An Ordered Lasso and Sparse Time-Lagged Regression.
Ontology highlight
ABSTRACT:
SUBMITTER: Tibshirani R
PROVIDER: S-EPMC10004099 | biostudies-literature | 2016
REPOSITORIES: biostudies-literature
Publications
An Ordered Lasso and Sparse Time-Lagged Regression.
Tibshirani Robert R Suo Xiaotong X
Technometrics : a journal of statistics for the physical, chemical, and engineering sciences 20161011 4
We consider regression scenarios where it is natural to impose an order constraint on the coefficients. We propose an order-constrained version of <i>ℓ</i> <sub>1</sub>-regularized regression (Lasso) for this problem, and show how to solve it efficiently using the well-known Pool Adjacent Violators Algorithm as its proximal operator. The main application of this idea is to time-lagged regression, where we predict an outcome at time <i>t</i> from features at the previous <i>K</i> time points. In ...[more]
Similar Datasets
Project description:BackgroundAccurate gene regulatory networks can be used to explain the emergence of different phenotypes, disease mechanisms, and other biological functions. Many methods have been proposed to infer networks from gene expression data but have been hampered by problems such as low sample size, inaccurate constraints, and incomplete characterizations of regulatory dynamics. Since expression regulation is dynamic, time-course data can be used to infer causality, but these datasets tend to be short or sparsely sampled. In addition, temporal methods typically assume that the expression of a gene at a time point depends on the expression of other genes at only the immediately preceding time point, while other methods include additional time points without any constraints to account for their temporal distance. These limitations can contribute to inaccurate networks with many missing and anomalous links.ResultsWe adapted the time-lagged Ordered Lasso, a regularized regression method with temporal monotonicity constraints, for de novo reconstruction. We also developed a semi-supervised method that embeds prior network information into the Ordered Lasso to discover novel regulatory dependencies in existing pathways. R code is available at https://github.com/pn51/laggedOrderedLassoNetwork .ConclusionsWe evaluated these approaches on simulated data for a repressilator, time-course data from past DREAM challenges, and a HeLa cell cycle dataset to show that they can produce accurate networks subject to the dynamics and assumptions of the time-lagged Ordered Lasso regression.
| S-EPMC6311035 | biostudies-literature
Project description:For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if ρ=limpn=0 , where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additional assumptions such as sparsity must be imposed in order to ensure consistency for SIR. By constructing artificial response variables made up from top eigenvectors of the estimated conditional covariance matrix, we introduce a simple Lasso regression method to obtain an estimate of the SDR space. The resulting algorithm, Lasso-SIR, is shown to be consistent and achieve the optimal convergence rate under certain sparsity conditions when p is of order o(n 2 λ 2), where λ is the generalized signal-to-noise ratio. We also demonstrate the superior performance of Lasso-SIR compared with existing approaches via extensive numerical studies and several real data examples.
| S-EPMC7500493 | biostudies-literature
Project description:BackgroundStatistical analyses of biological problems in life sciences often lead to high-dimensional linear models. To solve the corresponding system of equations, penalization approaches are often the methods of choice. They are especially useful in case of multicollinearity, which appears if the number of explanatory variables exceeds the number of observations or for some biological reason. Then, the model goodness of fit is penalized by some suitable function of interest. Prominent examples are the lasso, group lasso and sparse-group lasso. Here, we offer a fast and numerically cheap implementation of these operators via proximal gradient descent. The grid search for the penalty parameter is realized by warm starts. The step size between consecutive iterations is determined with backtracking line search. Finally, seagull -the R package presented here- produces complete regularization paths.ResultsPublicly available high-dimensional methylation data are used to compare seagull to the established R package SGL. The results of both packages enabled a precise prediction of biological age from DNA methylation status. But even though the results of seagull and SGL were very similar (R2 > 0.99), seagull computed the solution in a fraction of the time needed by SGL. Additionally, seagull enables the incorporation of weights for each penalized feature.ConclusionsThe following operators for linear regression models are available in seagull: lasso, group lasso, sparse-group lasso and Integrative LASSO with Penalty Factors (IPF-lasso). Thus, seagull is a convenient envelope of lasso variants.
| S-EPMC7493359 | biostudies-literature
Project description:We propose a multivariate sparse group lasso variable selection and estimation method for data with high-dimensional predictors as well as high-dimensional response variables. The method is carried out through a penalized multivariate multiple linear regression model with an arbitrary group structure for the regression coefficient matrix. It suits many biology studies well in detecting associations between multiple traits and multiple predictors, with each trait and each predictor embedded in some biological functional groups such as genes, pathways or brain regions. The method is able to effectively remove unimportant groups as well as unimportant individual coefficients within important groups, particularly for large p small n problems, and is flexible in handling various complex group structures such as overlapping or nested or multilevel hierarchical structures. The method is evaluated through extensive simulations with comparisons to the conventional lasso and group lasso methods, and is applied to an eQTL association study.
| S-EPMC4479976 | biostudies-literature
Project description:The impact of neurotoxic chemical mixtures on children's health is a critical public health concern. It is well known that during early life, toxic exposures may impact cognitive function during critical time intervals of increased vulnerability, known as windows of susceptibility. Knowledge on time windows of susceptibility can help inform treatment and prevention strategies, as chemical mixtures may affect a developmental process that is operating at a specific life phase. There are several statistical challenges in estimating the health effects of time-varying exposures to multi-pollutant mixtures, such as: multi-collinearity among the exposures both within time points and across time points, and complex exposure-response relationships. To address these concerns, we develop a flexible statistical method, called lagged kernel machine regression (LKMR). LKMR identifies critical exposure windows of chemical mixtures, and accounts for complex non-linear and non-additive effects of the mixture at any given exposure window. Specifically, LKMR estimates how the effects of a mixture of exposures change with the exposure time window using a Bayesian formulation of a grouped, fused lasso penalty within a kernel machine regression (KMR) framework. A simulation study demonstrates the performance of LKMR under realistic exposure-response scenarios, and demonstrates large gains over approaches that consider each time window separately, particularly when serial correlation among the time-varying exposures is high. Furthermore, LKMR demonstrates gains over another approach that inputs all time-specific chemical concentrations together into a single KMR. We apply LKMR to estimate associations between neurodevelopment and metal mixtures in Early Life Exposures in Mexico and Neurotoxicology, a prospective cohort study of child health in Mexico City.
| S-EPMC5991212 | biostudies-literature
Project description:Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths and the tuning parameters are determined by a cross validation procedure to achieve the largest prediction accuracy. We provide a theoretical result for simultaneous model selection consistency and parameter estimation consistency of our method in high dimension. This new framework is then generalized such that it can be applied to principal components analysis, partial least squares and canonical correlation analysis. We also adapt this framework for discriminant analysis. Compared to the existing methods, where there is relatively little control of the dependency among the sparse components, our method can control the relationships among the components. We present efficient algorithms and related theory for solving the sparse regression by projection problem. Based on extensive simulations and real data analysis, we demonstrate that our method achieves good predictive performance and variable selection in the regression setting, and the ability to control relationships between the sparse components leads to more accurate classification. In supplemental materials available online, the details of the algorithms and theoretical proofs, and R codes for all simulation studies are provided.
| S-EPMC4560121 | biostudies-literature
Project description:Identification of genetic variants associated with complex traits is a critical step for improving plant resistance and breeding. Although the majority of existing methods for variants detection have good predictive performance in the average case, they can not precisely identify the variants present in a small number of target genes. In this paper, we propose a weighted sparse group lasso (WSGL) method to select both common and low-frequency variants in groups. Under the biologically realistic assumption that complex traits are influenced by a few single loci in a small number of genes, our method involves a sparse group lasso approach to simultaneously select associated groups along with the loci within each group. To increase the probability of selecting out low-frequency variants, biological prior information is introduced in the model by re-weighting lasso regularization based on weights calculated from input data. Experimental results from both simulation and real data of single nucleotide polymorphisms (SNPs) associated with Arabidopsis flowering traits demonstrate the superiority of WSGL over other competitive approaches for genetic variants detection.
| S-EPMC7063084 | biostudies-literature
Project description:Non-invasive recordings of human brain activity through electroencephalography (EEG) or magnetoencelphalography (MEG) are of value for both basic science and clinical applications in sensory, cognitive, and affective neuroscience. Here we introduce a new approach to estimating the intra-cranial sources of EEG/MEG activity measured from extra-cranial sensors. The approach is based on the group lasso, a sparse-prior inverse that has been adapted to take advantage of functionally-defined regions of interest for the definition of physiologically meaningful groups within a functionally-based common space. Detailed simulations using realistic source-geometries and data from a human Visual Evoked Potential experiment demonstrate that the group-lasso method has improved performance over traditional ℓ2 minimum-norm methods. In addition, we show that pooling source estimates across subjects over functionally defined regions of interest results in improvements in the accuracy of source estimates for both the group-lasso and minimum-norm approaches.
| S-EPMC5467834 | biostudies-literature
Project description:Public hospital spending consumes a large share of government expenditure in many countries. The large cost variability observed between hospitals and also between patients in the same hospital has fueled the belief that consumption of a significant portion of this funding may result in no clinical benefit to patients, thus representing waste. Accurate identification of the main hospital cost drivers and relating them quantitatively to the observed cost variability is a necessary step towards identifying and reducing waste. This study identifies prime cost drivers in a typical, mid-sized Australian hospital and classifies them as sources of cost variability that are either warranted or not warranted-and therefore contributing to waste. An essential step is dimension reduction using Principal Component Analysis to pre-process the data by separating out the low value 'noise' from otherwise valuable information. Crucially, the study then adjusts for possible co-linearity of different cost drivers by the use of the sparse group lasso technique. This ensures reliability of the findings and represents a novel and powerful approach to analysing hospital costs. Our statistical model included 32 potential cost predictors with a sample size of over 50,000 hospital admissions. The proportion of cost variability potentially not clinically warranted was estimated at 33.7%. Given the financial footprint involved, once the findings are extrapolated nationwide, this estimation has far-reaching significance for health funding policy.
| S-EPMC6179217 | biostudies-literature
Project description:The developmental timing of exposures to toxic chemicals or combinations of chemicals may be as important as the dosage itself. This concept is called "critical windows of exposure." The time boundaries of such windows can be detected if exposure data are collected repeatedly in short time intervals. The development of tooth-matrix biomarkers which provide prenatal and postnatal exposure measures in repeated intervals can provide such data. Using teeth, we use reverse distributed lagged models (DLMs) to incorporate weekly prenatal and postnatal measures of exposures to estimate time-varying associations with developmental effects. The analysis of such data using lagged weighted quantile sum (WQS) regression as an extension to reverse DLMs for complex mixtures was first proposed by Bello et al. This prior algorithm was not operationally generalizable to large numbers of components (say, more than five or six). We propose a revised algorithm that may be useful for larger mixtures by combining time-specific WQS(t) indices in a reverse DLM. We demonstrate the new algorithm using tooth data in association with a neurodevelopmental score and in simulated data from 3 cases wherein different components of a mixture have time varying associations and in the case where none have associations. The new algorithm correctly detects the simulated associations when the number of samples within the time-specific analyses is moderate to large.
| S-EPMC7489300 | biostudies-literature