Abstract: We develop a new scalable method for matrix completion via nuclear-norm regularization and alternating least squares. The algorithm has an EM flavor, which dramatically reduces the computational cost per iteration at the cost of more iterations. *joint work with Rahul Mazumder, Jason Lee and Reza Zadeh.

Abstract: Low-rank matrix estimation plays a key role in many scientific and engineering tasks, including collaborative filtering and image denoising. Low-rank procedures are often motivated by the statistical model where we observe a noisy matrix drawn from some distribution with expectation assumed to have a low-rank representation; the statistical goal is then to recover the signal from the noisy data. Given this setup, we develop a framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple parametric bootstrap. Effectively, our procedure seeks an autoencoding basis for the observed matrix that is robust with respect to the specified noise model. In the simplest case, with an isotropic noise model, our procedure is equivalent to a classical singular value shrinkage estimator. For non-isotropic noise models, however, our method does not reduce to singular value shrinkage, and instead yields new estimators that perform well in experiments. Moreover, by iterating our stable autoencoding scheme, we can automatically generate low-rank estimates without specifying the target rank as a tuning parameter.

Abstract: The Behance social network allows professionals of diverse artistic disciplines to exhibit their work and connect amongst each other. We investigate the network properties of the UX/UI designer subgraph. Considering the subgraph is motivated by the idea that professionals in the same discipline are more likely to give a realistic assessment of a colleague's work. We therefore developed a metric to assess the in uence and importance of a specic member of the community based on structural properties of the subgraph and additional measures of prestige. For that purpose, we identied appreciations as a useful measure to include in a weighted PageRank algorithm, as it adds a notion of perceived quality of the work in the artist's portfolio to the ranking, which is not contained in the structural information of the graph. With this weighted PageRank, we identied locations that have a high density of in uential UX/UI designers.

Abstract: The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istc-bigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.