arXiv subjects

Kazuyuki Tanaka

Publications and source records attributed to Kazuyuki Tanaka.

At least 37 records · Page 2Linked to original sources

arXiv2019

Dynamics of Order Parameters of Non-stoquastic Hamiltonians in the Adaptive Quantum Monte Carlo Method

We derive macroscopically deterministic flow equations with regard to the order parameters of the ferromagnetic $p$-spin model with infinite-range interactions. The $p$-spin model has a first-order phase transition for $p>2$. In the case of $p\geq5$ ,the $p$-spin model with anti-ferromagnetic XX interaction has a second-order phase transition in a certain region. In this case, however, the model becomes a non-stoqustic Hamiltonian, resulting in a negative sign problem. To simulate the $p$-spin model with anti-ferromagnetic XX interaction, we utilize the adaptive quantum Monte Carlo method. By using this method, we can regard the effect of the anti-ferromagnetic XX interaction as fluctuations of the transverse magnetic field. A previous study derived deterministic flow equations of the order parameters in the quantum Monte Carlo method. In this study, we derive macroscopically deterministic flow equations for the magnetization and transverse magnetization from the master equation in the adaptive quantum Monte Carlo method. Under the Suzuki-Trotter decomposition, we consider the Glauber-type stochastic process. We solve these differential equations by using the Runge-Kutta method and verify that these results are consistent with the saddle-point solution of mean-field theory. Finally, we analyze the stability of the equilibrium solutions obtained by the differential equations.

cond-mat.stat-mech↗

arXiv2018

EigenKernel - A middleware for parallel generalized eigenvalue solvers to attain high scalability and usability

An open-source middleware EigenKernel was developed for use with parallel generalized eigenvalue solvers or large-scale electronic state calculation to attain high scalability and usability. The middleware enables the users to choose the optimal solver, among the three parallel eigenvalue libraries of ScaLAPACK, ELPA, EigenExa and hybrid solvers constructed from them, according to the problem specification and the target architecture. The benchmark was carried out on the Oakforest-PACS supercomputer and reveals that ELPA, EigenExa and their hybrid solvers show better performance, when compared with pure ScaLAPACK solvers. The benchmark on the K computer is also used for discussion. In addition, a preliminary research for the performance prediction was investigated, so as to predict the elapsed time T as the function of the number of used nodes P (T=T(P)). The prediction is based on Bayesian inference using the Markov Chain Monte Carlo (MCMC) method and the test calculation indicates that the method is applicable not only to performance interpolation but also to extrapolation. Such a middleware is of crucial importance for application-algorithm-architecture co-design among the current, next-generation (exascale), and future-generation (post-Moore era) supercomputers.

physics.comp-ph↗

arXiv2018

Perturbative Interpretation of Adaptive Thouless-Anderson-Palmer Free Energy

In conventional well-known derivation methods for the adaptive Thouless-Anderson-Palmer (TAP) free energy, special assumptions that are difficult to mathematically justify except in some mean-field models, must be made. Here, we present a new adaptive TAP free energy derivation method. Using this derivation technique, without any special assumptions, the adaptive TAP free energy can be simply obtained as a high-temperature expansion of the Gibbs free energy.

cond-mat.dis-nn↗

arXiv2018

Momentum-Space Renormalization Group Transformation in Bayesian Image Modeling by Gaussian Graphical Model

A new Bayesian modeling method is proposed by combining the maximization of the marginal likelihood with a momentum-space renormalization group transformation for Gaussian graphical models. Moreover, we present a scheme for computint the statistical averages of hyperparameters and mean square errors in our proposed method based on a momentumspace renormalization transformation.

stat.ML↗

arXiv2018

Statistical-mechanical analysis of compressed sensing for Hamiltonian estimation of Ising spin glass

Several powerful machines, such as the D-Wave 2000Q, dedicated to solving combinatorial optimization problems through the Ising-model formulation have been developed. To input problems into the machines, the unknown parameters on the Ising model must be determined, and this is necessarily a nontrivial task. It could be beneficial to construct a method to estimate the parameters of the Ising model from several pairs of values of the energy and spin configurations. In the present paper, we propose a simple method employing the $L_1$-norm minimization, which is based on the concept of the compressed sensing. Moreover, we analyze the typical performance of our proposed method of the Hamiltonian estimation by using the replica method. We also compare our analytical results through several numerical experiments using the alternating direction method of multipliers.

cond-mat.stat-mech↗

arXiv2017

Susceptibility Propagation by Using Diagonal Consistency

A susceptibility propagation that is constructed by combining a belief propagation and a linear response method is used for approximate computation for Markov random fields. Herein, we formulate a new, improved susceptibility propagation by using the concept of a diagonal matching method that is based on mean-field approaches to inverse Ising problems. The proposed susceptibility propagation is robust for various network structures, and it is reduced to the ordinary susceptibility propagation and to the adaptive Thouless-Anderson-Palmer equation in special cases.

cond-mat.stat-mech↗

arXiv2017

Deep Neural Network Detects Quantum Phase Transition

We detect the quantum phase transition of a quantum many-body system by mapping the observed results of the quantum state onto a neural network. In the present study, we utilized the simplest case of a quantum many-body system, namely a one-dimensional chain of Ising spins with the transverse Ising model. We prepared several spin configurations, which were obtained using repeated observations of the model for a particular strength of the transverse field, as input data for the neural network. Although the proposed method can be employed using experimental observations of quantum many-body systems, we tested our technique with spin configurations generated by a quantum Monte Carlo simulation without initial relaxation. The neural network successfully classified the strength of transverse field only from the spin configurations, leading to consistent estimations of the critical point of our model $Γ_c =J$.

cond-mat.stat-mech↗

arXiv2017

An extension of estimation of critical points in ground state for random spin systems

Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten- sion of the approaches on the phase transition in spin glasses is demonstrated. To validate our extension, we compared our estimates on the critical points with the existing numerical results.

cond-mat.dis-nn↗

arXiv2016

Community Detection Algorithm Combining Stochastic Block Model and Attribute Data Clustering

We propose a new algorithm to detect the community structure in a network that utilizes both the network structure and vertex attribute data. Suppose we have the network structure together with the vertex attribute data, that is, the information assigned to each vertex associated with the community to which it belongs. The problem addressed this paper is the detection of the community structure from the information of both the network structure and the vertex attribute data. Our approach is based on the Bayesian approach that models the posterior probability distribution of the community labels. The detection of the community structure in our method is achieved by using belief propagation and an EM algorithm. We numerically verified the performance of our method using computer-generated networks and real-world networks.

cs.SI↗

arXiv2015

Statistical Analysis of Loopy Belief Propagation in Random Fields

Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched average of LBP in random fields by using the replica cluster variation method. The proposed analytical method is applicable to general pair-wise MRFs with random fields whose distributions differ from each other and can give the quenched averages of the Bethe free energies over random fields, which are consistent with numerical results. The order of its computational cost is equivalent to that of standard LBP. In the latter part of this paper, we describe the application of the proposed method to Bayesian image restoration, in which we observed that our theoretical results are in good agreement with the numerical results for natural images.

stat.ML↗

arXiv2015

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.

stat.ML↗

arXiv2015

Inverse Renormalization Group Transformation in Bayesian Image Segmentations

A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation with an inverse real space renormalization group transformation to reduce the computational time. In results of our experiment, we observe that the proposed method can reduce the computational time to less than one-tenth of that taken by conventional Bayesian approaches.

cs.CV↗

arXiv2014

Commuting Quantum Circuits with Few Outputs are Unlikely to be Classically Simulatable

We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an exponentially small additive error in classical polynomial time. First, we show that there exists a commuting quantum circuit that is not classically simulatable unless the polynomial hierarchy collapses to the third level. This is the first formal evidence that a commuting quantum circuit is not classically simulatable even when the number of output qubits is exponentially small. Then, we consider a generalized version of the circuit and clarify the condition under which it is classically simulatable. Lastly, we apply the argument for the above evidence to Clifford circuits in a similar setting and provide evidence that such a circuit augmented by a depth-1 non-Clifford layer is not classically simulatable. These results reveal subtle differences between quantum and classical computation.

quant-ph↗

arXiv2014

Bayesian image segmentations by Potts prior and loopy belief propagation

This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in LBP's for Potts models influence our hyperparameter estimation procedures.

cs.CV↗

arXiv2014

Composite Likelihood Estimation for Restricted Boltzmann machines

Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood estimation which are higher-order generalizations of the maximum pseudo-likelihood estimation. In this paper, we propose a composite likelihood method and investigate its property. Furthermore, we apply our composite likelihood method to restricted Boltzmann machines.

cs.LG↗

arXiv2013

Traffic data reconstruction based on Markov random field modeling

We consider the traffic data reconstruction problem. Suppose we have the traffic data of an entire city that are incomplete because some road data are unobserved. The problem is to reconstruct the unobserved parts of the data. In this paper, we propose a new method to reconstruct incomplete traffic data collected from various traffic sensors. Our approach is based on Markov random field modeling of road traffic. The reconstruction is achieved by using mean-field method and a machine learning method. We numerically verify the performance of our method using realistic simulated traffic data for the real road network of Sendai, Japan.

stat.ML↗

arXiv2006

Replica analysis of a preferential urn model

We analyse a preferential urn model with randomness using the replica method. The preferential urn model is a stochastic model based on the concept "the rich get richer." The replica analysis clarifies that the preferential urn model with randomness shows a fat-tailed occupation distribution. The analytical treatments and results would be useful for various research fields such as complex networks, stochastic models, and econophysics.

cond-mat.dis-nn↗

arXiv2005

Statistical-mechanical iterative algorithms on complex networks

The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a statistical-mechanical iterative algorithm is often used. We study the statistical-mechanical iterative algorithm on complex networks. To investigate effects of heterogeneous structures on the iterative algorithm, we introduce an iterative algorithm based on information of heterogeneity of complex networks, in which higher-degree nodes are likely to be updated more frequently than lower-degree ones. Numerical experiments clarified that the usage of the information of heterogeneity affects the algorithm in BA networks, but does not influence that in ER networks. It is revealed that information of the whole system propagates rapidly through such high-degree nodes in the case of Barab{á}si-Albert's scale-free networks.

cond-mat.dis-nn↗