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. M\'ezard [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.Comment: 5 pages, 2 figures, to submit to EP

Bayesian Reconstruction of Missing Observations

We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated probabilistically using a Bayesian treatment. In this paper, we address the framework of Bayesian reconstruction and its application to the traffic data reconstruction problem in the field of traffic engineering. In the latter part of this paper, we describe the evaluation of the statistical performance of our Bayesian traffic reconstruction model using a statistical mechanical approach and clarify its statistical behavior

Free Energy Evaluation Using Marginalized Annealed Importance Sampling

The evaluation of the free energy of a stochastic model is considered to be a significant issue in various fields of physics and machine learning. However, the exact free energy evaluation is computationally infeasible because it includes an intractable partition function. Annealed importance sampling (AIS) is a type of importance sampling based on the Markov chain Monte Carlo method, which is similar to a simulated annealing, and can effectively approximate the free energy. This study proposes a new AIS-based approach, referred to as marginalized AIS (mAIS). The statistical efficiency of mAIS is investigated in detail based on a theoretical and numerical perspectives. Based on the investigation, it has been proved that mAIS is more effective than AIS under a certain condition