The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi-Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper, we propose a stochastic quasi-Newton method that is efficient, robust and scalable. It employs the classical BFGS update formula in its limited memory form, and is based on the observation that it is beneficial to collect curvature information pointwise, and at regular intervals, through (sub-sampled) Hessian-vector products. This technique differs from the classical approach that would compute differences of gradients at every iteration, and where controlling the quality of the curvature estimates can be difficult. We present numerical results on problems arising in machine learning that suggest that the proposed method shows much promise.

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Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback-Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton and quasi-Newton methods. We compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.

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The amount of content on online music streaming platforms is immense, and most users only access a tiny fraction of this content. Recommender systems are the application of choice to open up the collection to these users. Collaborative filtering has the disadvantage that it relies on explicit ratings, which are often unavailable, and generally disregards the temporal nature of music consumption. On the other hand, item co-occurrence algorithms, such as the recently introduced word2vec-based recommenders, are typically left without an effective user representation. In this paper, we present a new approach to model users through recurrent neural networks by sequentially processing consumed items, represented by any type of embeddings and other context features. This way we obtain semantically rich user representations, which capture a user's musical taste over time. Our experimental analysis on large-scale user data shows that our model can be used to predict future songs a user will likely listen to, both in the short and long term