Present expectations for artificial intelligence rely on the idea that the vast quantity of data collected from real systems could be used to train ‘intelligent’ machines that will become capable of modelling and predicting the behavior of these systems [1]. However, in complex systems the collective dynamics is the emerging effect of large number of variables where each variable can be of critical importance for the overall system behavior [2]. This makes complex systems, such as markets or societies, hard to model, predict and understand. Indeed, there are many potentially important variables but there is only a limited number of observations available.  Machines can process very large amounts of data, however predictive models that contain a large number of variables also depend on a larger number of parameters. Indeed, the number of model-parameters typically increases with the square of the number of variables or faster, conversely information about the system increases at most linearly with the number of observed variables.  

In this lecture I will show that the way forward to the solution to this challenge is to use sparse models where the number of parameters to be ‘learned’ by the machines scales, at most, linearly with the number of variables. I will first discuss some established methodologies that implicitly or explicitly enforce sparsity into models. I will then introduce a novel approach that makes direct use of network filtering methods [3-6] to impose sparsity in probabilistic models [7,8]. I will finally show how, by learning these models, machines can make reliable forecasts even in practical cases where uncertainty is present, statistical stability is poor, time series are short and no reliable training sets are available [9].


  1. Nilsson, Nils J. Principles of artificial intelligence. Morgan Kaufmann,2014.
  2. Aste, Tomaso, and Tiziana Di Matteo. "Introduction to Complex and Econophysics Systems: A navigation map." Complex physical, biophysical and econophysical systems(2010): 1-35.
  3. R. N. Mantegna., Eur. Phys. J. B 11 (1999) 193-197.
  4. T. Aste, T. Di Matteo, S. T. Hyde, Physica A 346 (2005) 20.
  5. M. Tumminello, T. Aste, T. Di Matteo, R. N. Mantegna, PNAS 102, n. 30 (2005) 10421.
  6. W.-M. Song, T. Di Matteo, and T. Aste, PLoS ONE 7 (2012) e31929.
  7. Massara, Guido Previde, Tiziana Di Matteo, and Tomaso Aste. "Network filtering for big data: triangulated maximally filtered graph." Journal of complex Networks 5, no. 2 (2016): 161-178.
  8. Aste, Tomaso, and T. Di Matteo. "Causality network retrieval from short time series." arXiv preprint arXiv:1706.01954(2017).
  9. Wolfram Barfuss, Guido Previde Massara, T. Di Matteo, T. Aste, Phys.Rev. E 94 (2016) 062306.