1 Multiple Choice Questions
1. (1 point) true/false We are machine learners with a slight gambling problem (very different
from gamblers with a machine learning problem!). Our friend, Bob, is proposing the following
payout on the roll of a dice:
$2 =il
POy { —$1/4 z#1 ®
where z € {1,2,3,4,5,6} is the outcome of the roll, (+) means payout to us and (—) means
payout to Bob. Is this a good bet i.e. are we expected to make money?
Q True () False
2. (1 point) X is a continuous random variable with the probability density function:
i dr 0<z<1/2
p(z)‘{ —do+4 1/2<z<1 @
Which of the following statements are true about equation for the corresponding cumulative
'!
distribution function (CDF) C(z)?
|
[Hint: Recall that CDF is defined as C(z) = Pr(X < z).]
|
® Cz) =222 for 0<z <1/2
O C(z)=-22+4z—1for1/2<az
<1
O All of the above |
O None of the above
3. (2 point) A random variable z in standard normal distribution has the following
probability
density
if Lok
I p(z) =——e"7
= ®)3
Evaluate following integral
o
/ p(z)(az? + bz + ¢)dz 4)
~o
[Hint: We are not sadistic (okay, we're a little sadistic, but not for this
question). This is not
a calculus question.]
Oa+b+c Q¢ Rat+c Ob+ec
, 4. (2 points) Consider the following function of x = (21,2, T3, T4, T5, T6):
o (log (5 (max{lnl‘?) 4 E — (25 + za))) + %)
(5)
where o is the sigmoid function
o(z) = 1—_'}2—_; (6)
Compute the gradient Vxf(-) and evaluate it at at X = (-1,3,4,5, -5, 7.
0 0 0 0
0.031 0.157 0.358 0.358
0.026 0.131 0.269 0.269
o —-0.013 o —0.065 o —-0.215 ® -0.215
—0.062 —0.314 —0.846 —0.448
—0.062, —0.314 —0.846, —0.448
5. (2 points) Suppose your machine learner friend trains two classification models A and B on
the same data set. Their training routine produces the following learning curves. You are
told one of the models has higher model complexity (by some sufficient definition of model
complexity). Generally this would lead us to believe which of the following is True?
score vs iterations for two models
model A model B
10
1.0
0.8 08
] 5
206 R b I /
@ = 2 0.6 e
<
5 04 =
s
P / w 044/
02 Lt o 4
/' ~—— training score . / —— train score
g ~—— val score £ —— val score
0.0
= increasing iterations - - increasing iterations —
® Model A complexity > Model B complexity
O Model A complexity < Model B complexity
6. (2 points) Which of the following functions are convex?
O Il
O minf_, al'x for x € R", and a finite set of arbitrary vectors: {ay,...,a5}
1. (1 point) true/false We are machine learners with a slight gambling problem (very different
from gamblers with a machine learning problem!). Our friend, Bob, is proposing the following
payout on the roll of a dice:
$2 =il
POy { —$1/4 z#1 ®
where z € {1,2,3,4,5,6} is the outcome of the roll, (+) means payout to us and (—) means
payout to Bob. Is this a good bet i.e. are we expected to make money?
Q True () False
2. (1 point) X is a continuous random variable with the probability density function:
i dr 0<z<1/2
p(z)‘{ —do+4 1/2<z<1 @
Which of the following statements are true about equation for the corresponding cumulative
'!
distribution function (CDF) C(z)?
|
[Hint: Recall that CDF is defined as C(z) = Pr(X < z).]
|
® Cz) =222 for 0<z <1/2
O C(z)=-22+4z—1for1/2<az
<1
O All of the above |
O None of the above
3. (2 point) A random variable z in standard normal distribution has the following
probability
density
if Lok
I p(z) =——e"7
= ®)3
Evaluate following integral
o
/ p(z)(az? + bz + ¢)dz 4)
~o
[Hint: We are not sadistic (okay, we're a little sadistic, but not for this
question). This is not
a calculus question.]
Oa+b+c Q¢ Rat+c Ob+ec
, 4. (2 points) Consider the following function of x = (21,2, T3, T4, T5, T6):
o (log (5 (max{lnl‘?) 4 E — (25 + za))) + %)
(5)
where o is the sigmoid function
o(z) = 1—_'}2—_; (6)
Compute the gradient Vxf(-) and evaluate it at at X = (-1,3,4,5, -5, 7.
0 0 0 0
0.031 0.157 0.358 0.358
0.026 0.131 0.269 0.269
o —-0.013 o —0.065 o —-0.215 ® -0.215
—0.062 —0.314 —0.846 —0.448
—0.062, —0.314 —0.846, —0.448
5. (2 points) Suppose your machine learner friend trains two classification models A and B on
the same data set. Their training routine produces the following learning curves. You are
told one of the models has higher model complexity (by some sufficient definition of model
complexity). Generally this would lead us to believe which of the following is True?
score vs iterations for two models
model A model B
10
1.0
0.8 08
] 5
206 R b I /
@ = 2 0.6 e
<
5 04 =
s
P / w 044/
02 Lt o 4
/' ~—— training score . / —— train score
g ~—— val score £ —— val score
0.0
= increasing iterations - - increasing iterations —
® Model A complexity > Model B complexity
O Model A complexity < Model B complexity
6. (2 points) Which of the following functions are convex?
O Il
O minf_, al'x for x € R", and a finite set of arbitrary vectors: {ay,...,a5}
