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Nitanda A.,Mathematical Systems Inc.
Advances in Neural Information Processing Systems

Proximal gradient descent (PGD) and stochastic proximal gradient descent (SPGD) are popular methods for solving regularized risk minimization problems in machine learning and statistics. In this paper, we propose and analyze an accelerated variant of these methods in the mini-batch setting. This method incorporates two acceleration techniques: one is Nesterov's acceleration method, and the other is a variance reduction for the stochastic gradient. Accelerated proximal gradient descent (APG) and proximal stochastic variance reduction gradient (Prox-SVRG) are in a trade-off relationship. We show that our method, with the appropriate mini-batch size, achieves lower overall complexity than both APG and Prox-SVRG. Source

Suizu Y.,Chiyoda Corporation | Asaumi K.,Mizuho Information and Research Institute | Mochizuki S.,Mathematical Systems Inc.
Journal of the Vacuum Society of Japan

MEMS (Micro Electro Mechanical Systems) are an important technological ̂eld that is expected as a small-sized, energy-saving and high-performance key device. However, since development of MEMS requires considerable expenses and time, reduction of the testing expense, shortening of the development period and improvement of the yield ratio are expected with use of a simulator. Although leadingMEMS foundries have begun to utilize simulators made abroad, purely domestic ̀̀Computer Aided Engineering System for Micro Electro-Mechanical Systems (MemsONE)'' developed in a national project have come into use recently. Source

Iwanaga J.,Mathematical Systems Inc. | Nishimura N.,Chiyoda Corporation | Sukegawa N.,Chuo University | Takano Y.,Senshu University
Knowledge-Based Systems

This paper investigates the relationship between customers' page views (PVs) and the probabilities of their product choices on e-commerce sites. For this purpose, we create a probability table consisting of product-choice probabilities for all recency and frequency combinations of each customers' previous PVs. To reduce the estimation error when there are few training samples, we develop optimization models for estimating the product-choice probabilities that satisfy monotonicity, convexity and concavity constraints with respect to recency and frequency. Computational results demonstrate that our method has clear advantages over logistic regression and kernel-based support vector machine. © 2016. Source

Matsushita R.,Mathematical Systems Inc. | Tanaka T.,Kyoto University
Advances in Neural Information Processing Systems

We study the problem of reconstructing low-rank matrices from their noisy ob-servations. We formulate the problem in the Bayesian framework, which allows us to exploit structural properties of matrices in addition to low-rankedness, such as sparsity. We propose an efficient approximate message passing algorithm, de-rived from the belief propagation algorithm, to perform the Bayesian inference for matrix reconstruction. We have also successfully applied the proposed algorithm to a clustering problem, by reformulating it as a low-rank matrix reconstruction problem with an additional structural property. Numerical experiments show that the proposed algorithm outperforms Lloyd's K-means algorithm. Source

Yamashita H.,Mathematical Systems Inc. | Yabe H.,Tokyo University of Science
Mathematical Programming

In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. We propose primal-dual interior point methods based on the unscaled and scaled Newton methods, which correspond to the AHO, HRVW/KSH/M and NT search directions in linear SDP problems. We analyze local behavior of our proposed methods and show their local and superlinear convergence properties. © 2010 Springer and Mathematical Programming Society. Source

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