COMP5318/COMP4318 Machine Learning and Data Mining
Week 13 Revision and Preparation for the Exam
s1 2025
Exercise 1. Markov models
Given is the following Markov model for the weather in Sydney:
If the weather yesterday was Rainy, and today is Foggy, what is the probability that tomorrow it will be Sunny?
Exercise 2. Hidden Markov models
Julia tested positive to COVID and had to quarantine at home for several days. Her friend Nicole came to bring her food every day. We don’t know what the weather was on the quarantine days but we know the type of clothing Nicole wore and it provides evidence about the weather.
The following Hidden Markov Model models the situation. The initial state probabilities are: A0(Sunny)=0.5 and A0(Cloudy)=0.5.
Suppose that on the first quarantine day Nicole wore a dress and on the second she wore a blazer.
a) What is the probability of the observation sequence?
b) What is the most likely sequence of hidden states?
Briefly show your calculations.
Exercise 3. Perceptron
Given is the following training set:
input output
ex. 1: 1 0 0 1
ex. 2: 0 1 1 0
ex. 3: 1 1 0 1
ex. 4: 1 1 1 0
ex. 5: 0 0 1 0
a) Train a perceptron with a bias on this training set. Assume that all initial weights (including the bias of the neuron) are 0. Show the set of weights (including the bias) at the end of the first epoch. Apply the examples in the given order.
Recall that the perceptron uses a step function defined as:
step(n) = 1, if n >= 0
= 0, otherwise.