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H. Unsupervised Learning

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9
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Medium
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Small Description
Modelling data without labels.
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Goal of unsupervised learning is to discover hidden patterns in unlabeled data. {x(1),…,x(m)}\left\{x^{(1)}, \ldots, x^{(m)}\right\}
Unsupervised learning learning is divided into clustering, and dimensionality reduction techniques.
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Clustering methods (CM) self-organize data into groups using their individual attributes.
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Dimensional reduction (DR) methods reduce the number of features of the dataset.
The only requirement to be called an unsupervised learning strategy is to learn a new feature space that captures the characteristics of the original space while maximizing some objective function or minimizing loss function.
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PCA (DR) develops new features that maximize the variance in the data.
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K-means (CM) finds clusters that minimizes the distances between samples.
Clustering is a special form of dimensionality reduction, where the cluster labels themselves can be used as a new feature.

Hyperparameters

Note that many unsupervised learning methods still requires some hyperparameter inputs.
When you are doing K-Means clustering you have to select KK the number of clusters.
Using the elbow method, the optimal number of clusters is when the total within cluster sum of squares clearly begins to level off (so it forms an elbow).
A. Introduction

Clustering

Clustering is the process of grouping similar entities together. Each similar group is called a cluster and contains statistically similar data points.

Clustering Tasks

Clustering Problems

Data clustering is just starting to take root in Finance. The potential of clustering is enormous as these applications to solve open problems illustrate:
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Pre-hedging in execution: finding the most similar instruments.
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Selling in crisis: again, sell the most similar liquid instrument.
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Loan ratings: have ratings for public companies, quickly find most similar ones for private loans.
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Consumer ratings: based on online behavior, match consumers into credit buckets with known credit ratings.

Clustering Types

Clustering is divided into two subgroups based on the assignment of data points to clusters:
B. Clustering

Dimensionality Reduction

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Reminder, with unsupervised learning there are only features (X)(X) and no labels (y)(y). There is nothing to predict as such. Really, unsupervised learning is about detecting patterns in some dataset XX.
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Dimensionality reduction is one kind of unsupervised learning, with the explicit goal of turning high-dimensional data into lower-dimensional data.

Why do we perform dimensionality reduction?

When Features>Samples
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Why reduce dimensions? Why not use the entire data set available? Many financial applications use daily data. Daily data suffer from relatively small sample size.
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If you consider financial data analysis that covers the entire healthcare industry (665665 stocks), but only over the past quarter (6363 trading days) your optimization methods would fail.
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The failure of a model due to the large dimensions and a small number of samples is called the curse of dimensionality.
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To calculate the mean-variance portfolio you would need N(N−1)/2=220kN(N-1)/2=220k trading days.
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In this scenario traditional econometrician would insist that no such analysis can be performed on data with fewer than 665665 daily observations.
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As machine learning engineers we will intelligently compress the number of features using dimensionality reduction methods.
Sparse Feature Space
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Another reason for turning to dimensionality reduction schemes, especially when we work with high-frequency data sets, is the empty space phenomenon.
C. Dimensionality Reduction
The problem with PCAs before decision trees:
if you are predicting some decision that happens in real-life and people use a threshold on a single one of your features, then dimension reducing with PCA can only hurt performance (probably not a situation in which you'd want to use Machine Learning, really).
Continued

Financial Applications of the PCA:

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Systematic trading: construction of market-neutral portfolios with low volatility, extraction of trading signals (second eigenportfolio is market neutral).
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Systemic risk detection methods by developing new factors (e.g. M. Kritzman et. al. "Principal Components as a Measure of Systemic Risk", 2010)
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Risk management: assess sector risk exposure management of trading book or banking book portfolios.
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2D PCA for data visualization which also works well as an intermediate clustering method.
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PCA for yield curve modeling (fixed income, commodities).

PCA Portfolio Optimization

In finance, we enjoy separating the systematic components of stock returns from the company-specific, or idiosyncratic components.
The issue with the above approaches is that we can’t guarantee that the selected factors are the most statistically relevant ones to create the best portfolio.
Mean-Variance portfolio optimization seeks to minimize idiosyncratic risk εi\varepsilon_{i} by allocating capital across various assets, by doing so the only risks that remain is systematic risks, and CAPM makes the argument that the market beta βM\beta^{M} captures all this systematic risks.
D. Portfolio Management
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