[SOLVED] algorithm solution

solution

Location Time Item SUM(Quantity)

ALL ALL ALL 5100

ALL ALL PS2 2900

ALL ALL XBox 360 1700

ALL ALL Wii 500

ALL 2005 ALL 3100

ALL 2005 PS2 1400

ALL 2005 XBox 360 1700

ALL 2005 Wii 0

ALL 2006 ALL 2000

ALL 2006 PS2 1500

ALL 2006 XBox 360 0

ALL 2006 Wii 500

Sydney ALL ALL 3400

Sydney ALL PS2 2900

Sydney ALL XBox 360 0

Sydney ALL Wii 500

Sydney 2005 ALL 1400

Sydney 2005 PS2 1400

Name: Yufei Xie

Student ID: z5134233

ASSIGNMENT 1

Q1

1.1

Sydney 2005 XBox 360 0

Sydney 2005 Wii 0

Sydney 2006 ALL 2000

Sydney 2006 PS2 1500

Sydney 2006 XBox 360 0

Sydney 2006 Wii 500

Melbourne ALL ALL 1700

Melbourne ALL PS2 0

Melbourne ALL XBox 360 1700

Melbourne ALL Wii 0

Melbourne 2005 ALL 1700

Melbourne 2005 PS2 0

Melbourne 2005 XBox 360 1700

Melbourne 2005 Wii 0

Melbourne 2006 ALL 0

Melbourne 2006 PS2 0

Melbourne 2006 XBox 360 0

Melbourne 2006 Wii 0

1.2

1.3

SELECTLocation, Time, Item, SUM(Quantity)
FROMSales
GROUP BY Location, Time, Item

Location Time Item SUM(Quantity)

ALL ALL ALL 5100

ALL ALL PS2 2900

ALL ALL XBox 360 1700

ALL ALL Wii 500

ALL 2005 ALL 3100

ALL 2005 PS2 1400

ALL 2005 XBox 360 1700

ALL 2006 ALL 2000

ALL 2006 PS2 1500

ALL 2006 Wii 500

Sydney ALL ALL 3400

Sydney ALL PS2 2900

Sydney ALL Wii 500

Sydney 2005 ALL 1400

Sydney 2005 PS2 1400

Sydney 2006 ALL 2000

Sydney 2006 PS2 1500

Sydney 2006 Wii 500

Melbourne ALL ALL 1700

Melbourne ALL XBox 360 1700

Melbourne 2005 ALL 1700

Melbourne 2005 XBox 360 1700

1.4

the function I chose to map a multi-dimensional point to a one-dimensioinal point

ArrayIndex Value

0 5100

1 2900

2 1700

3 500

4 3100

5 1400

6 1700

8 2000

9 1500

11 500

12 3400

13 2900

15 500

16 1400

17 1400

20 2000

21 1500

23 500

24 1700

26 1700

28 1700

30 1700

Q2

2.1

We classfiyas 1 when

Thus, letand letfor. Thus the Naive Bayes

classifier is a linear classifier in a d + 1-dimension space.

2.2

To get, we need to compute the class prior probability and probability ofconditioned
on class. Through maximum likelyhood estimation, these can be computed just by computing
the ratio of counts.

For, we need to use gradient descent algorithm to iterate optimize the parameters.

Thusis much easier than learning

Q3

3.1

The likelihood ofis

The likelihood of training dataset is

We can use the negative log-likelihood as the loss function. Thus

3.2

ASSIGNMENT 1
Q1
1.1

1.2
1.3
1.4
Q2
2.1
2.2

Q3
3.1
3.2