數值方法

munchsistersΤεχνίτη Νοημοσύνη και Ρομποτική

17 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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1
頁共
6


1

機器學習



考試


號:

姓名:



100
/
6

一、

是非題
(
1
4
%)

(


)
1
.

In s
emiparametric

estimation, t
he density is written as a disjunction of a small number of
parametric models.

(


)
2
.

A decision tree
is a

hierarchical model

using

a
d
ivided
-
and
-
conquer strategy
.

(


)
3
.

To r
emove subtrees
i
n a

decision tree
,

postpruning is faster

and

p
repruning is more
accurate
.

(


)
4
.

The impurity measure of a classification tree should be
satisfies the following properties:

(1)
, (2)

, and (3)


(


)
5
.

Rule induction works similar to tree induction except that rule induction does a
breadth
-
first search, whereas tree induct
ion goes depth
-
first
.

(


)
6
.

When classes are Gaussian with a shared covariance matrix, the optimal discriminant is
linear
.

(


)
7
.

S
upport vector machines are

likel
i
hood
-
based method
s
.

(


)
8
.

In SIMD machines,

a
ll processors execute the same
instruction but on different pieces of
data
.

(


)
9
.

Hints can be used to create virtual examples
.

(


)
10
.

A

real
-
valued function
f

defined on an interval is called convex, if for any two points
x

and
y

in its domain
C

and any
t

in [0,1], we have
.

(


)
11
.

Adaptive
r
esonance theory (ART)

neural networks are unsupervised learning.

(


)
1
2
.

In a multilayer perceptron, if the number of hidden units is less than the number of
inputs, the first layer performs a dimensionality
reduction
.

(


)
1
3
.

The self
-
organizing map (SOM) is a winner
-
take
-
all neural network.
I
t is as if one
neuron wins and gets updated, and the others are not updated at all.

(


)
1
4
.

In a local representation, the input is encoded by the simultaneous a
ctivation of many
hidden units

such as R
adial
b
asis function
s
.

二、

簡答


1.

(4%)
W
hat are the advantages and the disadvantages of the nonparametric
density estimation
?






2
頁共
6


2

2.

(1)
(
4
%)

What is the meanings of a leaf
node
and an internal node in a decision tree?

(2)
(4%)
How to decide to split a node in a decision tree?

What are the split critira?





3.

(
4
%) In
a
neural network, can

we have more
than one
hidden layers
?
W
hy or why not?





4.

(4%)
Why
is
a neural network
overtraining (or overfitting)
?






5.

(4%)
(1)
What are s
upport
v
ector
s in support vector machine?



(2) Given an example as follows. Please show the supports vectors.











6.

(4%)
W
hat
is

the different between

a
likelihood
-
based method and
a
d
iscriminant
-
based

method?




3
頁共
6


3


7.


(
10
%)
Here shows
the batch
k
-
means algorithm and the online
k
-
means algorithm,
respectively.

(1)

(4%)
What are the differences between these two methods?


(2)

(6%)
What are their advantages and disadvantages?

















8.

(4%)
Condensed Nearest Neighbor

algorithm

is used to f
ind a subset
Z

of
X

that is small and is
accurate in classifying
X
.

Please finish the following
Condensed Nearest Neighbor

algorithm.





4
頁共
6


4

9.

(
4
%) In n
onparametric

r
egression
, given a r
unning mean smoother
as follows, please finish the
graph with
h

=
1
.


where


10.

(
12
%)
Let

be the distance to the
k
-
nearest sample,
N

the total sample number, and
K

is a
kernel

function.


The following

shows some d
ensity estim
ators, can you

(1)

(4%)
link the fomulars
to

their corresponding graph
s
, and

(2)

(8%)
calculate the values of
k

or
h
?




















5
頁共
6


5

11.

(
4
%)
Given a regression tree as follows. Please draw its corresponding regression result.






12.

(
6
%)
In
a
p
airwise
s
eparation

example as follows, and
H
ij

indicate
s

the hyperplane

separate the
examples of
C
i

and the examples of
C
j

Please

decide each region belongs to

which class
.




13.

Given a perceptron as follows:

(1)

(4%) What are the values of these weights if we
use this pe
rceptron to implement the AND gate?

(2)

(4%)

Why can’t a perceptron learn the Boolean
function XOR?






6
頁共
6


6

三、
計算
證明


1.

(
10
%)
Given a
backpropogation neural network,
where

,

.

If
the learning factor is

and
the error function is
defined as



Please find the weight update rules

and
,

where
.

ANS: