: Applications, Challenges Coordinated Modeling-Optimization Framework –Inter-sensor models –Embedded sensing models –Optimization for data integrity Attack Resilient Location Discovery –Problem formulation and attack models –Robust random sample consensus for attack detection Sensor Networks: Applications, Challenges

3 Sensor Networks Comprehensive monitoring and analysis of complex physical environments Imagine… Flood in Houston Vibration in Abercrombie Texas wine!! Air pollution

4 Sensor Networks, How? Networks of embedded sensing (actuating) and computing devices Mica2Dot, CrossBow Tech. Courtesy of Prof. Estrin, CENS, ULCA

5 Challenges in Sensor Networks System: sensors, actuators, hardware, software, communication network layers, Limited: battery, bandwidth, cost Unique to sensor networks: Sensing –Abstract the system state, complex properties, and model physical phenomena accurately, without biases Parametric models: a priori assumptions Often do not capture the complex relationships –Optimization based on such models have a limited effectiveness

6 Challenges in Sensing Massive datasets –Structure response in USGS building: 72 channels of 24 bit data, 500 samples/sec. Energy consumption of the wireless nodes –Motes take 36mW in active mode  AA batteries + storage capacity of 1850mWh  50h active mode Diversity in applications –Marine biology, seismic sensing, battlefield, contaminant transport, home sensors, laboratories, hospitals, etc. Harsh environmental conditions –Battlefield, earthquakes, automatic detection, etc. Wireless channel data loss Sensor cost Sensitivity of applications Privacy and security

7 Inconsistencies in the Measured Sensor Data Erroneous measurements –Noisy readings: inevitable due to power and cost constraints and environmental impact –Systematic errors: offset bias, calibration effect, etc –Partially corrupted, still useful Faulty (corrupted) measurements –Remove faults to get a consistent picture –Can be accidental (e.g. bad link), or malicious Missing data –May be accidental, intentional (sleeping, subsampling, compression, filtering), or malicious

8 Outline Sensor Networks: Applications, Challenges Coordinated Modeling-Optimization Framework –Inter-sensor models –Embedded sensing models –Optimization for data integrity Attack Resilient Location Discovery –Problem formulation and attack models –Robust random sample consensus for attack detection Coordinated Modeling-Optimization Framework

9 Motivational Example Deployments show a gap b/w models and the reality Example: preliminary analysis of temperature sensor traces at UCLA BG 23 sensor nodes, sampling each 5 mins Question: does the locality assumption hold?

10 Motivational Example (Cont’d) No consistent relation b/w sensing and distance Discontinuities, exposure differences, global sources Also, some highly correlated close- by sensors Best previous effort: local basis functions Need new models for simultaneous abstraction of sensing and distance What about other properties?

11 Motivational Example (Cont’d) Separation of concerns Embedded sensing models: –Define multiple graphs G 1, G 2, …, G M, that share vertices E.g., sensing, distance –d ij : distance b/w s i,s j –e ij : sensing prediction error, for the model s j =f ij (s i ) The distance and sensing are not jammed into one model, but are being simultaneously considered

12 Motivational Example-2 Cross-domain optimization: Sensor deployment –Objective: select up to S candidate points for adding an extra sensor –For each s i, a TL sensor is Delaunay neighbor but cannot be predicted within  th error bound –Denote the edges of TL sensors as candidates –Find intelligent ways to select the best set of candidate points

13 Motivational Example (Cont’d) Coordinated modeling-optimization –Q1: How to do cross-domain optimization? –Q2: Can the models be of higher dimensions? –Q3: Can they help us to address data-integrity problem? –Q4: How effective are they?

14 Outline Sensor Networks, Applications, Challenges Coordinated Modeling-Optimization Framework –Inter-sensor models –Embedded sensing models –Optimization for data integrity Attack Resilient Location Discovery –Problem formulation and attack models –Robust random sample consensus for attack detection Inter-sensor models

15 Inter-sensor Models Intra-sensor models (autoregressive models) Have shown the effectiveness of adding shape constraints to univariate models –Isotonicity –Unimodularity –Number of level sets –Convexity –Bijection –Transitivity Combinatorial isotonic regression (CIR), finds the optimal nonparametric shape constrained univariate fit for an arbitrary error norm in average linear time Models are precursor for subsequent optimization

16 Application of CIR on Temperature Sensors at Intel Berkeley* Prediction error over all node pairs Limiting the number of level sets * Koushanfar, Taft (Intel), Potkonjak Infocom’06

17 Multivariate CIR Recent result*: –The first optimal, polynomial-time DP-based approach for multi-dimensional CIR: (1) Build the relative importance matrix R (2) Build the error matrix E (3) Build a cumulative error matrix C by using a nested DP (4) Starting at the minimum value in the last column of C, trace back a path to the first column that minimizes the cumulative error Thanks to Prof. D. Brillinger (UCB), Prof. M. Potkonjak (UCLA) for the useful discussions

18 Example

19 Multivariate CIR - complexity T sensor values drawn from a finite alphabet A Complexity of univariate case is dominated by sorting (T log T) C m (M): complexity of multivariate with M explanatory variables C m (M)=A M+1 C m (M-1), pseudo-polynomial complexity

20 Open Questions How to speed up the Multivariate CIR? –Pruning algorithms that exploit sparsity (?) Is it possible to make CIR locally adaptive? –In principle, finding the min error is a global optimization that cannot be locally addressed Can one guarantee convergence and correctness of CIR among sensors? Is it possible to have continuous approximations to address the problem? How can one build efficient models in presence of missing and/or faulty data?

21 Outline Sensor Networks, Applications, Challenges Coordinated Modeling-Optimization Framework –Inter-sensor models –Embedded sensing models –Optimization for data integrity Attack Resilient Location Discovery –Problem formulation and attack models –Robust random sample consensus for attack detection –Evaluation and comparison to competing methods Embedded sensing models

22 State-of-the-Art Sensing Models Parametric models –Gaussian random fields, graphical models (GM), message passing, iterative message passing, belief propagation (BP) Nonparametric models –Marginalized kernels (GM), alternating projections, distributed EM, nonparametric BP Common thread: capture dependence among sensor data, no edge means no dependence, Need to capture the shape of field discontinuities and/or lack of correlations b/w adjacent nodes

23 Embedded Sensing Models Principle of separation of concerns (SoC) Example: Geometric graph (planar-2D) Delaunay edges (adjacency) Sensing graph: higher dimensional embedded graph Idea: Map the sensing graph into lower dimensions. Exploit the discrepancy between the higher dimensional topology and the lower dimensional space to identify the obstacles

24 Open Questions Efficient computation and handling of embedded sensing models in higher dimensions Joint compression of multiple entities How can we capture dynamic topologies, i.e. mobility, dynamic time series, sleeping Efficient structures/data formats for representing the multi-dimensional topologies

25 Coordinated Modeling and Optimization Paramount importance of interface in system and software development Create statistical models suitable for optimization –Paradigms: continuous, smooth, consistent –Small number of level sets –Convexity –Bijection x' i = G(F(x i )) = x i, where y i =F(x i ) and x i =G(y i ) –Transitivity z i = F(x i ) = G(y i ) Create optimization mechanisms resilient to statistical variability –Paradigms: randomization –Multiple validations –Constructive probabilistic –Reweighting of OF and constraints

26 Outline Sensor Networks, Applications, Challenges Coordinated Modeling-Optimization Framework –Inter-sensor models –Embedded sensing models –Optimization for data integrity Attack Resilient Location Discovery –Problem formulation and attack models –Robust random sample consensus for attack detection –Evaluation and comparison to competing methods Optimization for data integrity

27 Data Integrity: Multiple Validations The data-integrity problems are complex due to the complex environments and uncertainties –Proof of NP-completeness (PhD’05) Data integrity (noise reduction, calibration, fault detection, data recovery) exploits system redundancies Coordinated modeling-optimization Multiple validations (MV) optimization algorithms –The solutions are validated using multiple input samples –Similar in spirit to cross-validation (CV) in statistics –MV is more comprehensive than CV, since it is a generic optimization paradigm based on resampling the input space and validating the output of a complex algorithm rather than a model

28 Example: Missing Data Between 40%-50% missing data at Intel Berkeley testbed Limited A2D: discrete level sets

29 Missing Data Recovery (MSD) Problem formulation: Given: –N sensors s 1, …,s N, –Sensor’s data at time t: (d 1 (t), d 2 (t),…,d N (t)) –Some sensor data missing in an arbitrary way, i.e. there is i, such that d i (t)=NA Objective: recover the missing data in such a way that the consistency between the readings of different sensors is maximized (prediction error is minimized)

30 State-of-the-Art in MSD MSD is a prevalent problem in many fields Expectation maximization (EM) Dempster et al.’77 –Assuming multivariate density –Local optimization, likely to be trapped in the local max of the likelihood function Multiple imputations (MI) Rubin 1987 –Missing data replaced by multiple simulated versions –May distort variable association dues to treating the completed dataset as the actual one Both MI/EM can be computationally intensive MV often combines lower dimensional models

31 MV for Missing Data Recovery Iteratively select a sub-sample of available nodes (the present set) and optimize for it Remaining nodes (holdout set) used for validating the solution, quantify its uncertainty –1) Randomly assign  :{1,…,|V|}  {1,…,K}; –2) for (  =1 to  =K) a: calculate OF -  (O); b: compute MVC -k (O); –3) MVC(O)=G(MVC -k (O)),  =1, …, K; –4) O best = argmin O MVC(O); Advantage: not only a solution, but an uncertainty bound for the solutions

32 Open Questions Theoretical proof of correctness of MV, which of the properties of CV holds for MV? Which MV criteria (MVC) are robust to outliers: e.g., order statistics Which objective function (OF) to use? –Ensemble-voting of weak classifiers by boosting (exponential loss function) Real-time implementation on sensor networks testbeds Scaling properties of the MV algorithm

33 Outline Sensor Networks, Applications, Challenges Coordinated Modeling-Optimization Framework –Inter-sensor models –Embedded sensing models –Optimization for data integrity Attack Resilient Location Discovery –Problem formulation and attack models –Robust random sample consensus for attack detection –Evaluation and comparison to competing methods Attack Resilient Location Discovery

34 Location Discovery* A number of nodes have location data (beacons) Other nodes estimate their distance to beacons to find their locations Many distance estimation methods (e.g., AoA, ToA) If more than three beacons, node can estimate location We focus on the atomic case (one unknown) s1s1 s7s7 s5s5 s 10 s0s0 s9s9 s6s6 s8s8 s4s4 s3s3 s2s2 * Joint work with N. Kiyavash, UIUC

35 Robust Location Discovery: Problem Formulation Instance: –A node s 0 with unknown coordinates (x 0,y 0 ), –Set L of location tuples {(x n,y n,d n )} (n beacons), –Consistency metric  (s n,s 0 ), consistency threshold t Problem: –Find an estimate for (x 0,y 0 ) s.t. it is at least  (s n,s 0 )-consistent with t points in set L

36 Attack Model The attackers can modify the distance measurement of any beacon without any limits The network is cryptographically protected against protocol attackes, e.g., wormhole, sybil The measurements from each beacon are only considered once Both independent and coalition (colluding) attacks In coalition attacks, the attacking beacons coordinate their efforts There is a minimum number of correct beacons, otherwise colluding beacons will mislead the target

37 Robust Random Sample Consensus 1.Initialize i; 2.While (i<i max ) a.Randomly draw a subset Si of size 3 from L; b.Use Si to estimate s ^ 0 ; c.Calculate K, the number of  consistent points w.r.t s ^ 0 in L\Si; d.If (K>t) i.{form a new s ^ 0 from the K points; Terminate;} e.Increment i; 3.Terminate and output the largest consistent estimate;

38 Selecting the parameters: i max,t q - prob. of correctness of a randomly drawn point Expected number of trials, E[i]=1/q 3  - threshold for the prob of missing a good subset, (1- q 3 ) imax =  Or, i max = ln(  ) / ln(1-q 3 ) I – set of inliers;  - percentage of inliers  =1-N a /N For large datasets q=  3, E[i]=  -9 The number of iterations is

39 Evaluation – Random Sample consensus N a /N|s ^ 0 -s 0 |FN % 10% % % % %

40 Comparison to Other Algorithms Independent attackers Colluding attackers

41 Summary sensor networks: importance of sensing, data integrity – missing data, faults, noise, systematic errors Coordinated modeling and optimization framework –Nonparametric models, shape constraints –Multivariate CIR, optimal algorithm, slow in multiple dimensions –Embedded sensing models, separation of concerns –Projection into lower dimensions –Optimization algorithm: multiple validations (MV) Attack-resilient location discovery –25% more effective in presence of coalition attackers, 35+% more effective on independent attackers