arXiv subjects

Takashi Shinzato

Publications and source records attributed to Takashi Shinzato.

21 records · Page 2Linked to original sources

arXiv2010

Belief Propagation Algorithm for Portfolio Optimization Problems

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. Mézard [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

q-fin.PM↗

arXiv2008

Learning of correlated patterns by simple perceptrons

Learning behavior of simple perceptrons is analyzed for a teacher-student scenario in which output labels are provided by a teacher network for a set of possibly correlated input patterns, and such that teacher and student networks are of the same type. Our main concern is the effect of statistical correlations among the input patterns on learning performance. For this purpose, we extend to the teacher-student scenario a methodology for analyzing randomly labeled patterns recently developed in {\em J. Phys. A: Math. Theor.} {\bf 41}, 324013 (2008). This methodology is used for analyzing situations in which orthogonality of the input patterns is enhanced in order to optimize the learning performance.

cond-mat.dis-nn↗

arXiv2007

Perceptron capacity revisited: classification ability for correlated patterns

In this paper, we address the problem of how many randomly labeled patterns can be correctly classified by a single-layer perceptron when the patterns are correlated with each other. In order to solve this problem, two analytical schemes are developed based on the replica method and Thouless-Anderson-Palmer (TAP) approach by utilizing an integral formula concerning random rectangular matrices. The validity and relevance of the developed methodologies are shown for one known result and two example problems. A message-passing algorithm to perform the TAP scheme is also presented.

cond-mat.dis-nn↗