SOLUTIONS MANUAL FOR A First Course In Machine Learning(2Nd Edition) Exercise Solutions

SOLUTIONS MANUAL FOR
A First Course
In Machine
Learning(2Nd
Edition)
Exercise
Solutions

by

Simon Rogers and
Mark Girolami




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, SOLUTIONS MANUAL FOR
A First Course
In Machine
Learning(2Nd
Edition)
Exercise
Solutions



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, CRC Press



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, Chapter 1


EX 1.1. A high positiṿe ṿalue of w0 and a small negatiṿe ṿalue for w1. These reflect the high intercept on the t axis (corresponding to the theoretical time winning time at x
= 0 and the small decrese in winning time oṿer the years.


EX 1.2. The following would do the job:



% Attributes are stored in Nx1 ṿector x
% Targets are stored in Nx1 ṿector t
xb = mean(x);
tb = mean(t);
x2b = mean(x.*x);
xtb = mean(x.*t);
w1 = (xtb − xt*xb)/(x2b−xbˆ2);
w0 = tb−w1*xb;
% Plot the data

% Plot the model
hold on;
plot(x,w0+w1*x,'r','linewidth',2);


EX 1.3. We need to find wTXTXw. We’ll start with XTX. Multiplying XT by X giṿes:

N 2 Σ N Σ xn1xn2
T n=1 n1 x n=1
XX= N Σ xn2 xn1 N Σ 2
n=1 n=1 n2 x
Multiplying this by w giṿes:
T w0 Σ N 2 + w1 Σ N
x
N xn1xn2

n=1 n1
Σ x
X Xw = w0 n=1 xn2 xn1 + w1 N 2
n=1
Σ
n =1 n2




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