Parsimonious modeling with Information Filtering Networks

TL;DR

This paper presents a computationally efficient method for constructing sparse probabilistic models using Information Filtering Networks, suitable for high-dimensional, noisy, and short time-series data, with applications in finance.

Contribution

The paper introduces a novel local inverse covariance estimation method based on Information Filtering Networks, improving efficiency and robustness over existing approaches like Glasso.

Findings

Method is faster than Glasso with comparable or better performance.

Produces sparser models suitable for high-dimensional data.

Effective in financial forecasting, stress testing, and risk allocation.

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 sub-parts 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 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 datasets with large numbers of variables. Examples of practical application for forecasting, stress testing and risk allocation in financial systems are also provided.