Parsimonious modeling with Information Filtering Networks
This method addresses the challenge of handling big datasets with many variables in fields like finance, offering incremental improvements in efficiency and robustness for tasks such as forecasting and risk allocation.
The authors tackled the problem of constructing parsimonious probabilistic models for high-dimensional, noisy data by introducing a method using Information Filtering Networks to estimate sparse inverse covariance efficiently. They demonstrated that this approach is computationally more efficient than state-of-the-art methods like Glasso, producing models with equivalent or better performance and sparser structures in a fraction of the time.
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.