Hybrid PDE solver for data-driven problems and modern branching

The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations about the parallelization and scalability of realistic problems are often critical enough to warrant acknowledgement in the modelling phase. The purpose of this paper is to spread awareness of the Probabilistic Domain Decomposition (PDD) method, a fresh approach to the parallelization of PDEs with excellent scalability properties. The idea exploits the stochastic representation of the PDE and its approximation via Monte Carlo in combination with deterministic high-performance PDE solvers. We describe the ingredients of PDD and its applicability in the scope of data science. In particular, we highlight recent advances in stochastic representations for nonlinear PDEs using branching diffusions, which have significantly broadened the scope of PDD. We envision this work as a dictionary giving large-scale PDE practitioners references on the very latest algorithms and techniques of a non-standard, yet highly parallelizable, methodology at the interface of deterministic and probabilistic numerical methods. We close this work with an invitation to the fully nonlinear case and open research questions.Comment: 23 pages, 7 figures; Final SMUR version; To appear in the European Journal of Applied Mathematics (EJAM

Role of Matrix Factorization Model in Collaborative Filtering Algorithm: A Survey

Recommendation Systems apply Information Retrieval techniques to select the online information relevant to a given user. Collaborative Filtering is currently most widely used approach to build Recommendation System. CF techniques uses the user behavior in form of user item ratings as their information source for prediction. There are major challenges like sparsity of rating matrix and growing nature of data which is faced by CF algorithms. These challenges are been well taken care by Matrix Factorization. In this paper we attempt to present an overview on the role of different MF model to address the challenges of CF algorithms, which can be served as a roadmap for research in this area.Comment: 8 pages, 1 figure in IJAFRC, Vol.1, Issue 12, December 201

Detection of Review Abuse via Semi-Supervised Binary Multi-Target Tensor Decomposition

Product reviews and ratings on e-commerce websites provide customers with detailed insights about various aspects of the product such as quality, usefulness, etc. Since they influence customers' buying decisions, product reviews have become a fertile ground for abuse by sellers (colluding with reviewers) to promote their own products or to tarnish the reputation of competitor's products. In this paper, our focus is on detecting such abusive entities (both sellers and reviewers) by applying tensor decomposition on the product reviews data. While tensor decomposition is mostly unsupervised, we formulate our problem as a semi-supervised binary multi-target tensor decomposition, to take advantage of currently known abusive entities. We empirically show that our multi-target semi-supervised model achieves higher precision and recall in detecting abusive entities as compared to unsupervised techniques. Finally, we show that our proposed stochastic partial natural gradient inference for our model empirically achieves faster convergence than stochastic gradient and Online-EM with sufficient statistics.Comment: Accepted to the 25th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2019. Contains supplementary material. arXiv admin note: text overlap with arXiv:1804.0383