类似的作业代写任务还有COMP7710 Homework 4 – Dimensionality Reduction，以下是5的内容

Data pre-processing (1 mark)
1. Load the ’virusdata.csv’ dataset.
2. Preprocess the data by dropping any unnecessary columns.
3. Extract a subset of data by considering all columns, but only the first 1000 rows.
4. Now, extract the values of 4th and 5th columns from the above dataset (similar to what was done in the tutorial). Your new dataset should now be of size (1000,2). Use this sub-dataset for all subsequent problems.

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Choosing the optimal number of clusters (3 marks)
For this question, use the silhouette score metric to choose an optimal number of clusters from a range of clusters.
1. Define a range of clusters to apply GMM. The minimum number of clusters should be 2, and the maximum can be a number between 12-15.
2. For each number of clusters
• Apply a Gaussian Mixture Model on your dataset.
• Using the trained GMM, predict the cluster of each datapoint.
• Calculate the average silhouette score for the number of clusters chosen at each iteration. Use the
Euclidean distance as the distance metric to calculate this score.
3. Plot the average silhouette score against the number of clusters

Optimal GMM (3 marks)
1. From the above plot, what would you choose as the optimal number of clusters?
2. Apply a GMM on your dataset with the optimal number of clusters that you chose.
3. Find the cluster centers for the optimal GMM.
4. Plot the clustered data points and the means of each cluster. (Assign different colours to each cluster for clear visualization)
Discussion (3 marks)
1. Consider K-means discussed in the tutorial, and GMM for clustering. Explain which method you think is most suitable for the problem of clustering the virus-MNIST dataset and why.
2. GMM is considered to be an unsupervised clustering technique. However, a small part of training data might contain labels. Explain how this information can be used to improve the performance of GMM. Tip: think about the initialisation.

Refereed Book Chapter:
Pattern Recognition and Machine Learning, by Christopher M. Bishop
Chapter 12.1

在作业四中

Questions
In this homework, you will use PCA and LDA to reduce the dimensions of the cyber attack dataset collected by the University of New South Wales.
You may use scikit-learn functions to answer these questions (or any implementations you built from scratch).

Before embarking on this assignment, you should read this pdf file:
SDEs.pdf
Then work on the problems in this Jupyter notebook:
StochasticDiffEqs-1.ipynb

We saw how Brownian motion paths can be constructed by using cumulative sums of innitesimal stochastic jumps in each innitesimal time step. At rst glance, this might seem vaguely similar to what we do when we solve dierential equations, except that the jumps, while innitesimal, are stochastic.
Before talking about stochastic dierential equations, it is helpful to review some ordinary dierential equation (ODE) concepts.

Brownian Motion
In order to understand what happens on the stochastic side, with stochastic dierential equations, we start with the intuitive construction to an approximation for standard Brownian motion based on a random walk that has been re-scaled in time and space.

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If we transform Brownian motion with drift by exponentiation i.e. by defining $G_t = \\exp(S_t)$ (so that the updates are *multiplicative* rather than *additive*) we get what is referred to as \n”,
“**geometric Brownian motion** (with drift) a process often used in finance to model asset prices since it cannot become negative.

用到的数据文件

SP500Daily.csv
SP500Weekly.csv

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论文题目会有十几个，来提供选择

题目较为开放，有时候甚至有一种不听课查查资料就能写的错觉

reading list冗长复杂，最好多看看readings，会得高分

1. How is IPE distinct from Economics as a discipline concerned with ‘markets’?
2. Why do we need ‘theory’ in IPE?
3. Is economic nationalism progressive?
4. A critical analysis of neoliberalism.
5. Why do critical political economists focus on class?
6. How do ideas matter in IPE?
7. Why is gender relevant for the analysis of global market life?
8. How do colonial assumptions persist in IPE?
9. The everyday is a site of domination ‘and’ resistance. Discuss.
10. Is global trade good for development?
11. Who benefits from global supply chains?
12. How are everyday actors relevant for the study of global finance?
13. A critical analysis of consumption.
14. How, if at all, do migrants matter in IPE?
15. Can markets save the environment?
16. Is global governance democratic? Should it be?
17. ‘Global resistance is futile.’ Discuss
18. What are the key empirical challenges that IPE must adapt to in future?

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Exam tips
• Make a formula sheet
• Make a sheet of proofs
• Write out exam answers in full sentences
• Show all your working out

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(a) Explain one by one the interpretation of the estimates in model (3.2)?
(b) Based on the estimates in (3.1) and (3.2), from 2006 to 2010, what is the average
price change for all houses in Sydenham?
(c) Explain why we cannot infer from the estimates in (3.1) that the location of the
hospital caused the price of houses located nearby to increase? What evidence from
model (3.2) supports this conclusion?
(d) Using the information from models (3.1) and (3.2), calculate the dierence-in-dierences
estimate of the impact of the new hospital on the price of nearby houses?
(e) Propose a linear regression model that can directly estimate the eect of new hospital
on housing price.

GLS
• GLS estimation is a way of addressing heteroskedasticity
• GLS works by transforming the regression by weighting each observation to put less weight on the observations that vary a lot, and more weight on the observations that vary a little
• Must mention: you can only use GLS if you know the form of the heteroskedasticity
• The form of the heteroskedasticity is used to weight the regression

1 Introduction, Linear Regression with Treatment Effects
2 OLS and GLS in Matrix, Panel Data Models
3 Endogeneity, Pooled IV and 2SLS Estimators
4 Pooled OLS, First Difference Estimator, Pooled 2SLS
5 Fixed-Effect and Random-Effect Estimators
6 Social and Natural Experiments, DID Estimation
7 Mid-semester Exam
8 Modeling Issues in Panel Data
9 Generalized Method of Moments (GMM) and MLE
10 Dynamic Linear Panel Data Models
11 Simultaneous Equation Models for Panel Data
12 Discrete Choice Models for Panel Data
13 Review

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第一部分

LEBESGUE INTEGRATION FOR FUNCTIONS OF A SINGLE REAL VARIABLE

第二部分

ABSTRACT SPACES: METRIC, TOPOLOGICAL, BANACH, AND HILBERT SPACES

虽然期末考试量不多，但是做题还是挺煎熬的，尤其是对于第一次研修这门的童鞋来讲！

III Measure and Integration: General Theory 335
17 General Measure Spaces: Their Properties and Construction 337
17.1 Measures and Measurable Sets ……………………… 337
17.2 Signed Measures: The Hahn and Jordan Decompositions ……….. 342
17.3 The Carath6odory Measure Induced by an Outer Measure ……….. 346

22 Invariant Measures 477
22.1 Topological Groups: The General Linear Group ……………. 477
22.2 Kakutani’s Fixed Point Theorem ……………………. 480
22.3 Invariant Borel Measures on Compact Groups: von Neumann’s Theorem . . 485
22.4 Measure Preserving Transformations and Ergodicity: The Bogoliubov-Krilov
Theorem ………………………………… 488

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