“If we think about the quantitative side, I probably don’t have to convince you that probability theory and mathematical statistics are both fundamental in this area. You cannot really do quantitative finance without basing it in some way in probability and statistics.”

In this MarketsWiki Education presentation, Pierre Nyquist, a professor at the Royal Institute of Technology (KTH) in Stockholm, decided to answer: How can mathematical statistics and computer intensive methods be integrated with advances in technology?

Nyquist emphasized three terms: mathematical statistics, computer-intensive methods, and machine learning, and said that if you remember nothing else, recognize that they are intrinsically connected. You can’t do machine learning without statistics – it’s build on statistical principles. If you want to do real statistics you have to use computer-intensive methods, and if you want to do machine learning you have to use computer intensive methods. Research into machine learning should include research into these other areas as well.

He said there is a focus now on the need for efficient computational methods and a mathematical foundation for machine learning, and the key phrase is “stochastic numerical methods.”

Europe is way behind in machine learning, he said.  But KTH and others are doing research into statistical learning and machine learning where they can actually provide something that has an impact on the financial industry.

One use is risk calculation for portfolio optimization. For example, if you have a large pool of assets and you want to construct an optimal portfolio from those assets, you need to somehow measure what is an optimal portfolio.

The methods to do this are difficult to train computers in, however, and they cost a lot, and take a lot of time, which is at a premium in the trading world. So there is a need for speed but without the loss of accuracy. Stochastic numerical methods can be useful in this respect.

We have all these wonderful methods, Nyquist said, but we are not always sure why they work and when they work. A machine learning algorithm can run for a while and be fine, and then suddenly you hit a scenario where it no longer works. And it’s better to know why it no longer works and how you can fix it.

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