42 research outputs found
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