Learning Positive Functions with Pseudo Mirror Descent
Yingxiang Yang · Haoxiang Wang · Negar Kiyavash · Niao He

Tue Dec 10th 05:10 -- 05:15 PM @ West Exhibition Hall B

The nonparametric learning of positive-valued functions appears widely in machine learning, especially in the context of estimating intensity functions of point processes. Yet, existing approaches either require computing expensive projections or semidefinite relaxations, or lack convexity and theoretical guarantees after introducing nonlinear link functions. In this paper, we propose a novel algorithm, pseudo mirror descent, that performs efficient estimation of positive functions within a Hilbert space without expensive projections. The algorithm guarantees positivity by performing mirror descent with an appropriately selected Bregman divergence, and a pseudo-gradient is adopted to speed up the gradient evaluation procedure in practice. We analyze both asymptotic and nonasymptotic convergence of the algorithm. Through simulations, we show that pseudo mirror descent outperforms the state-of-the-art benchmarks for learning intensities of Poisson and multivariate Hawkes processes, in terms of both computational efficiency and accuracy.

Author Information

Yingxiang Yang (University of Illinois at Urbana-Champaign)

About me: I'm a graduate student in ECE of UIUC expecting my degree late 2019. My current research interests include machine learning, and its intersection with optimization. In my spare time, I also like to play music and trade/watch the markets. About my research: My recent projects mainly focus on learning point processes, including non-homogeneous Poisson processes, and multivariate Hawkes processes, using various nonparametric methods. I'm also working on entry-level deep learning projects including its application on Bayesian inference and its application to point processes to study diffusion on large networks. Programming skills: Most of the simulations involved in my research are MATLAB code, until recently, when I started to program my research in python.

Haoxiang Wang (University of Illinois, Urbana-Champaign)

1st year PhD student working on machine learning from UIUC.

Negar Kiyavash (EPFL)
Niao He (UIUC)

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