Toward a generic representation of random variables for machine learning

• Introduce a non-parametric representation of i.i.d. stochastic processes.
• The presented pre-processing boosts performance of algorithms.
• Clusterings of financial time series become more stable.
• Prices clustering allows one to recover idiosyncratic risk.
• Experiments results available at www.datagrapple.com.

This paper presents a pre-processing and a distance which improve the performance of machine learning algorithms working on independent and identically distributed stochastic processes. We introduce a novel non-parametric approach to represent random variables which splits apart dependency and distribution without losing any information. We also propound an associated metric leveraging this representation and its statistical estimate. Besides experiments on synthetic datasets, the benefits of our contribution is illustrated through the example of clustering financial time series, for instance prices from the credit default swaps market. Results are available on the website http://www.datagrapple.com and an IPython Notebook tutorial is available at http://www.datagrapple.com/Tech for reproducible research.

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