arXiv subjects

Zebang Shen

Publications and source records attributed to Zebang Shen.

39 records · Page 3Linked to original sources

arXiv2017

Riemannian Tensor Completion with Side Information

By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily accessible side information, due to their format mismatch. Consequently, there is still room for improvement in such methods. To fill the gap, in this paper, a novel Riemannian model is proposed to organically integrate the original model and the side information by overcoming their inconsistency. For this particular model, an efficient Riemannian conjugate gradient descent solver is devised based on a new metric that captures the curvature of the objective.Numerical experiments suggest that our solver is more accurate than the state-of-the-art without compromising the efficiency.

stat.ML↗

arXiv2016

Accelerated Variance Reduced Block Coordinate Descent

Algorithms with fast convergence, small number of data access, and low per-iteration complexity are particularly favorable in the big data era, due to the demand for obtaining \emph{highly accurate solutions} to problems with \emph{a large number of samples} in \emph{ultra-high} dimensional space. Existing algorithms lack at least one of these qualities, and thus are inefficient in handling such big data challenge. In this paper, we propose a method enjoying all these merits with an accelerated convergence rate $O(\frac{1}{k^2})$. Empirical studies on large scale datasets with more than one million features are conducted to show the effectiveness of our methods in practice.

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arXiv2014

Kinetic Energy Plus Penalty Functions for Sparse Estimation

In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct the KEP function by using the concave conjugate of a $χ^2$-distance function and present several novel insights into the KEP function with $q=1$. In particular, we derive a thresholding operator based on the KEP function, and prove its mathematical properties and asymptotic properties in sparsity modeling. Moreover, we show that a coordinate descent algorithm is especially appropriate for the KEP function. Additionally, we discuss the relationship of KEP with the penalty functions $\ell_{1/2}$ and MCP. The theoretical and empirical analysis validates that the KEP function is effective and efficient in high-dimensional data modeling.

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