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.

Sparse Causality Network Retrieval from Short Time Series

“…Therefore, a standard approach is to reduce the number of variables and lags to keep dimensionality low and estimate conditional covariances with appropriate penalizers [3,8,9,14]. An alternative approach is to invert the covariance matrix only locally on low dimensional subsets of variables selected by using information filtering networks [5][6][7] and then reconstruct the global inversion by means of the LoGo approach [4]. Let us here briefly account for these two approaches.…”

“…Because of this Local-Global construction this method is named LoGo. It has been shown that LoGo method yields to statistically significant sparse precision matrices that outperform the ones with the same sparsity computed with lasso method [4].…”

“…(1) ℓ 1 norm penalization (Glasso [14]); (2) ℓ 2 norm penalization (ridge [8]); (3) information filtering network (LoGo [4]). …”

“…Such networks are then compared with the known network of true causalities in the underlying process which is defined by the nonzero elements in the matrices (see (4)). The overlapping between the retrieved links in the inference or causality networks with the ones in the true network underlying the process is an indication of a discovery of a true causality relation.…”

“…Such models with reduced numbers of parameters are referred to in the literature as sparse models. In this paper we consider two instances of linear sparse modelling: Glasso [3] which penalizes nonzero parameters by introducing a ℓ 1 norm penalization and LoGo [4] which reduces the inference network to an O( ) number of links selected by using information filtering networks [5][6][7]. The results from these two sparse models are compared with the ℓ 2 norm penalization (nonsparse) ridge model [8,9].…”