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Learning to Discover Sparse Graphical Models
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
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