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Pramod K. VarshneyDistinguished Professor, EECS
Director of CASE: Center for Advanced Systems and Engineering
Syracuse University
E-mail: [email protected]
Distributed Inference in the Presence of
Byzantines
in collaboration with
K. Agrawal, P. Anand, A. RawatB. Kailkhura, V. S. S. Nadendla, A. Vempaty
S. K. Brahma , H. Chen , Y. S. Han, O. Ozdemir.
2
Signal Processing, Communications & Control
@ EECS Department, Syr. Univ.
Biao Chen
Makan Fardad
Yingbin Liang
Jian Tang
Mustafa Cenk Gursoy
Senem VelipasalarWenliang Du
Pramod K. Varshney
Sensor Fusion Lab
Distributed InferenceDetection, Estimation, Classification, TrackingFusion for Heterogeneous Sensor NetworksModeling (Dependent sensors using copula theory)Sensor Management (Traditional/Game-theoretic
designs)Compressed InferenceStochastic Resonance
Current Topics of Interest
Cognitive Radio NetworksSecurity for Spectrum
SensingSpectrum Auctions
Reliable Crowdsourcing
Ecological monitoringAcoustic monitoring of
wildlife in national forest reserves
Medical Image Processing
Applications
Distributed Inference and Data Fusion
Byzantine Attacks
Distributed Inference with Byzantines
Ongoing Research and Future Work
Outline
Distributed Inference in Practice
Different Sensors, Diverse Information
THROUGH-THE-WALL
ACOUSTIC SEISMIC
VIDEO
THZ IMAGING
Multi-sensor Inference: Information Fusion
Typical decision making processes involve combining information from various sources
Designing an automatic system to do this is a challenging task
Many benefits from such a system
Common source
Multiple sensors
Fusion center
Coverage
Robust system
Information Diversity
Six Blind Men and an Elephant
It was six men of IndostanTo learning much inclined,Who went to see the Elephant(Though all of them were blind),That each by observationMight satisfy his mind.
The First approached the Elephant,And happening to fallAgainst his broad and sturdy side,At once began to bawl:"God bless me! but the ElephantIs very like a wall!"……And so these men of IndostanDisputed loud and long,Each in his own opinionExceeding stiff and strong,Though each was partly in the right,And all were in the wrong!
- John Godfrey
Saxe
Inference NetworkPhenomenon
S-1 S-2 S-3 S-N
Fusion Center
y1
y2
y3
yN
u0
u1
u2
u3
uN...
Sensors collect raw-observations and transmit processed-observations to the fusion center.
Fusion center makes global inferences based on the sensor messages.
Inferences: Detection, Estimation, Classification.
Typical Inference Problems and Applications
DetectionExample: Spectrum
Sensing in Cognitive Radio Networks
EstimationExample: State
Estimation in Smart Grids
Primary User (PU)
Secondary Users (SUs)
Fusion Center
. . . . . . . . . .
Centralized vs. Distributed Inference
Centralized Inference All the sensor signals are
assumed to be available in one place for processing
Each detector acts independently and bases its decision on likelihood ratio test (LRT)
Distributed Inference Distributed processing Decision rules, both at the
local sensors and at the fusion center, are based on system wide joint optimization
Phenomenon
S-1 S-2 S-3 S-N
Fusion Center
y1 y2 y3yN
u0
u1 u2 u3 uN
Local Decision 1
Local Decision N
Global Decision
Phenomenon
S-1 S-2 S-3 S-N
y1 y2 y3yN
u1 u2 u3 uN
Decision 1 Decision N. . . . .
. . . . .. . . . .
Distributed Detection System Design
Local Sensors
Fusion Center
Datafusioncenter
u1
u2
uN
.. .
u0Local Sensor iyi ui
•Consider binary quantizers at the local sensors.
•Requires the design of local detectors and the fusion rule jointly
according to some optimization criterion.
•NP-hard, in general.
Design of Decision Rules
The crux of the distributed hypothesis testing problem is to derive decision rules of the form
and at the fusion center: u0
u0 =0, if H0 is decided
1, otherwise
0, if detector i decides H0
1, if detector i decides H1
ui =
Fusion rule at the FC: logical function with N binary inputs and one binary output
Number of fusion rules: 22N
Local decision rule can be defined by the conditional probability distribution function P(ui=1|yi )
Possible Fusion Rules for Two Binary
Input Output u0
u1 u2 f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 f 9 f10 f11 f12 f13 f14 f15 f16
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
In the binary hypothesis testing problem, we know that either H0 or H1 is true. Each time the experiment is conducted, one of the following can happen:
Decision Criteria
Types of Errors in Detection
DecideH0
DecideH1
H0 present
(noise)
True Null PR=1-PF
False alarmPF
H1 present
(signal+noise)
MissPM=1-PD
DetectionPD
Bayesian Framework
Neyman-Pearson Framework
Approaches for Signal Detection
Let .Bayes Risk: Total average cost of making decisions
where,
Then, the optimal fusion rule is given by the MAP (maximum a posteriori probability) rule
Bayesian FrameworkPhenomenon
S-1 S-2 S-3 S-N
Fusion Center
y1 y2 y3yN
u0
u1 u2 u3 uN
Let C10 = C01 = 1, C11 = C00 = 0.Then, for a given set of sensor quantizers, MAP
rule can be simplified as follows.
For identical sensors, the above fusion rule simplifies to a “K out of N” rule.
If {y1, … , yN} is conditionally independent, then the optimal sensor decision-rules are likelihood-ratio tests.
Bayesian Framework (cont…)
.log
00
10
1log)1(
1log
1
u
u
FiPMiP
iuFiPMiP
iuN
j
Maximize Probability of Detection under Constrained Probability of False alarm
Under the conditional independence assumption, the optimal local sensor decision rules are likelihood ratio based tests.
The optimal fusion rule is again likelihood ratio test
is chosen such that
Neyman-Pearson Framework
FP '
max PD s.t. PF
It has been shown that the use of identical thresholds is asymptotically optimal.
Asymptotic performance measure: N-P Setup: Kullback-Leibler distance (KLD)
Bayesian Setup: Chernoff Information
Asymptotic Results
Stein’s Lemma:
If u is a random vector having N statistically independent and identically distributed components, under both hypotheses, the optimal (likelihood ratio) detector results in error probability that obeys the asymptotics
Asymptotic Results (Cont.)
Security Threats on Distributed Inference
Attacks are of following types: Threats from External Sources Threats from Within
Can impact multiple layers simultaneously [Burbank,
2008].
Security Threats
Extrinsic
Primary User Emulation
Attacks (PUEA)
Insecure Channels
Eavesdroppers
Jammers
Intrinsic Byzantine Attacks
Byzantine Attacks
Malicious nodes – attack from within.
Byzantines send false information to the fusion center (FC).
Impact on performance of PHY (Spectrum Sensing) MAC (Spectrum
Management & Handoff) NET (Power Control &
Routing)A. Vempaty, L. Tong, and P. K. Varshney, "Distributed Inference with Byzantine Data: State-of-the-Art Review on Data Falsification Attacks," IEEE Signal Process. Mag., vol. 30, no. 5, pp. 65-75, Sept. 2013
Distributed detection in the Presence of Byzantine Attacks: An Instance of Distributed Inference
A. S. Rawat, P. Anand, H. Chen, P. K. Varshney, “Collaborative Spectrum Sensing in the Presence of Byzantine Attacks in Cognitive Radio Networks”, IEEE Trans. Signal Process., Vol. 59, No. 2, pp. 774-786, Feb 2011.
A. Vempaty, K. Agrawal, H. Chen, and P. K. Varshney, "Adaptive learning of Byzantines' behavior in cooperative spectrum sensing," in Proc. IEEE Wireless Comm. and Networking Conf. (WCNC), Cancun, Mexico, Mar. 2011, pp. 1310-1315.
Distributed Detection with Byzantines(Parallel Topology)
Let N be the number of nodesFraction of Byzantine attackers is α Nodes decide about the presence of primary transmitter and send ‘one bit’ decision (u) to the FCOperating points of nodes: Byzantines’: Honest node’s :
System Model
Fig. CRN: An example of such detection problems
Performance Metrics
Let vi be the true local node decisions and be the local messages transmitted to the FC.
FC receives z = [, … , ], For error free channels,
Performance Metric = KL distance,
Byzantines minimize KLD by flipping their local decisions
Binary Hypothesis Testing at the FC
• Byzantines degrade the performance by flipping their local decisions using flipping probabilities
H0 : Signal is absent
H1 : Signal is Present
What is the minimum fraction of Byzantine nodes, αblind, required to blind the FC?
What are the optimal flipping probabilities at the Byzantines to cause maximal damage to the performance at FC?
If modeled as a minimax game, what are the Nash equilibrium strategies?
How can we mitigate the impact of the Byzantine nodes?
Given a mitigation scheme, how will the Byzantine node behave if it does not want to be detected?
Questions to be investigated…
Distributed Detection in the Presence of Byzantine Attacks
What is the minimum fraction, αb of Byzantines to totally blind the fusion center?
If the Byzantine attacks are independent of each other, αb = 0.5 (PD
B = PDH, PF
B = PFH); and if
they cooperate, αb < 0.5.
Sensors/FC are built upon an intelligent platform with the capability of changing their parameters
Byzantines would try to choose their threshold in such a way that it results in the maximum damage no matter what strategy the FC chooses.
FC chooses the parameters in such a way that it minimizes the worst case damage by the Byzantines no matter what strategy they choose.
Zero Sum Game
The best strategy for both the players is to operate at the saddle point.
Minimax Game Formulation
Minimax Approach
Performance Metric: KLD
Reputation index, ni defined for each CR i over a time window T, as follows:
If this index reaches a threshold η, then the fusion center does not consider the node’s decisions in the subsequent stages of fusion.
Reputation-based Byzantine Identification and Removal
from the Fusion Rule
Adaptive Distributed Detection by Learning Byzantines’ Behavior
Identify Byzantines, learn their behavior, and use this information to improve the global performance.
Three-tier systemLocal processing of data at each node for
transmission to the FC.Byzantine identification and estimation of their
parameters at the FC.Adaptive fusion rule.Note: Byzantine Parameters can be learnt for any fraction of
Byzantine nodes.
For learning the behavior of the Byzantines, the FC would estimate the Byzantines’ operating point
The idea is to compare the behavior of nodes with expected behavior of Honest nodes to estimate
The final decision can be made using estimated probabilities in Chair-Varshney rule
It is shown that
Estimation of Probabilities
500 1000 1500 2000 2500 3000 3500 4000 4500 50000.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time
Estim
ated
pro
babil
ities
Estimated probabilities with time
PDB converging to the actual value of 0.3
PfaB converging to the actual value of 0.7
PDB converging to the actual value of 0.5
PfaB converging to the actual value of 0.8
0 50 100 150 200 250 300 350 400 450 5000.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time
Est
imat
ed
Estimating with time
= 0.3 = 0.7
0 100 200 300 400 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time
Pro
babi
litie
s
Probabilities with Time
Probability of mis-detection of byzantine identification
Probability of false alarm of byzantine identification
Distributed Detection in Tree Topologies with Byzantines
B. Kailkhura, S. Brahma, Y. S. Han , P. K. Varshney, “Distributed Detection in Tree Topologies with Byzantines”, IEEE Trans. Sig. Process., volume:62 , issue: 12, pp. 3208 – 3219, June 2014.
Distributed Detection with Byzantines
(Tree Topology)
Network Architecture: Tree Topology
Distributed Detection: N-P setup
Given the performance of both the honest nodes and Byzantines, what is the condition on attack configuration
to totally blind the fusion center?
Research Problem:
Distributed Detection in Tree Topologies with Byzantines
Attack is more severe : multiple attack configurations {Bk} can blind the FC. !!Challenges:
The Distributed Estimation Problem
Requires Design of an ESTIMATOR
Example: Distributed LocalizationParameter-of-interest: Location vectorIntractable MSE: Analyze upper-bounds
on MSE.Cramer-Rao Bound:
where
Example: ML Estimator
Target Localization in Sensor Networks with Quantized Data in the Presence of Byzantine Attacks
Distributed Estimation with Byzantines
A. Vempaty, O. Ozdemir, K. Agrawal, H. Chen, and P. K. Varshney, "Localization in Wireless Sensor Networks: Byzantines and Mitigation Techniques," IEEE Trans. Signal Process., vol. 61, no. 6, pp. 1495-1508, Mar. 15, 2013.
Let N sensors be randomly deployed (not necessarily in a regular grid) Estimate the unknown location of the target at where and denote the coordinates of the target Signal amplitude
Signal at the ith sensor is Sensors send quantized data to FC,
Problem Formulation
AssumptionsIdeal Channels between Sensors and FCIdentical Sensor Quantizers
Minimum Mean Square Error (MMSE) Estimation
where u=[] is the received observation vector Performance Metrics: PCRLB, Posterior-FIM
Problem Formulation
Monte Carlo based target localization
fraction of Byzantines in the network For an honest node =Di
Byzantines flip their quantized binary measurements with probability ‘p’
Attack Model
Making the FC incapable of using the data from the local sensors to estimate the target location
FC is blind when the data’s contribution to posterior Fisher Information matrix approaches zero
Blinding the FC
or
FC is blind when :
Let us denote as the cost function
Saddle point:
Best Honest and Byzantine Strategies: A Zero-Sum
Game
Observe a sensor’s behavior over time
This is done by comparing the observed values of
to the Estimate in an iterative manner
A sensor is declared Byzantine based on the test statistic
Mitigation of Byzantine Attacks: Byzantine
Identification
Numerical Results
Distributed Inference with M-ary Quantized Data with Byzantines
V. S. S. (Sid) Nadendla, Y. S. Han, and P. K. Varshney, “Distributed Inference with M-ary Quantized Data in the Presence of Byzantine Attacks,” IEEE Trans. Signal Process., vol. 62, no. 10, pp. 2681-2695, May 2014.
Distributed Inference with M-ary Quantized Data with Byzantines
Improvement in Security Performance
Reputation based Mitigation Scheme
• FC receives a vector v of received symbols from the sensors and fuses them to yield a global decision
• Observation model = is known to the FC.• Quantized message the sensor is
• Byzantine flips to according to flipping probability matrix
• FC calculates
• Accumulated square deviation is used to identify the Byzantines
Ongoing and Future Work
Distributed detection in the Presence of Byzantine Attacks (Parallel Topology)Minimum fraction of Byzantines required to blind the
network.Byzantine Identification
Reputation-based schemeLearning Byzantines’ parameters to design an adaptive FC.
Distributed Detection in Tree based Topologies with ByzantinesAttack Configuration required to blind the network.Robust Tree Topology Design
Distributed Estimation with ByzantinesOptimal strategies for both the Byzantines and the
network (zero-sum game)
Summary
Distributed detection in tree topology with labeled data.
Distributed inference in tree topology using error correcting codes.
Susceptibility and Protection of Consensus based Detection Algorithm.
Development of complex Byzantine misbehavior models and methods to detect and mitigate such Byzantines.
More sophisticated design across multiple layers of the networking protocol stack: advanced distributed inference at the physical layer, sophisticated network coding schemes for large networks, and a variety of cryptographic techniques for different applications.
What Next …
Questions ??