Wenjie Zheng

Wenjie Zheng

Compartmental epidemic models are among the most popular ones in epidemiology. For the parameters (e.g., the transmission rate) characterizing these models, the majority of researchers simplify them as constants, while some others manage to detect their continuous variations. In this paper, we aim at capturing, on the other hand, discontinuous variations, which better describe the impact of many noteworthy events, such as city lockdowns, the opening of field hospitals, and the mutation of the virus, whose effect should be instant. To achieve this, we balance the model's likelihood by total variation, which regulates the temporal variations of the model parameters. To infer these parameters, instead of using Monte Carlo methods, we design a novel yet straightforward optimization algorithm, dubbed Iterated Nelder--Mead, which repeatedly applies the Nelder--Mead algorithm. Experiments conducted on the simulated data demonstrate that our approach can reproduce these discontinuities and precisely depict the epidemics.

Wenjie Zheng, Aurélien Bellet, Patrick Gallinari

We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank structure of its updates to achieve efficiency in time, memory and communication usage. The step at the heart of DFW-Trace is solved approximately using a distributed version of the power method. We provide a theoretical analysis of the convergence of DFW-Trace, showing that we can ensure sublinear convergence in expectation to an optimal solution with few power iterations per epoch. We implement DFW-Trace in the Apache Spark distributed programming framework and validate the usefulness of our approach on synthetic and real data, including the ImageNet dataset with high-dimensional features extracted from a deep neural network.

Wenjie Zheng

Decentralized recommender system does not rely on the central service provider, and the users can keep the ownership of their ratings. This article brings the theoretically well-studied matrix factorization method into the decentralized recommender system, where the formerly prevalent algorithms are heuristic and hence lack of theoretical guarantee. Our preliminary simulation results show that this method is promising.