Pramod K. VarshneyDistinguished Professor, EECS

Director of CASE: Center for Advanced Systems and Engineering

Syracuse University

E-mail: varshney@syr.edu

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 ??