Statistical LEARNing HOMEWORK $1$

$1$ Multiple Choice Questions

Q$1(10$ points$)$ Which of the following option is unsupervised learning? Multiple answers are possible.

$($A$)$ Hierarchical clustering

$($B$)$ k$-$means clustering

$($C$)$ Classification

$($D$)$ Regression

Solution:

Q$2(10$ points$)$ Which of the following option is a supervised learning method? Multiple answers are possible.

$($A$)$ Single$-$Linkage hierarchical clustering

$($B$)$ Q$-$Reinforcement learning

$($C$)$ Na$$ve Bayes

$($D$)$ Linear regression

Solution:

Q$3(10$ points$)$ Given $P(A)=P(B)=P(C)=\frac{1}{4},P(AB)=0,P(AC)=P(BC)=\frac{1}{12},$ what is

the probability that exactly one event happens among events $A,B,C?$ Note: $P(AB)$ denotes the probability

that A and $B$ happen at the same time.

$($A$)\frac{3}{4}$

$($B$)\frac{5}{12}$

$($C$)\frac{1}{2}$

$($D$)\frac{2}{3}$

Solution:

Q$4(10$ points$)$ Which one of the following is the Na$$ve Bayes assumption?

$($A$)$ Conditional dependence of features

$($B$)$ Dependence of features

$($C$)$ Independence of features

$($D$)$ Conditional independence of features

Solution:

Q$5(10$ points$)$ Which of the following is FALSE about Na$$ve Bayes?

$($A$)$ Na$$ve Bayes can only be used for two classes, but not for multiclass.

$($B$)$ Naive Bayes is a generative approach.

$($C$)$ Features are assumed statistically independent of one another given the class label.

$($D$)$ Features can have discrete or continuous values.

Solution: