arXiv subjects

Shun Katakami

Publications and source records attributed to Shun Katakami.

13 recordsLinked to original sources

arXiv2025

A Message-Passing Perspective on Ptychographic Phase Retrieval

We introduce a probabilistic approach to ptychographic reconstruction in computational imaging. Ptychography is an imaging method where the complex amplitude of an object is estimated from a sequence of diffraction measurements. We formulate this reconstruction as a Bayesian inverse problem and derive an inference algorithm, termed "Ptycho-EP," based on belief propagation and Vector Approximate Message Passing from information theory. Prior knowledge about the unknown object can be integrated into the probabilistic model, and the Bayesian framework inherently provides uncertainty quantification of the reconstruction. Numerical experiments demonstrate that, when the probe's illumination function is known, our algorithm accurately retrieves the object image at a sampling ratio approaching the information theoretic limit. In scenarios where the illumination function is unknown, both the object and the probe can be jointly reconstructed via an Expectation-Maximization algorithm. We evaluate the performance of our algorithm against conventional methods, highlighting its superior convergence speed.

stat.AP↗

arXiv2025

Sequential Exchange Monte Carlo: A Sampling Method for Bayesian Data Analysis without Parameter Tuning

Bayesian data analysis is widely used across many disciplines, and representative examples in materials science include spectral analysis and sparse modeling. In such applications, the underlying models often become complex and yield multimodal posterior distributions, making efficient sampling from multimodal distributions essential. Replica exchange Monte Carlo has been commonly employed for this purpose; however, its performance strongly depends on difficult parameter tuning, such as the design of the inverse temperature. In this study, we comparatively investigate sampling algorithms that require fewer tuning parameters for Bayesian data analysis in materials science. Specifically, we compare three approaches: non-reversible parallel tempering (NRPT), sequential Monte Carlo samplers (SMCS), and a newly proposed method, sequential exchange Monte Carlo (SEMC). Our results indicate that NRPT can require computational time for parameter tuning, while SMCS requires careful adjustment of the number of MCMC steps at each temperature level. In contrast, SEMC achieves robust convergence across a range of problem settings without additional tuning, demonstrating its practicality for Bayesian inference.

cs.IT↗

arXiv2024

Stochastic Vector Approximate Message Passing with applications to phase retrieval

Phase retrieval refers to the problem of recovering a high-dimensional vector $\boldsymbol{x} \in \mathbb{C}^N$ from the magnitude of its linear transform $\boldsymbol{z} = A \boldsymbol{x}$, observed through a noisy channel. To improve the ill-posed nature of the inverse problem, it is a common practice to observe the magnitude of linear measurements $\boldsymbol{z}^{(1)} = A^{(1)} \boldsymbol{x},..., \boldsymbol{z}^{(L)} = A^{(L)}\boldsymbol{x}$ using multiple sensing matrices $A^{(1)},..., A^{(L)}$, with ptychographic imaging being a remarkable example of such strategies. Inspired by existing algorithms for ptychographic reconstruction, we introduce stochasticity to Vector Approximate Message Passing (VAMP), a computationally efficient algorithm applicable to a wide range of Bayesian inverse problems. By testing our approach in the setup of phase retrieval, we show the superior convergence speed of the proposed algorithm.

stat.CO↗

arXiv2024

Mesoscopic Bayesian Inference by Solvable Models

The rapid advancement of data science and artificial intelligence has affected physics in numerous ways, including the application of Bayesian inference, setting the stage for a revolution in research methodology. Our group has proposed Bayesian measurement, a framework that applies Bayesian inference to measurement science with broad applicability across various natural sciences. This framework enables the determination of posterior probability distributions of system parameters, model selection, and the integration of multiple measurement datasets. However, applying Bayesian measurement to real data analysis requires a more sophisticated approach than traditional statistical methods like Akaike information criterion (AIC) and Bayesian information criterion (BIC), which are designed for an infinite number of measurements $N$. Therefore, in this paper, we propose an analytical theory that explicitly addresses the case where $N$ is finite in the linear regression model. We introduce $O(1)$ mesoscopic variables for $N$ observation noises. Using this mesoscopic theory, we analyze the three core principles of Bayesian measurement: parameter estimation, model selection, and measurement integration. Furthermore, by introducing these mesoscopic variables, we demonstrate that the difference in free energies, critical for both model selection and measurement integration, can be analytically reduced by two mesoscopic variables of $N$ observation noises. This provides a deeper qualitative understanding of model selection and measurement integration and further provides deeper insights into actual measurements for nonlinear models. Our framework presents a novel approach to understanding Bayesian measurement results.

physics.data-an↗

arXiv2024

Bayesian Inference for Small-Angle Scattering Data II: Core-Shell Samples

Small-angle scattering (SAS) techniques, which utilize neutrons and X-rays, are employed in various scientific fields, including materials science, biochemistry, and polymer physics. During the analysis of SAS data, model parameters that contain information about the sample are estimated by fitting the observational data to a model of sample. Previous research has demonstrated the effectiveness of Bayesian inference in analyzing SAS data using a sphere model. However, compared with the sphere model, the core-shell model, which represents functional nanoparticles, offers higher application potential and greater analytical value. Therefore, in this study, we propose an analytical method for the more complex and practical core-shell model based on Bayesian inference. Through numerical experiments, we evaluated the performance of this method under different conditions, including measurement times, number of data points, and differences in scattering length density. As a result, we clarify the conditions under which accurate estimations are possible.

physics.app-ph↗

arXiv2024

Basis Function Dependence of Estimation Precision for Synchrotron-Radiation-Based M\"ossbauer Spectroscopy

M\"ossbauer spectroscopy is a technique employed to investigate the microscopic properties of materials using transitions between energy levels in the nuclei. Conventionally, in synchrotron-radiation-based M\"ossbauer spectroscopy, the measurement window is decided by the researcher heuristically, although this decision has a significant impact on the shape of the measurement spectra. In this paper, we propose a method for evaluating the precision of the spectral position by introducing Bayesian estimation. The proposed method makes it possible to select the best measurement window by calculating the precision of M\"ossbauer spectroscopy from the data. Based on the results, the precision of the M\"ossbauer center shifts improved by more than three times compared with the results achieved with the conventional simple fitting method using the Lorentzian function.

physics.comp-ph↗

arXiv2024

Quantitative Selection of Sample Structures in Small-Angle Scattering Using Bayesian Methods

Small-angle scattering (SAS) is a key experimental technique for analyzing nano-scale structures in various materials.In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting.This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models.We assess the performance of our method through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that our proposed method analysis approach yields highly accurate and interpretable results.We also discuss the ability of our method to analyze a range of mixing ratios and particle size ratios for mixed components, along with its precision in model evaluation by the degree of fitting.Our proposed method effectively facilitates quantitative analysis of nano-scale sample structures in SAS, which has traditionally been challenging, and is expected to significantly contribute to advancements in a wide range of fields.

physics.data-an↗

arXiv2023

Teaching Specific Scientific Knowledge into Large Language Models through Additional Training

Through additional training, we explore embedding specialized scientific knowledge into the Llama 2 Large Language Model (LLM). Key findings reveal that effective knowledge integration requires reading texts from multiple perspectives, especially in instructional formats. We utilize text augmentation to tackle the scarcity of specialized texts, including style conversions and translations. Hyperparameter optimization proves crucial, with different size models (7b, 13b, and 70b) reasonably undergoing additional training. Validating our methods, we construct a dataset of 65,000 scientific papers. Although we have succeeded in partially embedding knowledge, the study highlights the complexities and limitations of incorporating specialized information into LLMs, suggesting areas for further improvement.

cs.CL↗

arXiv2023

Bayesian Inference for Small-Angle Scattering Data

In this paper, we propose a method for estimating model parameters using Small-Angle Scattering (SAS) data based on the Bayesian inference. Conventional SAS data analyses involve processes of manual parameter adjustment by analysts or optimization using gradient methods. These analysis processes tend to involve heuristic approaches and may lead to local solutions.Furthermore, it is difficult to evaluate the reliability of the results obtained by conventional analysis methods. Our method solves these problems by estimating model parameters as probability distributions from SAS data using the framework of the Bayesian inference. We evaluate the performance of our method through numerical experiments using artificial data of representative measurement target models.From the results of the numerical experiments, we show that our method provides not only high accuracy and reliability of estimation, but also perspectives on the transition point of estimability with respect to the measurement time and the lower bound of the angular domain of the measured data.

stat.ME↗

arXiv2023

Sequential Experimental Design for Spectral Measurement: Active Learning Using a Parametric Model

In this study, we demonstrate a sequential experimental design for spectral measurements by active learning using parametric models as predictors. In spectral measurements, it is necessary to reduce the measurement time because of sample fragility and high energy costs. To improve the efficiency of experiments, sequential experimental designs are proposed, in which the subsequent measurement is designed by active learning using the data obtained before the measurement. Conventionally, parametric models are employed in data analysis; when employed for active learning, they are expected to afford a sequential experimental design that improves the accuracy of data analysis. However, due to the complexity of the formulas, a sequential experimental design using general parametric models has not been realized. Therefore, we applied Bayesian inference-based data analysis using the exchange Monte Carlo method to realize a sequential experimental design with general parametric models. In this study, we evaluated the effectiveness of the proposed method by applying it to Bayesian spectral deconvolution and Bayesian Hamiltonian selection in X-ray photoelectron spectroscopy. Using numerical experiments with artificial data, we demonstrated that the proposed method improves the accuracy of model selection and parameter estimation while reducing the measurement time compared with the results achieved without active learning or with active learning using the Gaussian process regression.

cs.LG↗

arXiv2023

Bayesian Inference of Absorption Spectra Based on Binomial Distribution

In this paper, we propose a Bayesian spectral deconvolution method for absorption spectra. In conventional analysis, the noise mechanism of absorption spectral data is never considered appropriately. In that analysis, the least-squares method, which assumes Gaussian noise from the perspective of Bayesian statistics, is frequently used. Since Bayesian inference is possible by introducing an appropriate noise model for the data, we consider the absorption process of a single photon to be a Bernoulli trial and develop a Bayesian spectral deconvolution method based on binomial distribution. We have evaluated our method on artificial data under several conditions by numerical experiments. The results show that our method not only allows us to estimate parameters with high accuracy from absorption spectral data, but also to infer them even from absorption spectral data with large absorption rates where the spectral structure is flattened, which was previously impossible to analyze.

stat.ME↗

arXiv2022

Bayesian Spectral Deconvolution of X-Ray Absorption Near Edge Structure Discriminating High- and Low-Energy Domains

In this paper, we propose a Bayesian spectral deconvolution considering the properties of peaks in different energy domains. Bayesian spectral deconvolution regresses spectral data into the sum of multiple basis functions. Conventional methods use a model that treats all peaks equally. However, in X-ray absorption near edge structure (XANES) spectra, the properties of the peaks differ depending on the energy domain, and the specific energy domain of XANES is essential in condensed matter physics. We propose a model that discriminates between the low- and high-energy domains. We also propose a prior distribution that reflects the physical properties. We compare the conventional and proposed models in terms of computational efficiency, estimation accuracy, and model evidence. We demonstrate that our method effectively estimates the number of transition components in the important energy domain, on which the material scientists focus for mapping the electronic transition analysis by first-principles simulation.

stat.ME↗

arXiv2022

Bayesian Inference on Hamiltonian Selections for Mössbauer Spectroscopy

Mössbauer spectroscopy, which provides knowledge related to electronic states in materials, has been applied to various fields such as condensed matter physics and material sciences. In conventional spectral analyses based on least-square fitting, hyperfine interactions in materials have been determined from the shape of observed spectra. In conventional spectral analyses, it is difficult to discuss the validity of the hyperfine interactions and the estimated values. We propose a spectral analysis method based on Bayesian inference for the selection of hyperfine interactions and the estimation of Mössbauer parameters. An appropriate Hamiltonian has been selected by comparing Bayesian free energy among possible Hamiltonians. We have estimated the Mössbauer parameters and evaluated their estimated values by calculating the posterior distribution of each Mössbauer parameter with confidence intervals. We have also discussed the accuracy of the spectral analyses to elucidate the noise intensity dependence of numerical experiments.

physics.comp-ph↗