# Learning to Discover Sparse Graphical Models Source: [Learning to Discover Sparse Graphical Models]() Collection index: [llms.txt]() Data updated: 2025-10-27T07:07:31.589Z Authors: Eugene Belilovsky, Kyle Kastner, Ga\\"el Varoquaux, Matthew Blaschko Published: 2016-05-20T13:58:21.000Z ## Abstract We consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring the formulation of priors and sophisticated inference procedures. Popular methods rely on estimating a penalized maximum likelihood of the precision matrix. However, in these approaches structure recovery is an indirect consequence of the data-fit term, the penalty can be difficult to adapt for domain-specific knowledge, and the inference is computationally demanding. By contrast, it may be easier to generate training samples of data that arise from graphs with the desired structure properties. We propose here to leverage this latter source of information as training data to learn a function, parametrized by a neural network that maps empirical covariance matrices to estimated graph structures. Learning this function brings two benefits: it implicitly models the desired structure or sparsity properties to form suitable priors, and it can be tailored to the specific problem of edge structure discovery, rather than maximizing data likelihood. Applying this framework, we find our learnable graph-discovery method trained on synthetic data generalizes well: identifying relevant edges in both synthetic and real data, completely unknown at training time. We find that on genetics, brain imaging, and simulation data we obtain performance generally superior to analytical methods. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Binary graph structure recovery on Small-world (WS) binary (test)](): Binary graph structure recovery; Small-world (WS) binary (test); Avg Shortest Path Length: 1.111. - [Brain functional connectivity estimation on Brain functional connectivity (Control Group)](): Brain functional connectivity estimation; Brain functional connectivity (Control Group); Mean Spearman Correlation: 0.23. - [Brain Functional Connectivity Estimation on Autistic Group Data](): Brain functional connectivity estimation; Brain functional connectivity (Autistic Group); Mean Spearman Correlation: 0.17. - [Binary Graph Structure Recovery on Scale-free BA (test)](): Binary graph structure recovery; Scale-free BA binary (test); KS Test Score: 68.32. - [Graph Reconstruction on Scale-free BA (test)](): Graph Reconstruction; Scale-free BA (test); GMSE: 0.8423. - [Graph Reconstruction on Random sparse (ER) (test)](): Graph Reconstruction; Random sparse (ER) (test); GMSE: 0.8179. - [Graph Reconstruction on Community SBM (test)](): Graph Reconstruction; Community SBM (test); GMSE: 0.8931. - [Graph Reconstruction on Small-world (WS) (test)](): Graph Reconstruction; Small-world (WS) (test); GMSE: 0.8498. - [Binary graph structure recovery on Community (SBM) binary (test)](): Binary graph structure recovery; Community (SBM) binary (test); Community Score: 34.3. ## Original sources and implementation [Original paper]() [PDF]()