Machine Learning: Bayesian Networks

Last week, I introduced the topic of Machine learning and how it was possible to train algorithms to learn from a set of data. A common technique used for supervised learning is a bayesian network. Simply, a tool to analyse large sets of multivariate probability models to discern relationships between models. What is most interesting about bayesian networks is that it combines both quantitative analysis and user intuition to "learn". These may come in the form of graphical representations such as the network seen below.

Although it is not often accurate to model stock price behaviour in this way, for the sake of simplicity, let us consider the network below. Each nodes represents a random variable. The arrow pointed from stock 1 to stock 2 and stock 4 essentially mean that stock 2 and 4 are conditionally independent given stock 1. Given a movement in the price of Stock1 (increase or decrease in price for example), if the price of Stock2 moves, it does not tell us anything about how the price of Stock4 moves. It is easy to see how extending the model to only 5 stocks starts creating fairly complex networks.



In recent years, the quantitative hedge fund industry has shifted away from using traditional predictive tools in favour for adopting more complex models such as bayesian networks and other machine learning algorithms in the hope of achieving a deeper understanding of inter market relationships. They then use these patterns to trade in inefficient financial markets. The main goal of algorithmic trading is to find statistical anomalies in the data and determine profitable ways of exploiting them. It has become increasingly difficult in the past decade however, as the rise in algorithmic trading participants have removed many of these market anomalies, making many of them unprofitable.

The potential of ML algorithms such as bayesian networks in the finance industry extends much beyond this particular example. It can be recorded to detect fraud, assist in risk management and even create models to price insurance policies.

Writing References:
https://kuscholarworks.ku.edu/bitstream/handle/1808/161/CF99.pdf;jsessionid=8EE7C78BF26BD0F349409F5AEFFE91EE?sequence=1
https://www.ics.uci.edu/~rickl/courses/cs-171/cs171-lecture-slides/cs-171-17-BayesianNetworks.pdf

Image Reference:
http://www.qminitiative.org/UserFiles/files/S_Clémençon_ML.pdf