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Consistency of high-dimensional AIC-type and C_p-type criteria in multivariate linear regression

JOURNAL OF multivariate ANALYSIS 2014年 123卷 184-200页

作者： Fujikoshi, Yasunori Sakurai, Tetsuro Yanagihara, Hirokazu Hiroshima Univ Grad Sch Sci Dept Math Hiroshima 7398626 Japan Tokyo Univ Sci Ctr Gen Educ Nagano 3910292 Japan

The AIC, the multivariate C-p and their modifications have been proposed for multivariate linear regression models under a large-sample framework when the sample size n is large, but the dimension p of the response variables is fixed. In this paper, first we propose a high-dimensional AIC (denoted by HAIC) which is an asymptotic unbiased estimator of the risk function defined by the expected log-predictive likelihood or equivalently the Kullback-Leibler information under a high-dimensional framework p/n -> c is an element of [0, 1). It is noted that our new criterion provides better approximations to the risk function in a wide range of p and n. Recently Yanagihara et al. (2012) [17] noted that AIC has a consistency property under Omega = O(np) when p/n -> c is an element of [0, 1), where 51 is a noncentrality matrix. In this paper we show that several criteria including HAIC and C-p have also a consistency property under Omega = O(n) as well as Omega = O(np) when p/n -> c is an element of [0, 1). Our results are checked numerically by conducting a Monte Carlo simulation. (C) 2013 Elsevier Inc. All rights reserved.

关键词： AIC C-p Consistency property High-dimensional criteria Modified criteria multivariate linear regression

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Quantile modeling through multivariate log-normal/independent linear regression models with application to newborn data

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BIOMETRICAL JOURNAL 2021年第6期63卷 1290-1308页

作者： Moran-Vasquez, Raul Alejandro Mazo-Lopera, Mauricio A. Ferrari, Silvia L. P. Univ Antioquia Inst Matemat Calle 67 53-108 Medellin 050010 Colombia Univ Nacl Colombia Escuela Estadist Medellin Colombia Univ Sao Paulo Dept Estat Sao Paulo Brazil

In this article, we propose and study the class of multivariate log-normal/independent distributions and linear regression models based on this class. The class of multivariate log-normal/independent distributions is very attractive for robust statistical modeling because it includes several heavy-tailed distributions suitable for modeling correlated multivariate positive data that are skewed and possibly heavy-tailed. Besides, expectation-maximization (EM)-type algorithms can be easily implemented for maximum likelihood estimation. We model the relationship between quantiles of the response variables and a set of explanatory variables, compute the maximum likelihood estimates of parameters through EM-type algorithms, and evaluate the model fitting based on Mahalanobis-type distances. The satisfactory performance of the quantile estimation is verified by simulation studies. An application to newborn data is presented and discussed.

关键词： EM algorithm multivariate linear regression multivariate normal independent distribution newborn quantile modeling

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multivariate cluster-weighted models based on seemingly unrelated linear regression

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2022年 171卷 107451-107451页

作者： Diani, Cecilia Galimberti, Giuliano Soffritti, Gabriele Univ Bologna Dept Stat Sci Via Belle Arti 41 I-40126 Bologna Italy

A class of cluster-weighted models for a vector of continuous random variables is proposed. This class provides an extension to cluster-weighted modelling of multivariate and correlated responses that let the researcher free to use a different vector of covariates for each response. The class also includes parsimonious models obtained by imposing suitable constraints on the component-covariance matrices of either the responses or the covariates. Conditions for model identifiability are illustrated and discussed. Maximum likelihood estimation is carried out by means of an expectation-conditional maximisation algorithm. The effectiveness and usefulness of the proposed models are shown through the analysis of simulated and real datasets. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Cluster analysis ECM algorithm Gaussian mixture model multivariate linear regression Parsimonious model

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Bayesian linear regression for multivariate responses under group sparsity

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BERNOULLI 2020年第3期26卷 2353-2382页

作者： Ning, Bo Jeong, Seonghyun Ghosal, Subhashis Yale Univ Dept Stat & Data Sci 24 Hillhouse Ave New Haven CT 06511 USA Univ Chicago Booth Sch Business 5807 S Woodlawn Ave Chicago IL 60637 USA North Carolina State Univ Dept Stat 4276 SAS Hall2311 Stinson Dr Raleigh NC 27695 USA

We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is predetermined. Two features of the model are unique: (i) group sparsity is imposed on the predictors;(ii) the covariance matrix is unknown and its dimensions can also be high. We choose a product of independent spike-and-slab priors on the regression coefficients and a new prior on the covariance matrix based on its eigendecomposition. Each spike-and-slab prior is a mixture of a point mass at zero and a multivariate density involving the 2,1-norm. We first obtain the posterior contraction rate, the bounds on the effective dimension of the model with high posterior probabilities. We then show that the multivariate regression coefficients can be recovered under certain compatibility conditions. Finally, we quantify the uncertainty for the regression coefficients with frequentist validity through a Bernstein-von Mises type theorem. The result leads to selection consistency for the Bayesian method. We derive the posterior contraction rate using the general theory by constructing a suitable test from the first principle using moment bounds for certain likelihood ratios. This leads to posterior concentration around the truth with respect to the average Renyi divergence of order 1/2. This technique of obtaining the required tests for posterior contraction rate could be useful in many other problems.

关键词： Bayesian variable selection covariance matrix group sparsity multivariate linear regression posterior contraction rate Renyi divergence spike-and-slab prior

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A theoretical view of the envelope model for multivariate linear regression as response dimension reduction

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2013年第2期42卷 143-148页

作者： Yoo, Jae Keun Ewha Womans Univ Dept Stat Seoul 120750 South Korea

The envelope model recently developed for the classical multivariate linear regression have potential gain in efficiency in estimating unknown parameters over usual maximum likelihood estimation. In this paper, we theoretically investigate the envelope model as dimension reduction for response variables and connect them to existing methods. (C) 2012 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

关键词： Envelope model multivariate linear regression Reducing subspaces Response dimension reduction

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On the likelihood ratio test for envelope models in multivariate linear regression

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BIOMETRIKA 2013年第2期100卷 531-537页

作者： Schott, James R. Univ Cent Florida Dept Stat Orlando FL 32816 USA

We investigate the likelihood ratio test for a hypothesis regarding the dimension of the Sigma-envelope of span(beta) in a multivariate linear regression model. The asymptotic null distribution of the likelihood ratio statistic is obtained as some nuisance parameters approach infinity. A saddlepoint approximation is also given for this limiting distribution. The accuracy of this approximation and its comparison to the standard chi-squared approximation are assessed via simulation. The results can be used in a similar test for partial envelope models.

关键词： Asymptotic null distribution Envelope model Likelihood ratio test multivariate linear regression Partial envelope model Saddlepoint approximation

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Experimental investigation on mechanical property and hydration process of sintered sludge cement paste at different water-binder ratios and curing ages

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STRUCTURAL CONCRETE 2025年第2期26卷 1654-1672页

作者： Zhang, Jinrui Li, Chenjiang Lv, Tong Hou, Dongshuai Hong, Shuxian Dong, Biqin Tianjin Univ State Key Lab Hydraul Engn Intelligent Construct Tianjin 300072 Peoples R China Qingdao Univ Technol Dept Civil Engn Qingdao Peoples R China Shenzhen Univ Guangdong Prov Key Lab Durabil Marine Civil Engn Shenzhen Peoples R China

This research investigated the mechanical property and hydration process of sintered sludge cement (SSC) paste, focusing on the effects of calcination temperature of sludge, sintered sludge ash (SSA) content, curing age, and water-binder ratio using isothermal calorimetry, X-ray diffraction, scanning electron microscopy, and multiple regression. Increasing calcination temperature enhanced the compressive strength of SSC paste due to the decomposition of minerals like Clinochlore and Muscovite. The compressive strength decreased by 2.4%-49.4% when the SSA content increased from 0% to 50%, with more significant declines noted at higher water-binder ratios. Notably, the 7-day compressive strength of the cement paste with 10% SSA showed little change, and the 28-day compressive strength actually increased at a water-binder ratio of 0.4. SSA slowed down the hydration rate of cement and induced more Monocarbonate to form in the early stage. A multiple linear regression model was developed to predict SSC compressive strength with a 12% error margin.

关键词： hydration process mechanical property multivariate linear regression sintered sludge ash sintered sludge cement paste

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Synergistic approach: Peridynamics and machine learning regression for efficient pitting corrosion simulation

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COMPUTERS & STRUCTURES 2024年 305卷

作者： Babu, J. Ramesh Gopalakrishnan, S. Indian Inst Sci Bangalore 560012 India

Corrosion-induced material deterioration poses a pervasive threat to structural integrity, necessitating an indepth understanding of its intricate behaviors. Pitting corrosion, a critical concern in this context, accelerates the degradation of materials. The limitations of conventional models arise from their neglect of the subsurface electrode boundary layer dynamics during the dissolution process. In this study, we present a novel approach that combines Peridynamics (PD) diffusion framework with machine learning (ML) techniques to develop an efficient predictive model and computational efficiency. The proposed hybrid PD-ML model leverages the non-local effects inherent to Peridynamics and the pattern recognition capabilities of machine learning. It establishes an analytical connection between the concentration value at a specific material point and the concentrations exhibited by related constituents within its spatial horizon, considering the external mass flux applied. The adaptability of the model is achieved through the utilization of weighted regression coefficients, determined via multivariate linear regression. Validation against experiments and conventional PD model demonstrates the model's precision and efficiency using diverse micro-diffusivity scenarios. For 1D uniform and 2D pitting corrosion cases, our hybrid model yields precise concentration predictions while showcasing a remarkable improvement in computational speed compared to conventional approaches. Specifically, the hybrid model achieves an impressive speedup, approximately 4 times faster per time step and 2.5 times faster overall simulation. The study presents a promising tool for predicting corrosion-induced material deterioration in practical systems, offering accuracy, efficiency, and potential for broader applications.

关键词： Pitting corrosion Peridynamics Damage Machine learning multivariate linear regression Computational efficiency

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Thermal diffusion in discontinuous media: A hybrid peridynamics-based machine learning model

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COMPUTERS & STRUCTURES 2024年 290卷

作者： Babu, J. Ramesh Gopalakrishanan, S. Inst Sci Bangalore 560012 India

This paper introduces a novel hybrid formulation of a peridynamics-based machine learning model for thermal diffusion analysis in one-dimensional and two-dimensional problems with evolving discontinuities. The hybrid model employs a multivariate linear regression approach to establish the relationship between the temperature values of material points, their neighboring points, and the applied external heat flux. The thermal modal analysis method uses the finite element method to generate training and testing data. An efficient numerical procedure is also developed to couple the peridynamics model and the peridynamics-based machine learning model. The model is analyzed under multiple configurations of micro-thermal conductivity functions for one-dimensional thermal bar problems, under both steady-state and transient loading conditions, to identify the configuration that exhibits superior convergence behavior towards the local solution. Furthermore, benchmark problems demonstrate the high accuracy of the formulated hybrid model, including the analysis of thermal plates with discontinuities, such as a plate with a hole, a plate with a pre-existing insulated crack, and plate with a bi-material interface with stationary and evolving discontinuances. The hybrid model effectively captures intricate discontinuities and boundaries while being computationally efficient, indicating its potential for thermal diffusion analysis in one-and two-dimensional problems with stationary and evolving discontinuities.

关键词： Peridynamics Thermal diffusion Damage Machine learning multivariate linear regression Thermal modal analysis

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Correlations of facial soft tissue thicknesses with craniometric dimensions improve craniofacial identification estimates: Fact or fiction?

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JOURNAL OF FORENSIC SCIENCES 2025年第2期70卷 430-445页

作者： Hona, Te Wai Pounamu T. Stephan, Carl N. Univ Queensland Sch Biomed Sci Lab Human Craniofacial & Skeletal Identificat HuCS Brisbane 4072 Australia

linear regression (LR) models that use cranial dimensions to estimate facial soft tissue thicknesses (FSTTs) have been posited by Simpson and Henneberg to assist craniofacial identification. For these regression equations to work well, the independent (craniometrics) and dependent (FSTTs) variables must be tightly correlated;however, such relationships have not been routinely demonstrated for adult humans. To examine the strength of these relationships further, this study employed magnetic resonance (MR) imaging to unambiguously measure cranial dimensions and FSTTs for 38 adult cadavers. This contrasts with prior published use of (a) spreading calipers to compress the face in an attempt to measure cranial dimensions through the soft tissues of the head and (b) needle puncture to measure the FSTT (a + b = legacy methods). To provide direct comparisons to prior work, this study also conducted legacy measurements for reproducibility tests. Previously published LR models were not supported by either the legacy or MR data. In the MR data, correlations between the cranial dimensions and FSTTs were generally weak with a mean absolute r = 0.13 and r range = -0.40 to 0.33. Compared to previously published arithmetic means, LR models did not improve FSTT estimates in the MR sample (SEE for LR = 5.5 mm;SEE for arithmetic mean = 5.2 mm). Using the latest MR imaging technologies, these results underscore prior warnings that cranial dimensions hold weak correlations with FSTTs and possess limited utility for improved FSTT estimation over and/or above arithmetic means.

关键词： correlation coefficient cranial dimensions estimation model facial approximation facial soft tissue depth magnetic resonance imaging multivariate linear regression

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