ER4165 - Advanced Topics in Machine Intelligence - IT Assignment Help

Assignment Task

Question 1
(A) Compute probability density function py(y) for a random variable Y, if the values of this random variable are calculated from y = ex, where values x are drawn from the uniform probability density function on interval [0,1], i.e. x~px(x)=U(0,1). Explain how would you verify this result experimentally?

(B) Using a fern approach, find the class of a test object if the fern F binary observations, for that test object are given as F=[1,0]. The fern is built based on observations of two binary examinations’ results, with the fern’s training data given as follows:

The 1st fern training observations for five samples drawn for the first object class:
{[0,0]; [1,0]; [0,1]; [1,1]; [1,1]}
The 1st fern training observations for five samples drawn for the second object class:
{[0,1]; [0,0]; [0,1]; [1,1]; [0,1]}

Question 2
(A)
Explain how principal component analysis (PCA) can be used to mitigate the effects of the curse of dimensionality.

(B)
Given dataset D, consistenting of eight two-dimensional observations [xi, yi]:
D = {[2,1],[3,2],[5,4],[4,2],[5,5],[6,4],[6,7],[7,5]},

(i) Compute coordinates of the dataset D in the principal components coordinate system, i.e. transform the observed dataset D to align its principal component with the x-axis of the observation space. It is essential that you include all stages of the computation in your solution, providing relevant formulas and intermediate results.

(ii) Compute the proportion of variance explained by each principal component.

Question 3
(A)
Explain the taxonomy of artificial intelligence, machine learning, and deep learning.

(B)
Using LDA, compute the optimal projection line in a single dimension, for two labelled sets of 2-dimensional points given below:
Class 1 = { (1,0), (1,2), (3,0), (3,2) }
Class 2 = { (2,4), (3,2), (5,4), (6,2) }

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