Statistical mechanics of relaxation process for Bayesian inference and its application

贝叶斯推理松弛过程的统计力学及其应用

• 批准号: 14084212
• 负责人: OKADA Masato
• 金额: $ 19.46万
• 依托单位: University of Tokyo (2004-2005)The Institute of Physical and Chemical Research (2002-2003)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14084212/
• 关键词: Bayesian inference; CDMA; Image reconstruction; Error Correcting code; Principal Component Analysis; Quantum annealing; Rate distortion; Relaxation process; 統計力学; 確率的情報処理; 量子断熱発展; 主成分分; デコード; 復調

We investigated dynamics for CDMA multiuser detection. We applied the statistical neurodynamics, which is based on Gaussian approximation for input distribution, to a detection dynamics of a parallel interference canceller (PIC), and proposed a new detection algorithm based on this theoretical analysis. Recently, we have succeeded in obtaining an exact solution for the PIC detection dynamics without the Gaussian approximation using generating functional analysis (GFA). We applied a dynamical replica theory (DRT) to the CDMA detection dynamics. We also applied these theories to the image, restoration and the error-correcting code.We proposed a numerical approach for a class of non-mean field models and finite-size models with sufficient accuracy, in which principal component analysis (PCA) is employed to analyze configurations sampled through Monte Carlo simulations. We showed that the PCA approach will be effective even with general non-MF finite-size models using examples of two-and three-body mean-field Sourlas codes.The quantum annealing method exploits quantum fluctuations to search the ground state of classical disordered Hamiltonian, which corresponds to maximum a posteriori probability estimation. If the quantum fluctuation is reduced sufficiently slowly and linearly by the time, the residual energy after the quantum annealing falls as the inverse square of the annealing time. We show this feature of the residual energy by numerical calculations for small-sized systems and derive it on the basis of the quantum adiabatic theorem.Additionally, we proposed a new framework for the lossy date compression using a sparsely connected random network, which was originally used on the error-correcting code.

我们研究了CDMA多用户检测的动力学。将基于高斯近似的统计神经动力学应用于并行干扰消除器（PIC）的检测动力学，并在此基础上提出了一种新的检测算法。最近，我们已经成功地获得了一个精确的解决方案的PIC检测动力学没有高斯近似生成泛函分析（GFA）。我们应用动态副本理论（DRT）的CDMA检测动力学。我们还将这些理论应用到图像、恢复和纠错码中，提出了一类具有足够精度的非平均场模型和有限尺寸模型的数值方法，其中主成分分析（PCA）被用于分析通过Monte Carlo模拟采样的配置。我们以二体和三体平均场Sourlas码为例，证明了PCA方法在一般非MF有限尺寸模型下也是有效的;量子退火方法利用量子涨落搜索经典无序哈密顿量的基态，这对应于最大后验概率估计.如果量子涨落随时间充分缓慢地线性地减小，则量子退火后的剩余能量福尔斯作为退火时间的平方倒数下降。通过对小尺度系统的数值计算，我们证明了剩余能量的这一特性，并根据量子绝热定理导出了剩余能量的计算公式.此外，我们还提出了一种利用稀疏连接随机网络进行有损数据压缩的新框架，该框架最初用于纠错码.

项目成果

Evaluation of the adaptive natural gradient descent method for soft committee machines.

软委员会机自适应自然梯度下降法的评估。

• 发表时间: 2004
• 期刊: Physical Review E Vol.69
• 作者: Inoue;Park;Okada
• 通讯作者: Okada

Tatsuto Murayama: "One-step RSB scheme for the rate distortion functions."Journal of Physics A: Mathematical and General. vol.36. 11123-11130 (2003)

Tatsuto Murayama：“速率畸变函数的一步 RSB 方案。”物理学杂志 A：数学与综合。

Kazuyuki Hara: "On-line learning through simple perceptron learning with a margin"Neural Networks,. vol.17, No.2. 215-223 (2004)

Kazuyuki Hara：“通过简单感知器学习进行在线学习”神经网络，。

Masato Inoue: "On-line learning theory of soft committee machines with correlated hidden units.--Steepest gradient descent and natural gradient descent--"Journal of Physical Society of Japan. vol.72, No.4. 805-810 (2003)

井上雅人：“具有相关隐藏单元的软委员会机器的在线学习理论。--最速梯度下降和自然梯度下降--”日本物理学会杂志。

Analysis of ensemble learning using simple perceptrons based on online learning theory

基于在线学习理论的简单感知器集成学习分析

• 发表时间: 2005
• 期刊: Physical Review E 71
• 作者: Miyoshi;S.;Hara;K.;Okada;M.
• 通讯作者: M.