Natural Language Processing · TEE · papers

Q2c · Animal categorical Naive Bayes

2024-12-03 · final · recovered AI paper

Previous examination · complete worked answers

Question. Using the printed20-animal training table, classify an animal with Give Birth=Yes, Can Fly=No, Live in Water=Yes, Have Legs=No. Treat Name only as an identifier. [10 marks]

Answer

Rows below follow the source order: Human, Python, Salmon, Whale, Frog, Komodo, Bat, Pigeon, Cat, Leopard Shark, Turtle, Penguin, Porcupine, Eel, Salamander, Gila Monster, Platypus, Owl, Dolphin, Eagle. The source assigns Leopard Shark to Non-mammals and Platypus to Mammals; retain those labels.

Given

Give Birth	Can Fly	Live in Water	Have Legs	Class
Yes	No	No	Yes	Mammals
No	No	No	No	Non-mammals
No	No	Yes	No	Non-mammals
Yes	No	Yes	No	Mammals
No	No	Sometimes	Yes	Non-mammals
No	No	No	Yes	Non-mammals
Yes	Yes	No	Yes	Mammals
No	Yes	No	Yes	Non-mammals
Yes	No	No	Yes	Mammals
Yes	No	Yes	No	Non-mammals
No	No	Sometimes	Yes	Non-mammals
No	No	Sometimes	Yes	Non-mammals
Yes	No	No	Yes	Mammals
No	No	Yes	No	Non-mammals
No	No	Sometimes	Yes	Non-mammals
No	No	No	Yes	Non-mammals
No	No	No	Yes	Mammals
No	Yes	No	Yes	Non-mammals
Yes	No	Yes	No	Mammals
No	Yes	No	Yes	Non-mammals

Test: {'Give Birth': 'Yes', 'Can Fly': 'No', 'Live in Water': 'Yes', 'Have Legs': 'No'}

To find

Class under categorical Naive Bayes.

Formula: which one and why

\mathrm{score}(c)=P(c)\prod_jP(x_j\mid c)

Use empirical categorical frequencies, not a multinomial word model. No likelihood is zero for the requested test, so unsmoothed estimates are sufficient. Each feature contributes once; ignore names/identifiers as predictors.

Step 1. Count examples in each class

Class	Count	Prior
Mammals	7	7/20
Non-mammals	13	13/20

Step 2. Count each requested feature within each class and multiply

Class	n	Prior	Give Birth	Can Fly	Live in Water	Have Legs	Exact product	Decimal product
Mammals	7	7/20	6/7	6/7	2/7	2/7	36/1715	0.020991253644
Non-mammals	13	13/20	1/13	10/13	3/13	4/13	6/2197	0.002730996814

Step 3. Normalize for a posterior if wanted

Class	Score / score sum
Mammals	0.884876150
Non-mammals	0.115123850

Final answer

Predicted class: Mammals. The independence assumption is conditional on class, not a claim that these biological/weather features are truly independent.