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机器学习代写 | CMT311 Principles of Machine Learning

这个作业是完成线性回归、向量机、决策树、神经网络等相关的机器学习问题
CMT311 Principles of Machine Learning

Question 1. Linear Regression
The ERM problem of linear regression with respect to the loss function of maximum absolute
error can be cast as a linear program. Show mathematical derivation of writing this problem,
namely,
min
𝐰
max
𝑖∈[𝑚]
|〈𝐰, 𝐱𝑖
〉 − 𝑦𝑖
|
as a linear program.
Question 2. Support Vector Machine
Suppose we are using a linear SVM on the dataset showing below:
For each of the following cases, draw the decision boundary of linear SVM, indicate the
support vectors, and justify your answers in a few sentences:
a) The whole dataset is used as the training set, [5 marks]
b) The data ((2, 2), ‘+’) is excluded from the whole training set, [5 marks]
c) The data ((4,3), ‘-’) is excluded from the whole training set. [5 marks]
Question 3. Decision Tree
Consider the following training set, where 𝐗 = {0,1}
4
and 𝑌 = {0,1}:
a) Suppose we run the ID3 algorithm up to depth 3. Assume that the subroutine used to
measure the quality of each feature is based on information gain, and that if two
features get the same score, one of them is picked arbitrarily. Show that the training
error of the resulting decision tree is at least 1⁄8. [8 marks]
b) Find a decision tree of depth 3 that attains zero training error. [7 marks]
Question 4. Neural Networks
Deep learning is a machine learning method based on deep neural networks. Describe three
popular techniques that are used in deep learning but not in traditional neural network
learning and explain why they can improve the learning performance from the traditional
neural network learning techniques. [15 marks]
Question 5. Case Study
Suppose you are required to develop a software system to predict stock market and to provide
operation instructions for investors to maximize their stock gains. The software should have
the following functions:
1) It can apply all the stock market information (quantitative (numerical values) and
qualitative (text or symbolic information)).
2) It can provide the investors guidance about when and how much they should buy or
sell some shares to maximise their gains within a limited period, given the total
amount of available fund.


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