Sparse Network Inference using the k-Support Norm

Network inference is an important problem in a variety of domains. In computational biology, gene interaction networks can be learned using the mRNA expression levels of genes. These networks capture how genes influence each other and can be used to identify potential malfunctions. In the context of social network analysis, network inference refers to the problem of inferring underlying network of influence, given time series data of when users performed certain actions (e.g., post, retweet, share). These networks capture the dynamics of influence and information diffusion. In this position paper, we discuss various strategies to learn sparse networks with the help of the k-support norm, which corresponds to the tightest convex relaxation of sparsity combined with an l2 penalty. We also discuss specific applications of these strategies to the domains of computational biology and social network analysis.