Collaborative Hierarchical Sparse Modeling

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the sparsity-inducing property of the Lasso model, at the individual feature level, with the block-sparsity property of the group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the hierarchical Lasso, which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level but not necessarily at the lower one. Signals then share the same active groups, or classes, but not necessarily the same active set. This is very well suited for applications such as source separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the new framework and optimization approach is complemented with experimental examples and preliminary theoretical results.Comment: To appear in CISS 201

Bayesian Hierarchical Modelling for Tailoring Metric Thresholds

Software is highly contextual. While there are cross-cutting `global' lessons, individual software projects exhibit many `local' properties. This data heterogeneity makes drawing local conclusions from global data dangerous. A key research challenge is to construct locally accurate prediction models that are informed by global characteristics and data volumes. Previous work has tackled this problem using clustering and transfer learning approaches, which identify locally similar characteristics. This paper applies a simpler approach known as Bayesian hierarchical modeling. We show that hierarchical modeling supports cross-project comparisons, while preserving local context. To demonstrate the approach, we conduct a conceptual replication of an existing study on setting software metrics thresholds. Our emerging results show our hierarchical model reduces model prediction error compared to a global approach by up to 50%.Comment: Short paper, published at MSR '18: 15th International Conference on Mining Software Repositories May 28--29, 2018, Gothenburg, Swede