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Neural Graph Revealers
Harsh Shrivastava, Urszula Chajewska
Sparse graph recovery methods work well where the data follows their assumptions but often they are not designed for doing downstream probabilistic queries. This limits their adoption to only identifying connections among the input variables. On the other hand, the Probabilistic Graphical Models (PGMs) assume an underlying base graph between variables and learns a distribution over them. PGM design choices are carefully made such that the inference \& sampling algorithms are efficient. This brings in certain restrictions and often simplifying assumptions. In this work, we propose Neural Graph Revealers (NGRs), that are an attempt to efficiently merge the sparse graph recovery methods with PGMs into a single flow. The problem setting consists of an input data X with D features and M samples and the task is to recover a sparse graph showing connection between the features and jointly learn a probability distribution over them. NGRs view the neural networks as a `glass box' or more specifically as a multitask learning framework. We introduce `Graph-constrained path norm' that NGRs leverage to learn a graphical model that captures complex non-linear functional dependencies between the features in the form of an undirected sparse graph. Furthermore, NGRs can handle multimodal inputs like images, text, categorical data, embeddings etc. which is not straightforward to incorporate in the existing methods. We show experimental results of doing sparse graph recovery and probabilistic inference on data from Gaussian graphical models and a multimodal infant mortality dataset by Centers for Disease Control and Prevention.
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