Consider a smaller dataset with only four discrete attributes (Shipping Line, US Port, Foreign Port, Weight), and the following conditional probability distributions:
Shipping Line: CSCO (70%), ASCO (30%)
Foreign Port | Shipping Line = CSCO: Yokohama (40%), Vancouver (60%)
Foreign Port | Shipping Line = ASCO: Vancouver (100%)
US Port | Shipping Line = ASCO: Seattle (100%)
US Port | Shipping Line = CSCO: Seattle (80%), Los Angeles (20%)
Weight | Shipping Line = CSCO, Foreign Port = Vancouver: Light (30%), Medium (50%), Heavy (20%)
Weight | Shipping Line = CSCO, Foreign Port = Yokohama: Light (10%), Medium (30%), Heavy (60%)
Weight | Shipping Line = ASCO, Foreign Port = Vancouver: Light (15%), Medium (70%), Heavy (15%)
Which of the following packages is most anomalous?
a) A heavy package shipped from Vancouver to Seattle by ASCO
b) A heavy package shipped from Vancouver to Seattle by CSCO
c) A heavy package shipped from Yokohama to Los Angeles by CSCO
To answer this question, compute the likelihood of each package given the Bayesian Network (lowest likelihood = most anomalous). You must show your calculations to receive credit.
To calculate the likelihood of each package, we need to consider the conditional probability distributions given in the dataset. We will calculate the likelihood using the Bayesian Network and compare the results.
Let's calculate the likelihood of each package:
a) A heavy package shipped from Vancouver to Seattle by ASCO:
The likelihood for this package is calculated as the product of the probabilities of each attribute given its parent attribute(s):
P(ASCO) * P(Vancouver | ASCO) * P(Seattle | ASCO) * P(Heavy | ASCO, Vancouver)
P(ASCO) = 0.3 (given in the dataset for Shipping Line)
P(Vancouver | ASCO) = 1 (given in the dataset for Foreign Port | Shipping Line = ASCO)
P(Seattle | ASCO) = 1 (given in the dataset for US Port | Shipping Line = ASCO)
P(Heavy | ASCO, Vancouver) = 0.15 (given in the dataset for Weight | Shipping Line = ASCO, Foreign Port = Vancouver)
Likelihood = 0.3 * 1 * 1 * 0.15 = 0.045
b) A heavy package shipped from Vancouver to Seattle by CSCO:
The likelihood for this package is calculated as:
P(CSCO) * P(Vancouver | CSCO) * P(Seattle | CSCO) * P(Heavy | CSCO, Vancouver)
P(CSCO) = 0.7 (given in the dataset for Shipping Line)
P(Vancouver | CSCO) = 0.6 (given in the dataset for Foreign Port | Shipping Line = CSCO)
P(Seattle | CSCO) = 0.8 (given in the dataset for US Port | Shipping Line = CSCO)
P(Heavy | CSCO, Vancouver) = 0.2 (given in the dataset for Weight | Shipping Line = CSCO, Foreign Port = Vancouver)
Likelihood = 0.7 * 0.6 * 0.8 * 0.2 = 0.0672
c) A heavy package shipped from Yokohama to Los Angeles by CSCO:
The likelihood for this package is calculated as:
P(CSCO) * P(Yokohama | CSCO) * P(Los Angeles | CSCO) * P(Heavy | CSCO, Yokohama)
P(CSCO) = 0.7 (given in the dataset for Shipping Line)
P(Yokohama | CSCO) = 0.4 (given in the dataset for Foreign Port | Shipping Line = CSCO)
P(Los Angeles | CSCO) = 0.2 (given in the dataset for US Port | Shipping Line = CSCO)
P(Heavy | CSCO, Yokohama) = 0.6 (given in the dataset for Weight | Shipping Line = CSCO, Foreign Port = Yokohama)
Likelihood = 0.7 * 0.4 * 0.2 * 0.6 = 0.0336
Therefore, the lowest likelihood or the most anomalous package is option c) A heavy package shipped from Yokohama to Los Angeles by CSCO, with a likelihood of 0.0336.