Belief Propagation and Applications Prof. Srijan Kumar 1 Srijan - PowerPoint PPT Presentation

CSE 6240: Web Search and Text Mining. Spring 2020 Belief Propagation and Applications Prof. Srijan Kumar 1 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Today’s Lecture • Overview of collective classification • Relational classification • Iterative classification • Belief propagation Some of the slides have been borrowed from Prof. Jure Leskovec’ CS224w class 2 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Loopy Belief Propagation • Intuition: Use neighbors belief about a node to predict node label – Used to estimate marginals (beliefs) or the most likely states of all variables (nodes) • Iterative process in which neighbor variables “talk” to each other, passing messages • When consensus is reached, calculate final belief 3 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing Basics Task: Count the number of nodes in a graph* Condition: Each node can only interact (pass message) with its neighbors Example: straight line graph * Graph can not have loops. Explanation later. 4 adapted from MacKay (2003) textbook Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing Basics Task: Count the number of nodes in a graph Condition: Each node can pass message to its neighbors Solution: Each node listens to the message from its neighbor, updates it, and passes it forward there's 1 of me 1 2 3 4 5 before before before before before you you you you you 1 3 2 5 4 6 after after after after after after you you you you you you 5 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing Basics Each node only sees incoming messages there's Belief: 1 of me Must be 2 + 1 + 3 = 6 2 2 before before of us you you 3 only see behind my incoming you messages 6 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing Basics Each node only sees incoming messages there's Belief: Belief: 1 of me Must be Must be 1 + 1 + 4 = 6 2 + 1 + 3 = 6 1 before of us of us you 4 only see behind my incoming you messages 7 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing in a Tree Each node receives reports from all branches of tree 3 here 7 here 1 of me 11 here (= 7+3+1) 8 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing in a Tree Each node receives reports from all branches of tree 3 here 7 here (= 3+3+1) 3 here 9 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing in a Tree Each node receives reports from all branches of tree 11 here (= 7+3+1) 7 here 3 here 10 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing in a Tree Each node receives reports from all branches of tree 3 here 7 here Belief: Must be 3 here 14 of us 11 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Message Passing in a Tree Each node receives reports from all branches of tree 3 here 7 here Belief: Must be 3 here 14 of us 12 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Loopy BP algorithm What message will i send to j? - It depends on what i hears from its neighbors k - Each neighbor k passes a message to i: k’s beliefs of the state to i 13 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Notations • Label-label potential matrix : Dependency between a node and its neighbor. equals the probability of a node i being in state given that it has a j neighbor in state • Prior belief : Probability of node i being in state is i ’s estimate of j being in state • is the set of all states • 14 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Loopy BP algorithm 1. Initialize all messages to 1 2. Repeat for each node Label-label All messages from neighbors potential Prior Sum over all states 15 15 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Loopy BP algorithm After convergence: = i ’s belief of being in state All messages from neighbors Prior 16 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Loopy belief propagation • What if our graph has cycles? – Message from different subgraphs are no longer independent! – BP will give wrong results 17 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

BP and Loops T 4 T 2 F 1 • Messages loop around and around: F 1 T 2 F 1 2, 4, 8, 16, 32, ... More and more convinced that these variables are T! • BP incorrectly treats this message as separate evidence that the variable is T. • Multiplies these two messages as if T 2 T 2 T 4 F 1 F 1 they were independent. F 1 • But they don’t actually come from independent parts of the graph. • One influenced the other (via a cycle). T 2 F 1 18 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Advantages of Belief Propagation • Advantages: – Easy to program & parallelize – General: can apply to any graphical model w/ any form of potentials (higher order than pairwise) • Challenges: – Convergence is not guaranteed (when to stop), especially if many closed loops • Potential functions (parameters) – require training to estimate – learning by gradient-based optimization: convergence issues during training 19 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Application of belief propagation: Online auction fraud Netprobe: A Fast and Scalable System for Fraud Detection in Online Auction Networks Pandit et al., World Wide Web conference 2007 20 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Online Auction Fraud • Auction sites: attractive target for fraud • 63% complaints to Federal Internet Crime Complaint Center in U.S. in 2006 • Average loss per incident: = $385 21 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Online Auction Fraud Detection • Insufficient solution to look at individual features: user attributes, geographic locations, login times, session history, etc. • Hard to fake : graph structure • Capture relationships between users • Main question: how do fraudsters interact with other users and among each other? – In addition to buy/sell relations, are there more complex relations? 22 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Feedback Mechanism • Each user has a reputation score • Users rate each other via feedback • Question: How do fraudsters game the feedback system? 23 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Auction “Roles” of Users • Do they boost each other’s reputation? – No, because if one is caught, all will be caught • They form near-bipartite cores (2 roles) – Accomplice : trades with honest, looks legit – Fraudster : trades with accomplice, fraud with honest 24 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Detecting auction fraud • How to find near-bipartite cores? How to find roles (honest, accomplice, fraudster)? – Use belief propagation! • How to set BP parameters (potentials)? – prior beliefs: prior knowledge, unbiased if none – compatibility potentials: by insight 25 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Belief propagation in action Initialize all nodes as unbiased 26 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Belief propagation in action At each iteration, for each node, compute messages to its neighbors Initialize all nodes as unbiased 27 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Belief propagation in action At each iteration, for each node, compute messages to its neighbors Initialize all nodes as unbiased Continue till convergence 28 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Final Belief Scores = Final Roles P(honest) P(associate) P(fraudster) 29 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Application of belief propagation: Face-to-Face Deception Detection 30 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Face-to-Face Trust and Deception • Trust develops over time • Deceivers aim to win trust to deceive the victims • Face-to-face deception is very different from online deception • Key question: How can we identify deceivers? 31 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

Traditional Methods • Several ways to identify deception • Linguistic analysis: what is a person speaking? • Vocalic analysis: how is a person speaking? • Facial expressions: is the person smiling? Hiding her mouth? • Body language analysis: is the person confident? 32 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining