# M4_WQU_MLF_Module_4_Compiled_Content.pdf - MScFE xxx[Course...

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MScFE xxx [Course Name] - Module X: Collaborative Review Task 1 Revised: 09/07/2019
MScFE 650 Machine Learning in Finance Table of Contents © 2019 - WorldQuant University All rights reserved. 2 Module 4: Clustering Algorithms ..................................................................... 3 Unit 1: K -means Clustering .................................................................................................. 4 Unit 2: Gaussian Mixture Models ....................................................................................... 6 Unit 3: The Expectation Maximum (EM) Algorithm for Gaussian Mixture Models ........................................................................................................................... 9 Bibliography ............................................................................................................................. 11 Collaborative Review Task ................................................................................................. 12
MScFE 650 Machine Learning in Finance - Module 4: Summary © 2019 - WorldQuant University All rights reserved. 3 Module 4: Clustering Algorithms This module introduces you to k -means clustering, Gaussian Mixture Models, and the Expectation Maximization algorithm. Thereafter, it explores certain applications in finance, including regime detection and the Hierarchical Risk Parity algorithm used in portfolio optimization.
MScFE 650 Machine Learning in Finance - Module 4: Unit 1 © 2019 - WorldQuant University All rights reserved. 4 Unit 1: K -means Clustering Introduction In our discussion of classification, we assumed fully observed data i.e. each observation came with a class label. In many situations class labels are not available and need to be inferred from the data itself. This problem is often referred to as clustering , or unsupervised learning. The more general problem is to infer any missing information from the observed data. Throughout our discussion, the fundamental assumption is that, should the missing data somehow become available, the training can be done with ease. A general tool for dealing with partially observed data is the Expectation Maximization (EM) algorithm. The basic idea is very simple. Since we can proceed with the training (estimation of the parameter values) for the fully observed data, we estimate the missing values by calculating an expectation based on the current estimate of the parameters. Once we have values for the missing data, we proceed to maximize a likelihood to get an updated estimate for the parameters. These are then used to re-estimate the missing data, and so on. The simplest example of the EM algorithm is k -means clustering, the starting point of our discussion. K -means clustering We have N observations, each observation belonging to one of k classes, but we are not given any class information. Our task is to assign each observation to an appropriate class, more commonly referred to in this setting as clusters . It is important to note that we know, or guess, the value of k, i.e. we assume that we know the number of clusters. The intuition behind the k -means algorithm is straightforward and is based on the fact that if we know the cluster labels of each observation, then it is easy to calculate the mean of each cluster. On the other hand, if the mean of each cluster is known, then it is easy to assign each observation to a cluster. This allows the following procedure to be followed: choose a cluster mean for each cluster. For the time being, we choose these initial cluster means by selecting k random observations. Next, we assign each observation to the cluster mean closest to it 1 . Once all the 1 It is possible to do a more sophisticated assignment.