Least Angle Regression

描述（由申请人提供）：这个SBIR项目的目的是产生上级方法和软件的分类和回归时，有许多潜在的预测变量可供选择。这些方法应（1）产生稳定的结果，其中数据的微小变化不会导致所选变量或模型预测的重大变化;（2）产生准确的预测;（3）通过选择提供最佳预测的较小的预测因子子集，促进科学解释;（4）允许连续和分类变量;以及（5）支持线性回归、逻辑回归（预测二元结果）、生存分析和其他类型的回归。该项目基于最小角度回归，它统一并提供了一些现代回归技术的快速实现。最小角度回归具有很大的潜力，但目前可用的软件在范围和鲁棒性方面受到限制。这个项目的成果应该是更强大和广泛适用的软件。该软件将广泛应用于医疗诊断、癌症检测、微阵列特征选择以及血压等患者特征建模。第一阶段的工作证明了在三个关键方向上扩展最小角度工作的可行性-分类预测因子，逻辑回归和数字准确的实现。第二阶段的目标包括扩展到其他类型的解释变量（例如多项式或样条函数，变量之间的相互作用），生存和其他额外的回归模型，以及处理缺失数据和大量数据集。该软件将使医学研究人员在高维情况下获得高预测精度，并获得稳定和可解释的结果。基于协变量预测结果，确定哪些协变量最影响结果，以及调整协变量的治疗效果估计，是生物统计学中最重要的问题之一。当可能的特征比样本多时，预测和特征选择特别困难;基因微阵列和蛋白质质谱是这方面的极端例子，每个样本产生数千到数百万个测量结果。LARS擅长特征选择;所提出的软件应使医学研究人员能够获得稳定和可解释的模型，在高维情况下具有更好的预测精度。

DESCRIPTION (provided by applicant): This SBIR project aims to produce superior methods and software for classification and regression when there are many potential predictor variables to choose from. The methods should (1) produce stable results, where small changes in the data do not produce major changes in the variables selected or in model predictions; (2) produce accurate predictions; (3) facilitate scientific interpretation, by selecting a smaller subset of predictors which provide the best predictions; (4) allow continuous and categorical variables; and (5) support linear regression, logistic regression (predicting a binary outcome), survival analysis, and other types of regression. This project is based on least angle regression, which unifies and provides a fast implementation for a number of modern regression techniques. Least angle regression has great potential, but currently available software is limited in scope and robustness. The outcome of this project should be software which is more robust and widely applicable. This software would apply broadly, including to medical diagnosis, detecting cancer, feature selection in microarrays, and modeling patient characteristics like blood pressure. Phase I work demonstrates feasibility by extending least angle work in three key directions-categorical predictors, logistic regression, and a numerically-accurate implementation. Phase II goals include extensions to other types of explanatory variables (e.g. polynomial or spline functions, and interactions between variables), to survival and other additional regression models, and to handle missing data and massive data sets. This proposed software will enable medical researchers to obtain high prediction accuracy, and obtain stable and interpretable results, in high-dimensional situations. Predicting outcomes based on covariates, determining which covariates most affect outcomes, and adjusting treatment effects estimates for covariates, are among the most important problems in biostatistics. Prediction and feature selection are particularly difficult when there are more possible features than samples; gene microarrays and protein mass spectrometry are extreme examples of this, producing thousands to millions of measurements per sample. LARS excels at feature selection; the proposed software should enable medical researchers to obtain stable and interpretable models with better prediction accuracy in high-dimensional situations.