arXiv subjects

Kei Hirose

Publications and source records attributed to Kei Hirose.

At least 19 recordsLinked to original sources

arXiv2026

High solubility of water in post-perovskite and bridgmanite in the Earth's deep lower mantle

Water in the Earth's mantle induces melting, giving rise to strong chemical heterogeneity, and alters its rheological and transport properties, which are keys to understanding seismic-wave speeds anomalies, convective motions and electrical conductivity. However, the abundance of water and its role in the deep mantle remain uncertain and controversial, particularly at conditions of the core-mantle boundary (CMB) region. Here we carry out melting experiments on a hydrous, natural mantle composition including both $H_2O$ and $D_2O$ over the entire pressure range of the Earth's lower mantle, in which melt coexists with bridgmanite (Bdg) and/or post-perovskite (PPv), the primary constituents of the respective lower and lowermost mantle. High-resolution secondary-ion mass spectroscopy (Cryo-SIMS) measurements reveal high water concentrations in Bdg (up to 5,500 ppm by weight) and PPv (up to 1.22 wt%) with strong enrichment in deuterium/hydrogen (D/H) relative to coexisting melt. The high solubilities of water in Bdg and PPv at CMB conditions suggest that subducting slabs do not release water when they reach the bottom of the mantle, and such a process cannot account for strong chemical heterogeneities inferred in the lowermost mantle and the topmost outer core, nor for ultralow-velocity zone (ULVZ)-like structures in seismically fast regions. Water-rich Bdg and PPv may be present in the large low shear velocity provinces and ULVZs, which may be the residue of a basal magma ocean and are predicted to host a deep low D/H water reservoir inherited from the early Earth that is occasionally sampled by plumes of a lowermost-mantle origin.

physics.geo-ph↗

arXiv2026

Fe-H melting curve below 3 GPa: Implications for hydrogen in the lunar core

It has been assumed that hydrogen is negligibly incorporated into core-forming metals below $\sim$3 GPa, and therefore the presence of hydrogen in iron cores of small terrestrial bodies including the moon has not been considered. Here we performed high-pressure melting experiments on the Fe-H system under H$_2$-saturated conditions, combined with synchrotron X-ray diffraction (XRD) measurements. Results demonstrate substantial depression of the Fe-H melting curve compared to that for Fe at 1.0-3.3 GPa, indicating that hydrogen is incorporated into liquid iron even at low pressures less than 1 GPa and the solubility is enhanced with increasing pressure. Based on the density of liquid Fe-H derived from diffuse scattering signal in XRD data, we found that the solubility of hydrogen in liquid iron is about 0.9 wt% at 3.6 GPa and likely enhanced to 1.2 wt% at 5 GPa corresponding to lunar core conditions. The 1.2 wt% H causes 9 % density reduction, which might fully explain the observed density deficit of the lunar core with respect to iron, depending on the density estimate from seismological data.

cond-mat.mtrl-sci↗

arXiv2026

Consistency of the Bayesian Information Criterion for Model Selection in Exploratory Factor Analysis

We study model selection by the Bayesian information criterion (BIC) in fixed-dimensional exploratory factor analysis over a fixed finite family of compact covariance classes. Our main result shows that the BIC is strongly consistent for the pseudo-true factor order under misspecification, provided that all globally optimal models share a common pseudo-true covariance set, the population Gaussian criterion has a local quadratic margin away from that set, and the BIC complexity counts are order-separating at the pseudo-true order. The candidate models may have an unknown mean vector, exact-zero restrictions in the loading matrix, and either diagonal or spherical error covariance structures, and the selection target is the smallest candidate factor order that yields the best Gaussian approximation, in Kullback--Leibler divergence, to the data-generating covariance structure. The proof works directly in covariance space, so it does not require a regular loading parametrization and accommodates the familiar singularities caused by rotations and redundant factors. Under correct specification, the assumptions reduce to familiar properties of the true covariance matrix. More generally, the same argument applies to other information criteria whose penalties satisfy the same gap conditions, including several BIC-type modifications.

math.ST↗

arXiv2026

Numerical optimization for the compatibility constant of the lasso

The compatibility constant plays an important role in evaluating the prediction error of the lasso in high-dimensional settings. However, the computation of the compatibility constant is generally difficult because it is a complicated nonconvex optimization problem. In this study, we present a numerical approach to compute the compatibility constant when the support of true regression coefficients is given. We show that the optimization problem reduces to a quadratic programming (QP) once the signs of the nonzero coefficients are specified. In this case, the compatibility constant can be obtained by solving QPs for all possible sign combinations. We also formulate a mixed-integer QP (MIQP) approach that can be applied when the number of true nonzero coefficients is large. We investigate the finite-sample behavior of the compatibility constant for simulated data under various parameter settings and compare the prediction error with its theoretical upper bound. The behavior of the compatibility constant in finite samples is also investigated through a real data analysis.

stat.CO↗

arXiv2026

Data-driven configuration tuning of glmnet for balancing accuracy and computational efficiency

The glmnet package in R is widely used for lasso estimation because of its computational efficiency. Despite its popularity, glmnet occasionally yields solutions that deviate substantially from the true ones because of the inappropriate default configuration of the algorithm. The accuracy of the obtained solutions can be improved by appropriately tuning the configuration. However, such improvements typically increase computational time, resulting in a tradeoff between accuracy and computational efficiency. Therefore, a systematic approach is required to determine the appropriate configuration. To address this need, we propose a unified data-driven framework specifically designed to optimize the configuration by balancing solution path accuracy and computational cost. Specifically, we generate a large-scale training dataset by measuring the accuracy and computation time of glmnet. Using this dataset, we construct neural networks to predict accuracy and computation time from data characteristics and configuration. For a new dataset, the proposed framework uses the trained networks to explore the configuration space and derive a Pareto front that represents the tradeoff between accuracy and computational cost. This front enables automatic selection of the configuration that maximizes accuracy under a user-specified time constraint. The proposed method is implemented in the R package glmnetconf, available at https://github.com/Shuhei-Muroya/glmnetconf.git.

stat.CO↗

arXiv2025

Robust and consistent model evaluation criteria in high-dimensional regression

Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the data and phenomenon, we need to determine an adequate value of the regularization parameter. Regarding the determination of the regularization parameter in the linear regression model, we often apply the information criteria like the AIC and BIC, however, it has been pointed out that these criteria are sensitive to outliers and tend not to perform well in high-dimensional settings. Outliers generally have a negative effect on not only estimation but also model selection, consequently, it is important to employ a selection method with robustness against outliers. In addition, when the number of explanatory variables is quite large, most conventional criteria are prone to select unnecessary explanatory variables. In this paper, we propose model evaluation criteria based on the statistical divergence with excellence in robustness in both of parametric estimation and model selection, by applying the quasi-Bayesian procedure. Our proposed criteria achieve the selection consistency even in high-dimensional settings due to precise approximation, simultaneously with robustness. We also investigate the conditions for establishing robustness and consistency, and provide an appropriate example of the divergence and penalty term that can achieve the desirable properties. We finally report the results of some numerical examples to verify that the proposed criteria perform robust and consistent variable selection compared with the conventional selection methods.

stat.ME↗

arXiv2025

Core-mantle partitioning and the bulk Earth abundances of hydrogen and carbon: Implications for their origins

We determined the metal/silicate partition coefficients of hydrogen and carbon, DH and DC, simultaneously under typical conditions of Earth's core formation. Experiments demonstrate that both DH and DC diminish in the presence of carbon and hydrogen, respectively, indicating their strong interactions in liquid metal. With these partitioning data, we investigated the core and bulk Earth abundances of hydrogen and carbon based on core formation scenarios that are compatible with the bulk silicate Earth composition and the mass fraction and density deficit of the core. The results of the single-stage core formation modelling are markedly different from those using DH and DC individually determined in earlier experiments, indicating that the Earth building blocks do not match enstatite chondrites in water abundance and require contributions by carbonaceous chondrites. The multi-stage core formation models combined with an Earth accretion scenario accounting for isotopic composition show 0.18-0.49 wt% H and 0.19-1.37 wt% C in the core, leading to 0.53-1.40 wt% H2O (present as H in the core) and 0.07-0.44 wt% C in the bulk Earth. Our modelling also demonstrates that up to 53% and 72% of Earth's water (hydrogen) and carbon, respectively, could have been derived from non-carbonaceous chondritic materials.

astro-ph.EP↗

arXiv2025

Clustering-based aggregate value regression

In various practical situations, forecasting of aggregate values rather than individual ones is often our main focus. For instance, electricity companies are interested in forecasting the total electricity demand in a specific region to ensure reliable grid operation and resource allocation. However, to our knowledge, statistical learning specifically for forecasting aggregate values has not yet been well-established. In particular, the relationship between forecast error and the number of clusters has not been well studied, as clustering is usually treated as unsupervised learning. This study introduces a novel forecasting method specifically focused on the aggregate values in the linear regression model. We call it the Aggregate Value Regression (AVR), and it is constructed by combining all regression models into a single model. With the AVR, we must estimate a huge number of parameters when the number of regression models to be combined is large, resulting in overparameterization. To address the overparameterization issue, we introduce a hierarchical clustering technique, referred to as AVR-C (C stands for clustering). In this approach, several clusters of regression models are constructed, and the AVR is performed within each cluster. The AVR-C introduces a novel bias-variance trade-off theory under the assumption of a misspecified model. In this framework, the number of clusters characterizes model complexity. Monte Carlo simulation is conducted to investigate the behavior of training and test errors of our proposed clustering technique. The bias-variance trade-off theory is also demonstrated through the analysis of electricity demand forecasting.

stat.ME↗

arXiv2025

Electrical Conductivity of Superionic Hydrous SiO2 and the Origin of Lower-mantle High Conductivity Anomalies Beneath Subduction Zones

Electrical conductivity (EC) is one of the important physical properties of minerals and rocks that can be used to characterize the composition and structure of the deep interior of the Earth.Theoretical studies have predicted that the CaCl2-type hydrous Al-bearing SiO2 phase, present in subducted crustal materials, becomes superionic-meaning that protons are no longer bonded to a specific oxygen atom but instead become mobile within the SiO2 lattice-under high-pressure and high-temperature conditions corresponding to the lower mantle. The enhancement of the EC upon such superionic transition has not been experimentally verified yet. Here, we measured the EC of Al-bearing SiO2 containing 1750 ppm H2O at pressures up to 82 GPa and temperatures up to 2610 K by employing a recently developed technique designed for measuring transparent materials. Results demonstrate a sudden increase in EC to approximately 10 S/m at temperatures of 1100-2200 K, depending on pressure, which is several to ten times higher than that of the surrounding shallow to middle part of the lower mantle, which is attributed to a transition to the superionic state. If hydrous SiO2 is substantially weaker than other coexisting phases and thus forms an interconnected film in subducted MORB crust, the EC of the bulk MORB materials is significantly enhanced by superionic SiO2 in the lower mantle up to ~1800 km depth, which may explain the high EC anomalies observed at subduction zones underneath northeastern China. The observed EC anomalies can be matched by the EC of subducted MORB materials containing Al-bearing SiO2 with a water content of approximately 0.2 wt%, providing insights into the deep H2O circulation and distribution in the Earth's mantle.

physics.geo-ph↗

arXiv2025

Algebraic Approach for Orthomax Rotations

In exploratory factor analysis, rotation techniques are employed to derive interpretable factor loading matrices. Factor rotations deal with equality-constrained optimization problems aimed at determining a loading matrix based on measure of simplicity, such as ``perfect simple structure'' and ``Thurstone simple structure.'' Numerous criteria have been proposed, since the concept of simple structure is fundamentally ambiguous and involves multiple distinct aspects. However, most rotation criteria may fail to consistently yield a simple structure that is optimal for analytical purposes, primarily due to two challenges. First, existing optimization techniques, including the gradient projection descent method, exhibit strong dependence on initial values and frequently become trapped in suboptimal local optima. Second, multifaceted nature of simple structure complicates the ability of any single criterion to ensure interpretability across all aspects. In certain cases, even when a global optimum is achieved, other rotations may exhibit simpler structures in specific aspects. To address these issues, obtaining all equality-constrained stationary points -- including both global and local optima -- is advantageous. Fortunately, many rotation criteria are expressed as algebraic functions, and the constraints in the optimization problems in factor rotations are formulated as algebraic equations. Therefore, we can employ computational algebra techniques that utilize operations within polynomial rings to derive exact all equality-constrained stationary points. Unlike existing optimization methods, the computational algebraic approach can determine global optima and all stationary points, independent of initial values. We conduct Monte Carlo simulations to examine the properties of the orthomax rotation criteria, which generalizes various orthogonal rotation methods.

math.ST↗

arXiv2024

Formation of Iron-Helium Compounds under High Pressure

We report the formations of fcc and distorted hcp iron-helium compounds with x in FeHex up to 0.13 and 0.48, respectively, based on experiments at 5-54 GPa and ~1000-2820 K. Upon releasing pressure under room temperature, these fcc and distorted hcp FeHex were still observed by XRD and SIMS measurements. Our first-principles calculations indicate that fcc and hcp FeHex, with helium atoms occupying the tetrahedral and trigonal-planar interstitial sites (instead of the octahedral sites), are dynamically stable throughout 0-50 GPa. These results support that the Earth's core can be a large reservoir of primordial 3He.

cond-mat.mtrl-sci↗

arXiv2024

Fe-FeH Eutectic Melting Curve and the Estimates of Earth's Core Temperature and Composition

Fe and FeH form a binary eutectic system above ~40 GPa. Here we performed melting experiments in a laser-heated diamond-anvil cell (DAC) and obtained the Fe-FeH eutectic melting curve between 52 and 175 GPa. Its extrapolation shows the eutectic temperature to be 4700 K at the inner core boundary (ICB), which is lower than that in Fe-FeSi but is higher than those in the Fe-S, Fe-O, and Fe-C systems. In addition, its dT/dP slope is comparable to those of the melting curves of Fe and FeH endmembers, suggesting that the eutectic liquid composition changes little with increasing pressure and is about FeH0.6 at the ICB pressure. We also estimated the effect of each light element on depressing the liquidus temperature at 330 GPa based on a combination of binary eutectic temperature and composition and found that the effect is large for C and S, moderate for H and O, and small for Si when considering the amount of each element that reduces a certain percentage of a liquid iron density. Furthermore, we searched for a set of possible outer core liquid composition and ICB temperature (the liquidus temperature of the former at 330 GPa should match the latter), which explains the outer core density deficit that depends on core temperature. The results demonstrate that relatively low core temperatures, lower than the solidus temperature of a pyrolitic lowermost mantle at the core-mantle boundary (CMB), are possible when the core is poor in Si.

cond-mat.mtrl-sci↗

arXiv2024

Improving prediction accuracy by choosing resampling distribution via cross-validation

In a regression model, prediction is typically performed after model selection. The large variability in the model selection makes the prediction unstable. Thus, it is essential to reduce the variability in model selection and improve prediction accuracy. To achieve this goal, a parametric bootstrap smoothing can be applied. In this method, model selection is performed for each resampling from a parametric distribution, and these models are then averaged such that the distribution of the selected models is considered. Here, the prediction accuracy is highly dependent on the choice of a distribution for resampling. In particular, an experimental study shows that the choice of error variance significantly changes the distribution of the selected model and thus plays a key role in improving the prediction accuracy. We also observed that the true error variance does not always provide optimal prediction accuracy. Therefore, it would not always be appropriate to use unbiased estimators of the true parameters or standard estimators of the parameters for the resampling distribution. In this study, we propose employing cross validation to choose a suitable resampling distribution rather than unbiased estimators of parameters. Our proposed method was applied to electricity demand data. The results indicate that the proposed method provides a better prediction accuracy than the existing method.

stat.CO↗

arXiv2024

Algebraic approach to maximum likelihood factor analysis

In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is usually intractable, it is typically computed with continuous optimization methods, such as Newton-Raphson methods. With this procedure, however, the solution is inevitably dependent on the estimation algorithm and initial value since the log-likelihood function is highly non-concave. Particularly, the estimates of unique variances can result in zero or negative, referred to as improper solutions; in this case, the maximum likelihood estimate can be severely unstable. To delve into the issue of the instability of the maximum likelihood estimate, we compute exact solutions to the multivariate algebraic equation by using algebraic computations. We provide a computationally efficient algorithm based on the algebraic computations specifically optimized for maximum likelihood factor analysis. To be specific, Gröebner basis and cylindrical decomposition are employed, powerful tools for solving the multivariate algebraic equation. Our proposed procedure produces all exact solutions to the algebraic equation; therefore, these solutions are independent of the initial value and estimation algorithm. We conduct Monte Carlo simulations to investigate the characteristics of the maximum likelihood solutions.

math.ST↗

arXiv2024

Hot interiors of ice giant planets inferred from electrical conductivity of dense H2O fluid

Uranus and Neptune have intrinsic magnetic fields generated via convection in a molten H2O layer, where the field strength is determined by its electrical conductivity (EC) along with convection size and velocity. Previous shock experiments reported that the EC of molten H2O is high enough to generate magnetic fields of these ice giant planets with adiabatic thermal structures. Here we measured the EC of ionic H2O fluid for the first time by static compression experiments up to 45 GPa and 2,750 K. The EC determined is lower by a few orders of magnitude than earlier data by shock compression measurements and not capable of generating a magnetic field with the conventional interior thermal structures. Our results necessitate recently-suggested fewfold hotter interiors of Uranus and Neptune to explain their magnetic fields.

astro-ph.EP↗

arXiv2023

Fast same-step forecast in SUTSE model and its theoretical properties

We consider the problem of forecasting multivariate time series by a Seemingly Unrelated Time Series Equations (SUTSE) model. The SUTSE model usually assumes that error variables are correlated. A crucial issue is that the model estimation requires heavy computational loads because of a large matrix computation, especially for high-dimensional data. To alleviate the computational issue, we propose a two-stage procedure for forecasting. First, we perform the Kalman filter as if error variables are uncorrelated; that is, univariate time-series analyses are conducted separately to avoid a large matrix computation. Next, the forecast value is computed by using a distribution of forecast error. The proposed algorithm is much faster than the ordinary SUTSE model because we do not require a large matrix computation. Some theoretical properties of our proposed estimator are presented. Monte Carlo simulation is performed to investigate the effectiveness of our proposed method. The usefulness of our proposed procedure is illustrated through a bus congestion data application.

math.ST↗

arXiv2021

Hierarchical clustered multiclass discriminant analysis via cross-validation

Linear discriminant analysis (LDA) is a well-known method for multiclass classification and dimensionality reduction. However, in general, ordinary LDA does not achieve high prediction accuracy when observations in some classes are difficult to be classified. This study proposes a novel cluster-based LDA method that significantly improves the prediction accuracy. We adopt hierarchical clustering, and the dissimilarity measure of two clusters is defined by the cross-validation (CV) value. Therefore, clusters are constructed such that the misclassification error rate is minimized. Our approach involves a heavy computational load because the CV value must be computed at each step of the hierarchical clustering algorithm. To address this issue, we develop a regression formulation for LDA and construct an efficient algorithm that computes an approximate value of the CV. The performance of the proposed method is investigated by applying it to both artificial and real datasets. Our proposed method provides high prediction accuracy with fast computation from both numerical and theoretical viewpoints.

stat.ME↗

arXiv2021

Sparse multivariate regression with missing values and its application to the prediction of material properties

In the field of materials science and engineering, statistical analysis and machine learning techniques have recently been used to predict multiple material properties from an experimental design. These material properties correspond to response variables in the multivariate regression model. This study conducts a penalized maximum likelihood procedure to estimate model parameters, including the regression coefficients and covariance matrix of response variables. In particular, we employ $l_1$-regularization to achieve a sparse estimation of regression coefficients and the inverse covariance matrix of response variables. In some cases, there may be a relatively large number of missing values in response variables, owing to the difficulty in collecting data on material properties. A method to improve prediction accuracy under the situation with missing values incorporates a correlation structure among the response variables into the statistical model. The expectation and maximization algorithm is constructed, which enables application to a data set with missing values in the responses. We apply our proposed procedure to real data consisting of 22 material properties.

stat.ME↗