arXiv subjects

Kei Hirose

Publications and source records attributed to Kei Hirose.

32 records · Page 2Linked to original sources

arXiv2020

Interpretable modeling for short- and medium-term electricity load forecasting

We consider the problem of short- and medium-term electricity load forecasting by using past loads and daily weather forecast information. Conventionally, many researchers have directly applied regression analysis. However, interpreting the effect of weather on these loads is difficult with the existing methods. In this study, we build a statistical model that resolves this interpretation issue. A varying coefficient model with basis expansion is used to capture the nonlinear structure of the weather effect. This approach results in an interpretable model when the regression coefficients are nonnegative. To estimate the nonnegative regression coefficients, we employ nonnegative least squares. Three real data analyses show the practicality of our proposed statistical modeling. Two of them demonstrate good forecast accuracy and interpretability of our proposed method. In the third example, we investigate the effect of COVID-19 on electricity loads. The interpretation would help make strategies for energy-saving interventions and demand response.

stat.ME↗

arXiv2020

Thermal Conductivity of CaSiO$_3$ Perovskite at Lower Mantle Conditions

Thermal conductivity ($κ$) of mantle minerals is a fundamental property in geodynamic modeling. It controls the style of mantle convection and the time scale of the mantle and core cooling. Cubic CaSiO$_3$ perovskite (CaPv) is the third most abundant mineral in the lower mantle (LM) (7 vol%). However, despite its importance, no theoretical or experimental estimate of CaPv's $κ$ exists. Theoretical investigations of its properties are challenging because of its strong anharmonicity. Experimental measurements at relevant high pressures and temperatures are equally challenging. Here we present $ab$ $initio$ results for CaPv's $κ$ obtained using an established phonon quasiparticle approach that can address its strong anharmonicity. We also offer experimental measurements of $κ$. Predictions and measurements are in good agreement and reveal a surprisingly large $κ$ for cubic CaPv. Despite its relatively low abundance, CaPv's $κ$ might increase the lower mantle $κ$ by approximately 10%, if accounted for. $κ$ of mantle regions enriched in crust material will be more strongly impacted.

cond-mat.mtrl-sci↗

arXiv2018

Robust relative error estimation

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $γ$-likelihood function, which is constructed through $γ$-cross entropy with keeping the original statistical model in use. The estimating equation has a redescending property, a desirable property in robust statistics, for a broad class of noise distributions. To find a minimizer of the negative $γ$-likelihood function, a majorize-minimization (MM) algorithm is constructed. The proposed algorithm is guaranteed to decrease the negative $γ$-likelihood function at each iteration. We also derive asymptotic normality of the corresponding estimator together with a simple consistent estimator of the asymptotic covariance matrix, so that we can readily construct approximate confidence sets. Monte Carlo simulation is conducted to investigate the effectiveness of the proposed procedure. Real data analysis illustrates the usefulness of our proposed procedure.

stat.ME↗

arXiv2018

Simple structure estimation via prenet penalization

We propose a $prenet$ ($pr$oduct $e$lastic $net$), which is a new penalization method for factor analysis models. The penalty is based on the product of a pair of elements in each row of the loading matrix. The prenet not only shrinks some of the factor loadings toward exactly zero, but also enhances the simplicity of the loading matrix, which plays an important role in the interpretation of the common factors. In particular, with a large amount of prenet penalization, the estimated loading matrix possesses a perfect simple structure, which is known as a desirable structure in terms of the simplicity of the loading matrix. Furthermore, the perfect simple structure estimation via the prenet turns out to be a generalization of the $k$-means clustering of variables. On the other hand, a mild amount of the penalization approximates a loading matrix estimated by the quartimin rotation, one of the most commonly used oblique rotation techniques. Thus, the proposed penalty bridges a gap between the perfect simple structure and the quartimin rotation. Monte Carlo simulation is conducted to investigate the performance of the proposed procedure. Three real data analyses are given to illustrate the usefulness of our penalty.

stat.ME↗

arXiv2018

Persistence of Strong Silica-Enriched Domains in the Earth's Lower Mantle

The composition of the lower mantle $-$ comprising 56% of Earth's volume $-$ remains poorly constrained. Among the major elements, Mg/Si ratios ranging from $\sim$0.9$-$1.1, such as in rocky solar-system building blocks (or chondrites), to $\sim$1.2$-$1.3, such as in upper-mantle rocks (or pyrolite), have been proposed. Geophysical evidence for subducted lithosphere deep in the mantle has been interpreted in terms of efficient mixing and thus homogeneous Mg/Si across most of the mantle. However, previous models did not consider the effects of variable Mg/Si on the viscosity and mixing efficiency of lower-mantle rocks. Here, we use geodynamic models to show that large-scale heterogeneity with viscosity variations of $\sim$20$\times$, such as due to the dominance of intrinsically strong (Mg,Fe)SiO$_3-$bridgmanite in low-Mg/Si domains, are sufficient to prevent efficient mantle mixing, even on large scales. Models predict that intrinsically strong domains stabilize degree-two mantle-convection patterns, and coherently persist at depths of $\sim$1,000$-$2,200 km up to the present-day, separated by relatively narrow up-/downwelling conduits of pyrolitic material. The stable manifestation of such "bridgmanite-enriched ancient mantle structures" (BEAMS) may reconcile the geographical fixity of deep-rooted mantle-upwelling centers, and fundamental geophysical changes near 1,000 km depth (e.g. in terms of seismic-tomography patterns, radial viscosity increase, lateral deflections of rising plumes and sinking slabs). Moreover, these ancient structures may provide a reservoir to host primordial geochemical signatures.

astro-ph.EP↗

arXiv2018

Reconciling Magma-Ocean Crystallization Models with the present-day Structure of the Earth's mantle

Terrestrial planets are thought to experience episode(s) of large-scale melting early in their history. Fractionation during magma-ocean freezing leads to unstable stratification within the related cumulate layers due to progressive iron enrichment upward, but the effects of incremental cumulate overturns during MO crystallization remain to be explored. Here, we use geodynamic models with a moving-boundary approach to study convection and mixing within the growing cumulate layer, and thereafter within the fully crystallized mantle. For fractional crystallization, cumulates are efficiently stirred due to subsequent incremental overturns, except for strongly iron-enriched late-stage cumulates, which persist as a stably stratified layer at the base of the mantle for billions of years. Less extreme crystallization scenarios can lead to somewhat more subtle stratification. In any case, the long-term preservation of at least a thin layer of extremely enriched cumulates with Fe#>0.4, as predicted by all our models, is inconsistent with seismic constraints. Based on scaling relationships, however, we infer that final-stage Fe-rich magma-ocean cumulates originally formed near the surface should have overturned as small diapirs, and hence undergone melting and reaction with the host rock during sinking. The resulting moderately iron-enriched metasomatized/hybrid rock assemblages should have accumulated at the base of the mantle, potentially fed an intermittent basal magma ocean, and be preserved through the present-day. Such moderately iron-enriched rock assemblages can reconcile the physical properties of the large low shear-wave velocity provinces in the presentday lower mantle. Thus, we reveal Hadean melting and rock-reaction processes by integrating magmaocean crystallization models with the seismic-tomography snapshot.

astro-ph.EP↗

arXiv2017

Robust sparse Gaussian graphical modeling

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a high-dimensional graphical model. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the $γ$-divergence. The proposed method has a redescending property, which is known as a desirable property in robust statistics. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. Extensive simulation studies showed that our procedure performed much better than the existing methods, in particular, when the contamination ratio was large. Two real data analyses were carried out to illustrate the usefulness of our proposed procedure.

stat.ME↗

arXiv2015

Post-stishovite transition in hydrous aluminous SiO2

Lakshtanov et al. (2007) showed that incorporation of aluminum and some water into SiO2 significantly reduces the post-stishovite transition pressure in SiO2. This discovery suggested that the ferroelastic post-stishovite transition in subducted MORB crust could be the source of reflectors/scatterers with low shear velocities observed in the mid to upper lower mantle. A few years later, a similar effect was observed in anhydrous Al-bearing silica. In this paper, we show using first principles static calculations and molecular dynamics using inter-atomic potentials that hydrogen bonds and hydrogen mobility play a crucial role in lowering the post-stishovite transition pressure. A cooperative redistribution of hydrogen atoms is the main mechanism responsible for the transition pressure reduction in hydrous aluminous stishovite. The effect is enhanced by increasing hydrogen concentration. This perspective suggests a potential relationship between the depth of seismic scatterers and the water content in stishovite.

cond-mat.mtrl-sci↗

arXiv2013

Full information maximum likelihood estimation in factor analysis with a lot of missing values

We consider the problem of full information maximum likelihood (FIML) estimation in a factor analysis model when a majority of the data values are missing. The expectation-maximization (EM) algorithm is often used to find the FIML estimates, in which the missing values on observed variables are included in complete data. However, the EM algorithm has an extremely high computational cost when the number of observations is large and/or plenty of missing values are involved. In this paper, we propose a new algorithm that is based on the EM algorithm but that efficiently computes the FIML estimates. A significant improvement in the computational speed is realized by not treating the missing values on observed variables as a part of complete data. Our algorithm is applied to a real data set collected from a Web questionnaire that asks about first impressions of human; almost $90\%$ of the data values are missing. When there are many missing data values, it is not clear if the FIML procedure can achieve good estimation accuracy even if the number of observations is large. In order to investigate this, we conduct Monte Carlo simulations under a wide variety of sample sizes.

stat.CO↗

arXiv2013

Sparse estimation via nonconcave penalized likelihood in a factor analysis model

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates cannot be obtained when the number of variables is much larger than the number of observations. Furthermore, even if the maximum likelihood estimates are available, the rotation technique does not often produce a sufficiently sparse solution. In order to handle these problems, this paper introduces a penalized likelihood procedure that imposes a nonconvex penalty on the factor loadings. We show that the penalized likelihood procedure can be viewed as a generalization of the traditional two-step approach, and the proposed methodology can produce sparser solutions than the rotation technique. A new algorithm via the EM algorithm along with coordinate descent is introduced to compute the entire solution path, which permits the application to a wide variety of convex and nonconvex penalties. Monte Carlo simulations are conducted to investigate the performance of our modeling strategy. A real data example is also given to illustrate our procedure.

stat.ME↗

arXiv2013

Estimation of oblique structure via penalized likelihood factor analysis

We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated). However, the lasso-type penalization method based on the orthogonal model can often estimate a completely different model from that with the true factor structure when the common factors are correlated. In order to overcome this problem, we propose to incorporate a factor correlation into the model, and estimate the factor correlation along with parameters included in the orthogonal model by maximum penalized likelihood procedure. An entire solution path is computed by the EM algorithm with coordinate descent, which permits the application to a wide variety of convex and nonconvex penalties. The proposed method can provide sufficiently sparse solutions, and be applied to the data where the number of variables is larger than the number of observations. Monte Carlo simulations are conducted to investigate the effectiveness of our modeling strategies. The results show that the lasso-type penalization based on the orthogonal model cannot often approximate the true factor structure, whereas our approach performs well in various situations. The usefulness of the proposed procedure is also illustrated through the analysis of real data.

stat.ME↗

arXiv2012

Readouts for Echo-state Networks Built using Locally Regularized Orthogonal Forward Regression

Echo state network (ESN) is viewed as a temporal non-orthogonal expansion with pseudo-random parameters. Such expansions naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain amount of the generated echo-regressors effectively explain the variance of the teacher output and also that sole local regularization is not able to provide in-depth information concerning the importance of the generated regressors. The importance is therefore determined by a joint calculation of the individual variance contributions and Bayesian relevance using locally regularized orthogonal forward regression (LROFR) algorithm. This information can be advantageously used in a variety of ways for an in-depth analysis of an ESN structure and its state-space parameters in relation to the unknown dynamics of the underlying problem. We present locally regularized linear readout built using LROFR. The readout may have a different dimensionality than an ESN model itself, and besides improving robustness and accuracy of an ESN it relates the echo-regressors to different features of the training data and may determine what type of an additional readout is suitable for a task at hand. Moreover, as flexibility of the linear readout has limitations and might sometimes be insufficient for certain tasks, we also present a radial basis function (RBF) readout built using LROFR. It is a flexible and parsimonious readout with excellent generalization abilities and is a viable alternative to readouts based on a feed-forward neural network (FFNN) or an RBF net built using relevance vector machine (RVM).

stat.ML↗

arXiv2012

Efficient algorithm to select tuning parameters in sparse regression modeling with regularization

In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' $C_p$ type criteria may be used as a tuning parameter selection tool in lasso-type regularization methods, for which the concept of degrees of freedom plays a key role. In the present paper, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and non-convex penalties. Monte Carlo simulations demonstrate that our methodology performs well in various situations. A real data example is also given to illustrate our procedure.

stat.ME↗

arXiv2011

Experimental and theoretical evidence for pressure-induced metallization in FeO with the rock-salt type structure

Electrical conductivity of FeO was measured up to 141 GPa and 2480 K in a laserheated diamond-anvil cell. The results show that rock-salt (B1) type structured FeO metallizes at around 70 GPa and 1900 K without any structural phase transition. We computed fully self-consistently the electronic structure and the electrical conductivity of B1 FeO as a function of pressure and temperature, and found that although insulating as expected at ambient condition, B1 FeO metallizes at high temperatures, consistent with experiments. The observed metallization is related to spin crossover.

cond-mat.mtrl-sci↗