Angle Regression Research Articles

What life course theoretical models best explain the relationship between exposure to childhood adversity and psychopathology symptoms: recency, accumulation, or sensitive periods?

Although childhood adversity is a potent determinant of psychopathology, relatively little is known about how the characteristics of adversity exposure, including its developmental timing or duration, influence subsequent mental health outcomes. This study compared three models from life course theory (recency, accumulation, sensitive period) to determine which one(s) best explained this relationship. Prospective data came from the Avon Longitudinal Study of Parents and Children (n = 7476). Four adversities commonly linked to psychopathology (caregiver physical/emotional abuse; sexual/physical abuse; financial stress; parent legal problems) were measured repeatedly from birth to age 8. Using a statistical modeling approach grounded in least angle regression, we determined the theoretical model(s) explaining the most variability (r2) in psychopathology symptoms measured at age 8 using the Strengths and Difficulties Questionnaire and evaluated the magnitude of each association. Recency was the best fitting theoretical model for the effect of physical/sexual abuse (girls r2 = 2.35%; boys r2 = 1.68%). Both recency (girls r2 = 1.55%) and accumulation (boys r2 = 1.71%) were the best fitting models for caregiver physical/emotional abuse. Sensitive period models were chosen alone (parent legal problems in boys r2 = 0.29%) and with accumulation (financial stress in girls r2 = 3.08%) more rarely. Substantial effect sizes were observed (standardized mean differences = 0.22-1.18). Child psychopathology symptoms are primarily explained by recency and accumulation models. Evidence for sensitive periods did not emerge strongly in these data. These findings underscore the need to measure the characteristics of adversity, which can aid in understanding disease mechanisms and determining how best to reduce the consequences of exposure to adversity.

Global parameters sensitivity analysis and development of a two-dimensional real-time model of proton-exchange-membrane fuel cells

This paper presents a 2-D real-time modeling approach for a proton-exchange-membrane fuel cell (PEMFC). The proposed model covers multi-physical domains for both fluidic and electrochemical features, which considers in particular the flow field geometric form of fuel cell. The characteristics of reactant gas convection in the serpentine gas pipeline and diffusion phenomenon through the gas diffusion layer (GDL) are thoroughly considered in fluidic domain model. In addition, a three levels iterative solver is developed in order to accurately calculate the implicit spatial physical quantities distribution in electrochemical domain. Moreover, the proposed 2-D real-time modeling approach uses a numerical method to achieve a fast execution time, and can thus be further easily applied to any real-time control implementation or online diagnostic system. After experimental validation under different fuel cell operating conditions, an iterative Least Angle Regression (LAR) method is used to efficiently and accurately perform the global parameters sensitivity analysis based on Sobol definition. The online analysis results give an insight into the influences of modeling parameters on fuel cell performance. The effect of interactions between parameters’ sensitivities is especially investigated, which can provide useful information for degradation understanding, parameters tuning, re-calibration of the parameters and online prognostic.

A new strategy of least absolute shrinkage and selection operator coupled with sampling error profile analysis for wavelength selection

A new strategy based on sampling error profile analysis (SEPA) combined with least absolute shrinkage and selection operator (SEPA-LASSO) was proposed. LASSO has been proven to be effective for multivariate calibration with automatic variable selection for high-dimensional data.However, in the previous research, the critical process of multivariate calibration by LASSO was an optimization of 1-norm turning parameter for a fixed sample set without considering the behaviors of variable selection by different subsets of samples. In the present work, Monte Carlo Sampling (MCS), the core of SEPA framework, is used to investigate various sub-models. Least angle regression (LAR) is used to solve LASSO, and various LAR iteration including certain number of variables could be obtained instead of choosing the numerical values of 1-norm turning parameters. SEPA-LASSO algorithm consists of plenty of loops. Under the SEPA framework and LAR algorithm, a number of LASSO sub-models with the same dimensions are built by MCS in each loop, the vote rule is used to determine the importance of variables and select them to build variable subsets. After running the loops, several subsets of variables are obtained and their error profile is used to choose the optimal subset of variables. The performance of SEPA-LASSO was evaluated by three near-infrared (NIR) datasets. The results show that the model built by SEPA-LASSO has excellent predictability and interpretability, compared with some commonly used multivariate calibration methods, such as principal component regression (PCR) and partial least squares (PLS), as well as some wavelength selection methods including LASSO, moving window partial least squares regression (MWPLSR), Monte Carlo uninformative variable elimination (MC-UVE), ordered homogeneity pursuit lasso (OHPL) and stability competitive adaptive reweighted sampling (SCARS).

Efficient test-based variable selection for high-dimensional linear models

Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression (LARS), among others. These methods typically add variables into the model one by one. For such selection procedures, it is crucial to find a stopping criterion that controls model complexity. One of the most commonly used techniques to this end is cross-validation (CV) which, in spite of its popularity, has two major drawbacks: expensive computational cost and lack of statistical interpretation. To overcome these drawbacks, we introduce a flexible and efficient test-based variable selection approach that can be incorporated into any sequential selection procedure. The test, which is on the overall signal in the remaining inactive variables, is based on the maximal absolute partial correlation between the inactive variables and the response given active variables. We develop the asymptotic null distribution of the proposed test statistic as the dimension tends to infinity uniformly in the sample size. We also show that the test is consistent. With this test, at each step of the selection, a new variable is included if and only if the p-value is below some pre-defined level. Numerical studies show that the proposed method delivers very competitive performance in terms of variable selection accuracy and computational complexity compared to CV.

Efficient Global Sensitivity Analysis of 3D Multiphysics Model for Li-Ion Batteries

Parameter sensitivity analysis of mechanistic battery models has the power to quantify the individual and joint effects of parameters on the performance of lithium-ion cells. This information can be beneficial for industrial cell designs, cell testing, and battery management system (BMS) configurations. The numerical quantification of these parameter sensitivities, however, is challenging in terms of computational costs and is an active field of research. In this paper, based on a 3D multiphysics model, we conduct a global sensitivity analysis for the utilizable cell discharge capacity and the maximum cell temperature at the discharge rate of 1C. The least angle regression version of the polynomial chaos expansion (PCE) concept has been identified as an optimal trade-off between approximation power and computational complexity. As a result, the sensitivities of all parameters in the 3D multiphysics model were studied using a hierarchical design and a stepwise design. We conclude that the cell discharge capacity and the thermal behavior at 1C discharge are most sensitive to the electrode parameters and their pore structure. The results reveal different dependencies and lead to new insights for cell design and operation.

Discrete Element Method of Coke Accumulation: Calibration of the Contact Parameter

The calibration of contact parameters involved in the DEM model regarding coke accumulation process was performed. The simulation of coke accumulation was carried out by using Hertz-Mindlin (no slip) contact model. Furthermore, the Box-Behnken experiment method was used to conduct this numerical simulation. The repose angle regression model was obtained by multivariate regression analysis of the experimental results. The variance analysis of regression model shows that the regression model is significant. The complicated interaction of linear and quadratic terms exist between contact parameters. This study serves as a preliminary basis on the determination of the contact parameters.

Acute trajectories of neural activation predict remission to pharmacotherapy in late-life depression.

Pharmacological treatment of major depressive disorder (MDD) typically involves a lengthy trial and error process to identify an effective intervention. This lengthy period prolongs suffering and worsens all-cause mortality, including from suicide, and is typically longer in late-life depression (LLD). Our group has recently demonstrated that during an open-label venlafaxine (serotonin-norepinephrine reuptake inhibitor) trial, significant changes in functional resting state connectivity occurred following a single dose of treatment, which persisted until the end of the trial. In this work, we propose an analysis framework to translate these perturbations in functional networks into predictors of clinical remission. Participants with LLD (N = 49) completed 12-weeks of treatment with venlafaxine and underwent functional magnetic resonance imaging (fMRI) at baseline and a day following a single dose of venlafaxine. Data was collected at rest as well as during an emotion reactivity task and an emotion regulation task. Remission was defined as a Montgomery-Asberg Depression Rating Scale (MADRS) ≤10 for two weeks. We computed eigenvector centrality (whole brain connectivity) and activation during the emotion regulation and emotion reactivity tasks. We employed principal components analysis, Tikhonov-regularized logistic classification, and least angle regression feature selection to predict remission by the end of the 12-week trial. We utilized ten-fold cross-validation and Receiver Operator Curves (ROC) curve analysis. To determine task-region pairs that significantly contributed to the algorithm's ability to predict remission, we used permutation testing. Using the fMRI data at both baseline and after the first dose of treatment yielded a sensitivity of 72% and a specificity of 68% (AUC = 0.77), a 15% increase in accuracy over baseline MADRS. In general, the accuracy at baseline was further improved by using the change in activation following a single dose. Activation of the frontal cortex, hippocampus, parahippocampus, caudate, thalamus, medial temporal cortex, middle cingulate, and visual cortex predicted treatment remission. Acute, dynamic trajectories of functional imaging metrics in response to a pharmacological intervention are a valuable tool for predicting treatment response in late-life depression and elucidating the mechanism of pharmacological therapies in the context of the brain's functional architecture.

PKWmEB: integration of Kruskal\u2013Wallis test with empirical Bayes under polygenic background control for multi-locus genome-wide association study

Although nonparametric methods in genome-wide association studies (GWAS) are robust in quantitative trait nucleotide (QTN) detection, the absence of polygenic background control in single-marker association in genome-wide scans results in a high false positive rate. To overcome this issue, we proposed an integrated nonparametric method for multi-locus GWAS. First, a new model transformation was used to whiten the covariance matrix of polygenic matrix K and environmental noise. Using the transferred model, Kruskal–Wallis test along with least angle regression was then used to select all the markers that were potentially associated with the trait. Finally, all the selected markers were placed into multi-locus model, these effects were estimated by empirical Bayes, and all the nonzero effects were further identified by a likelihood ratio test for true QTN detection. This method, named pKWmEB, was validated by a series of Monte Carlo simulation studies. As a result, pKWmEB effectively controlled false positive rate, although a less stringent significance criterion was adopted. More importantly, pKWmEB retained the high power of Kruskal–Wallis test, and provided QTN effect estimates. To further validate pKWmEB, we re-analyzed four flowering time related traits in Arabidopsis thaliana, and detected some previously reported genes that were not identified by the other methods.

Sparse polynomial chaos expansion based on D-MORPH regression

Polynomial chaos expansion (PCE) is widely used by engineers and modelers in various engineering fields for uncertainty analysis. The computational cost of full PCE is unaffordable for the “curse of dimensionality” of the expansion coefficients. In this paper, a new method for developing sparse PCE is proposed based on the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) algorithm. D-MORPH is a regression technique, it can construct the full PCE models with model evaluations much less than the unknown coefficients. This technique determines the unknown coefficients by minimizing the least-squared error and an objective function. For the purpose of developing sparse PCE, an iterative reweighted algorithm is proposed to construct the objective function. As a result, the objective in D-MORPH regression is converted to minimize the ℓ1 norm of PCE coefficients, and the sparse PCE is established after the proposed algorithm converges to the optimal value. To validate the performance of the developed methodology, several benchmark examples are investigated. The accuracy and efficiency are compared to the well-established least angle regression (LAR) sparse PCE, and results show that the developed method is superior to the LAR-based sparse PCE in terms of efficiency and accuracy.

Fast incremental learning of logistic model tree using least angle regression

Expert and intelligent systems understand the underlying information behind the data by relying on a wide range of machine learning techniques. The interpretation of machine learning models is often the key to success in research areas such as business, finance, medical and health science, and bioinformatics; such research areas demand human understanding of the obtained model. The logistic model tree (LMT) algorithm is a popular classification method that combines a decision tree and logistic regression models. The combination of two complementary algorithms produces an accurate and interpretable classifier by combining the advantages of both logistic regression and tree induction. However, LMT has the disadvantage of high computational cost, which makes the algorithm undesirable in practice. In this paper, we propose an efficient method to learn the logistic regression models in the tree. We employ least angle regression to update the regression model in LogitBoost so that the algorithm efficiently learns sparse logistic regression models composed of relevant input variables. We compare the performance of our proposed method with the original LMT algorithm using 14 benchmark datasets and show that the training time dramatically decreases while the accuracy is preserved. Our proposed algorithm is not only accurate and intuitively interpretable but also computationally efficient. It helps users in making the best possible use of the data that are included in expert and intelligent systems.

Efficient Uncertainty Quantification for Unconfined Flow in Heterogeneous Media with the Sparse Polynomial Chaos Expansion

In this study, we explore an efficient stochastic approach for uncertainty quantification of unconfined groundwater flow in heterogeneous media, where a sparse polynomial chaos expansion (PCE) surrogate model is constructed with the aid of the feature selection method. The feature selection method is introduced to construct a sparse PCE surrogate model with a reduced number of basis functions, which is accomplished by the least absolute shrinkage and selection operator-modified least angle regression and cross-validation. The training samples are enriched sequentially with the quasi-optimal samples until the results are satisfactory. In this study, we test the performance of the sparse PCE method for unconfined flow with the presence of random hydraulic conductivity and recharge, as well as pumping well. Numerical experiments reveal that, even with large spatial variability and high random dimensionality, the sparse PCE approach is able to accurately estimate the flow statistics with greatly reduced computational efforts compared to Monte Carlo simulations.

Three $$l_1$$ Based Nonconvex Methods in Constructing Sparse Mean Reverting Portfolios

We study the problem of constructing sparse and fast mean reverting portfolios. The problem is motivated by convergence trading and formulated as a generalized eigenvalue problem with a cardinality constraint (d’Aspremont in Quant Finance 11(3):351–364, 2011). We use a proxy of mean reversion coefficient, the direct Ornstein–Uhlenbeck estimator, which can be applied to both stationary and nonstationary data. In addition, we introduce three different methods to enforce the sparsity of the solutions. One method uses the ratio of $$l_1$$ and $$l_2$$ norms and the other two use $$l_1$$ norm. We analyze various formulations of the resulting non-convex optimization problems and develop efficient algorithms to solve them for portfolio sizes as large as hundreds. By adopting a simple convergence trading strategy, we test the performance of our sparse mean reverting portfolios on both synthetic and historical real market data. In particular, the $$l_1$$ regularization method, in combination with quadratic program formulation as well as difference of convex functions and least angle regression treatment, gives fast and robust performance on large out-of-sample data set.

3.3 Developmental Timing of Exposure to Adversity Predicts DNA Methylation in Late Childhood More Than Recency or Accumulation of Exposure

Exposure to early life adversity (e.g., in the first two decades of life) is known to predict DNA methylation (DNAm). However, few studies have investigated whether adversity has time-dependent effects based on the age at exposure. Using an innovative two-stage structured lifecourse modeling approach (SLCMA) grounded in least angle regression (LARs), we tested the central hypothesis that there are sensitive periods associated with DNAm, or life stages when adversity induced greater DNAm changes. We tested this sensitive period hypothesis in relation to two alternative explanations: an accumulation hypothesis, in which the effect of adversity on DNAm increases with the number of occasions exposed, regardless of timing, and a recency hypothesis, in which the effect of adversity on DNAm is stronger for more proximal events.

A weighted method based on Lars algorithm

LASSO (Least Absolute Shrinkage and Selection Operator) is mainly used to realize variable selection, simultaneously its algorithm and some improved algorithm have gotten wide attention in many fields. To improve the accuracy of LASSO problem in calculating regression coefficients, this paper proposes a new algorithm based on LASR (Least Angle Regression) algorithm to change its approximation direction, which uses two weighted method (coefficient of variation method or entropy weight method) to calculate the weight of linear relationship between the independent and the dependent variables, so we can calculate a regression coefficients set of linear regression model. Compared with LARS algorithm, it can be proved that the improved algorithm mentioned in this paper has a more precise ability for prediction.

Robust locally linear embedding algorithm for machinery fault diagnosis

Locally linear embedding (LLE) is a classical nonlinear dimensionality reduction algorithm, and it has been widely used in machinery fault diagnosis. LLE reduces the dimensions of a data set only by exploring the geometry structure, that is, the geometry structure is one of the key factors for the embedding result. In conventional LLE algorithm, the geometry structure is calculated by ordinary least square (OLS) algorithm, which makes the embedding result be sensitive to noise. In order to resolve the problem, a robust LLE (RLLE) is investigated. In RLLE algorithm, the Least Angle Regression and the Elastic Net (LARS-EN) technologies are employed to compute the local structure. Besides, a novel fault diagnosis method based on RLLE and support vector machine (SVM) are proposed for machinery fault diagnosis. Experiments performed on both synthetic and real data sets demonstrate the advantages of the proposed method in the term of fault diagnosis.

Extended differential geometric LARS for high-dimensional GLMs with general dispersion parameter

A large class of modeling and prediction problems involves outcomes that belong to an exponential family distribution. Generalized linear models (GLMs) are a standard way of dealing with such situations. Even in high-dimensional feature spaces GLMs can be extended to deal with such situations. Penalized inference approaches, such as the $$\ell _1$$ or SCAD, or extensions of least angle regression, such as dgLARS, have been proposed to deal with GLMs with high-dimensional feature spaces. Although the theory underlying these methods is in principle generic, the implementation has remained restricted to dispersion-free models, such as the Poisson and logistic regression models. The aim of this manuscript is to extend the differential geometric least angle regression method for high-dimensional GLMs to arbitrary exponential dispersion family distributions with arbitrary link functions. This entails, first, extending the predictor–corrector (PC) algorithm to arbitrary distributions and link functions, and second, proposing an efficient estimator of the dispersion parameter. Furthermore, improvements to the computational algorithm lead to an important speed-up of the PC algorithm. Simulations provide supportive evidence concerning the proposed efficient algorithms for estimating coefficients and dispersion parameter. The resulting method has been implemented in our R package (which will be merged with the original dglars package) and is shown to be an effective method for inference for arbitrary classes of GLMs.

Construction cost estimation: A parametric approach for better estimates of expected cost and variation

As project planners continue to move towards frameworks such as probabilistic life-cycle cost analysis to evaluate competing transportation investments, there is a need to enhance the current cost-estimation approaches that underlie these models to enable improved project selection. This paper presents an approach for cost estimation that combines a maximum likelihood estimator for data transformations with least angle regression for dimensionality reduction. The authors apply the proposed method for 15 different pavement bid items across five states in the United States. The results from the study demonstrate that the proposed approach frequently leads to consistent parametric estimates that address the structural bias and heteroscedasticity that plague the current cost-estimation procedures. Both of these aspects are particularly important for large-scale construction projects, where traditional methods tend to systematically underestimate expected construction costs and overestimate the associated variance.

Method for Solving LASSO Problem Based on Multidimensional Weight

In the data mining, the analysis of high-dimensional data is a critical but thorny research topic. The LASSO (least absolute shrinkage and selection operator) algorithm avoids the limitations, which generally employ stepwise regression with information criteria to choose the optimal model, existing in traditional methods. The improved-LARS (Least Angle Regression) algorithm solves the LASSO effectively. This paper presents an improved-LARS algorithm, which is constructed on the basis of multidimensional weight and intends to solve the problems in LASSO. Specifically, in order to distinguish the impact of each variable in the regression, we have separately introduced part of principal component analysis (Part_PCA), Independent Weight evaluation, and CRITIC, into our proposal. We have explored that these methods supported by our proposal change the regression track by weighted every individual, to optimize the approach direction, as well as the approach variable selection. As a consequence, our proposed algorithm can yield better results in the promise direction. Furthermore, we have illustrated the excellent property of LARS algorithm based on multidimensional weight by the Pima Indians Diabetes. The experiment results show an attractive performance improvement resulting from the proposed method, compared with the improved-LARS, when they are subjected to the same threshold value.

An efficient stochastic approach for flow in porous media via sparse polynomial chaos expansion constructed by feature selection

An efficient method for uncertainty quantification for flow in porous media is studied in this paper, where response surface of sparse polynomial chaos expansion (PCE) is constructed with the aid of feature selection method. The number of basis functions in PCE grows exponentially as the random dimensionality increases, which makes the computational cost unaffordable in high-dimensional problems. In this study, a feature selection method is introduced to select major stochastic features for the PCE by running a limited number of simulations, and the resultant PCE is termed as sparse PCE. Specifically, the least absolute shrinkage and selection operator modified least angle regression algorithm (LASSO-LAR) is applied for feature selection and the selected features are assessed by cross-validation (CV). Besides, inherited samples are utilized to make the algorithm self-adaptive. In this study, we test the performance of sparse PCE for uncertainty quantification for flow in heterogeneous media with different spatial variability. The statistical moments and probability density function of the output random field are accurately estimated through the sparse PCE, meanwhile the computational efforts are greatly reduced compared to the Monte Carlo method.

One-Class Classification Framework Based on Shrinkage Methods

Statistical machine learning, such as kernel methods, have been widely used to discover hidden regularities and patterns in data. In particular, one-class classification algorithms gained a lot of interest in a large number of applications where the only available data designate a unique class, as in industrial processes. In this paper, we propose a sparse framework for one-class classification problems, by investigating the hypersphere enclosing the samples in a Reproducing Kernel Hilbert Space (RKHS). The center of this hypersphere is approximated using a sparse solution, by selecting an appropriate set of relevant samples. For this purpose, we investigate well-known shrinkage methods, namely Least Angle Regression, Least Absolute Shrinkage and Selection Operator, and Elastic Net. We revisit these methods and adapt their algorithms for estimating the sparse center in the RKHS. The proposed framework is extended to include the truncated Mahalanobis distance, which is necessary when dealing with heterogenous input variables. We also provide some theoretical results on the projection error and on the error of the first kind. The proposed algorithms are compared with well-known one-class classification approaches, with experiments conducted on simulated and real datasets.