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Xiaozhao Zhao

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2 papers

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AAAI Conference 2016 Conference Paper

Iterative Project Quasi-Newton Algorithm for Training RBM

Shuai Mi
Xiaozhao Zhao
Yuexian Hou
Peng Zhang
Wenjie Li
Dawei Song

The restricted Boltzmann machine (RBM) has been used as building blocks for many successful deep learning models, e. g. , deep belief networks (DBN) and deep Boltzmann machine (DBM) etc. The training of RBM can be extremely slow in pathological regions. The second order optimization methods, such as quasi-Newton methods, were proposed to deal with this problem. However, the non-convexity results in many obstructions for training RBM, including the infeasibility of applying second order optimization methods. In order to overcome this obstruction, we introduce an em-like iterative project quasi-Newton (IPQN) algorithm. Speciﬁcally, we iteratively perform the sampling procedure where it is not necessary to update parameters, and the sub-training procedure that is convex. In sub-training procedures, we apply quasi-Newton methods to deal with the pathological problem. We further show that Newton’s method turns out to be a good approximation of the natural gradient (NG) method in RBM training. We evaluate IPQN in a series of density estimation experiments on the artiﬁcial dataset and the MNIST digit dataset. Experimental results indicate that IPQN achieves an improved convergent performance over the traditional CD method.

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IJCAI Conference 2013 Conference Paper

A Global Constrained Optimization Method for Designing Road Networks with Small Diameters

Teng Ma
Yuexian Hou
Xiaozhao Zhao
Dawei Song

The road network design problem is to optimize the road network by selecting paths to improve or adding paths in the existing road network, under certain constraints, e. g. , the weighted sum of modifying costs. Since its multi-objective nature, the road network design problem is often challenging for designers. Empirically, the smaller diameter a road network has, the more connected and efficient the road network is. Based on this observation, we propose a set of constrained convex models for designing road networks with small diameters. To be specific, we theoretically prove that the diameter of the road network, which is evaluated w. r. t the travel times in the network, can be bounded by the algebraic connectivity in spectral graph theory since that the upper and lower bounds of diameter are inversely proportional to algebraic connectivity. Then we can focus on increasing the algebraic connectivity instead of reducing the network diameter, under the budget constraints. The above formulation leads to a semi-definite program, in which we can get its global solution easily. Then, we present some simulation experiments to show the correctness of our method. At last, we compare our method with an existing method based on the genetic algorithm.

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