title: Parsimonious modeling with information filtering networks.
abstract: We introduce a methodology to construct parsimonious probabilistic models. This method makes use of information filtering networks to produce a robust estimate of the global sparse inverse covariance from a simple sum of local inverse covariances computed on small subparts of the network. Being based on local and low-dimensional inversions, this method is computationally very efficient and statistically robust, even for the estimation of inverse covariance of high-dimensional, noisy, and short time series. Applied to financial data our method results are computationally more efficient than state-of-the-art methodologies such as Glasso producing, in a fraction of the computation time, models that can have equivalent or better performances but with a sparser inference structure. We also discuss performances with sparse factor models where we notice that relative performances decrease with the number of factors. The local nature of this approach allows us to perform computations in parallel and provides a tool for dynamical adaptation by partial updating when the properties of some variables change without the need of recomputing the whole model. This makes this approach particularly suitable to handle big data sets with large numbers of variables. Examples of practical application for forecasting, stress testing, and risk allocation in financial systems are also provided.
authors.affiliation: Department of Physics, FAU Erlangen-Nürnberg, Nägelsbachstrasse 49b, 91052 Erlangen, Germany.
authors.forename: Wolfram
authors.initials: W
authors.lastname: Barfuss
authors.affiliation: Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, United Kingdom.
authors.forename: Guido Previde
authors.initials: GP
authors.lastname: Massara
authors.affiliation: Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, United Kingdom.|Department of Mathematics, King's College London, The Strand, London, WC2R 2LS, United Kingdom.|Systemic Risk Centre, London School of Economics and Political Sciences, London, WC2A2AE, United Kingdom.
authors.forename: T
authors.initials: T
authors.lastname: Di Matteo
authors.affiliation: Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, United Kingdom.|Systemic Risk Centre, London School of Economics and Political Sciences, London, WC2A2AE, United Kingdom.
authors.forename: Tomaso
authors.initials: T
authors.lastname: Aste