Learning Networked Exponential Families with Network Lasso

05/22/2019 ∙ by Alexander Jung, et al. ∙ 22

The data arising in many important big-data applications, ranging from social networks to network medicine, consist of high-dimensional data points related by an intrinsic (complex) network structure. In order to jointly leverage the information conveyed in the network structure as well as the statistical power contained in high-dimensional data points, we propose networked exponential families. We apply the network Lasso to learn networked exponential families as a probabilistic model for heterogeneous datasets with intrinsic network structure. In order to allow for accurate learning from high-dimensional data we borrow statistical strength, via the intrinsic network structure, across the dataset. The resulting method aims at regularized empirical risk minimization using the total variation of the model parameters as regularizer. This minimization problem is a non-smooth convex optimization problem which we solve using a primal-dual splitting method. This method is appealing for big data applications as it can be implemented as a highly scalable message passing algorithm.

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