Missing Values in Multiple Joint Inference of Gaussian Graphical Models

Real-world phenomena are often not fully measured or completely observable, raising the so-called missing data problem. As a consequence, the need of developing ad-hoc techniques that cope with such issue arises in many inference contexts. In this paper, we focus on the inference of Gaussian Graphical Models (GGMs) from multiple input datasets having complex relationships (e.g. multi-class or temporal). We propose a method that generalises state-of-the-art approaches to the inference of both multi-class and temporal GGMs while naturally dealing with two types of missing data: partial and latent. Synthetic experiments show that our performance is better than state-of-the-art. In particular, we compared results with single network inference methods that suitably deal with missing data, and multiple joint network inference methods coupled with standard pre-processing techniques (e.g. imputing). When dealing with fully observed datasets our method analytically reduces to state-of-the-art approaches providing a good alternative as our implementation reaches convergence in shorter or comparable time. Finally, we show that properly addressing the missing data problem in a multi-class real-world example, allows us to discover interesting varying patterns.