Dr. Eick
COSC 6342“Machine Learning” Assignment3 Spring 2009
First Draft
Due: Problems 13, 14, 16: Monday, April 27, 11p; Problem 15: Tu., May 5, 10a!
13. G—Topic14
a) Assuming that k1(u,v) and k2(u,v) are kernels; show that
k(u,v)=k1(u,v)*k2(u,v)
is also a kernel!
b) Characterize the mapping f of the Gaussian kernel function
K(u,v)=exp(-||u-v||/2s2)
Hint: Conduct a web search, and find documents that shed some light on what f is!
14. G---Topic 14
a) Compute P(Earthquake|Mary_Calls) for the Alarm belief network (the second transparency in Dr. Eick’s Belief Network lecture). Justify all major steps in your computation!
b) Assume that the following belief network is given
i. Are F and E d-separable (independent)?
ii. Are A|E and C|E d-separable?
iii. Are A,B|F,D and E|F,D d-separable?
Give reasons for your answers!
15. G-Topic 12
Apply an ensemble method of your own preference to the Arsenic dataset. Compare the results with the classifier you developed in Homework1. Write a 2-3-page report that describes the chosen ensemble method, how the experimental results were obtained, and what the results are. Finally, write a 60-100 word abstract that summarizes the findings of the project!
16. G—Topic 18
Reinforcement Learning
a) Give the Bellman Equations for states 5, 6, 7 and 8 of the CHI word, depicted below![
U(5)=
U(6)=
U(7)=
U(8)=
b) Now assume you apply temporal difference learning to the GHI World relying on the following assumptions: [4]
· The agent visits the states in the following order: 1-2-3-5-2-3-5-7-5-7-4-1
· g is 1.0 and a is 0.5
· Utilities for all states are initialized with 0
Using temporal difference learning compute the utilities of all visited states! Do not only give the final result but also how you derived the final result including formulas used! Looking at the final result─did the agent leant anything? If yes, what did she learn?
GHI World
2