Social network based inference

Fraud Detection in R

Tim Verdonck

Professor Data Science at KU Leuven

Social network based inference

Goal

Predict the behavior of a node based on the behavior of other nodes

Social network based inference

Challenges

Data are not independent
- Behavior of one node might influence behavior of other nodes
- Correlated behavior between nodes
Collective inference: inferences about nodes can affect each other

Non-relational vs relational

Non-relational model

Only uses local information
Logistic regression, decision trees, ...

Relational model

Makes use of links in the network
Relational neighbor classifier

Relational neighbor classifier

Assumptions

Homophily: connected nodes have a propensity to belong to the same class ("guilt by association")
Some class labels are known

Relational neighbor classifier

Probability of fraud

$$P(F | ?) = \frac{1 + 1}{1 + 1 + 1 + 1 + 1}=\frac{2}{5}= 40\%$$

Relational neighbor classifier with weights

Probability of fraud

$$P(F | ?) = \frac{1 + 2}{3 + 1 + 1 + 2 + 1}=\frac{3}{8}=37.5\%$$

Relational neighbor classifier

vertex_attr(network) ## Nodes are labeled as 1 (fraud), 0 (not fraud), or NA (unknown)
$name

"?" "B" "C" "D" "E" "A"

$isFraud

NA  1  0  1  0  0

edge_attr(network) ## The edges have a weight

$weight

2 3 1 1 1

Relational neighbor classifier

## subgraph(): create subgraph containing nodes "?" and all fraudulent nodes
subnetwork <- subgraph(network, v = c("?", "B", "D"))

## strength(): sum up the edge weights of the adjacent edges for node "?"
prob_fraud <- strength(subnetwork, v = "?") / strength(network, v = "?")

prob_fraud

0.375

Let's practice!

Fraud Detection in R