Least Angle Regression

描述(由申请人提供)：这个SBIR项目旨在产生更好的方法和软件，当有许多潜在的预测变量可供选择时，用于分类和回归。这些方法应该(1)产生稳定的结果，其中数据的微小变化不会对所选变量或模型预测产生重大变化；(2)产生准确的预测；(3)通过选择提供最佳预测的较小预测子集来促进科学解释；(4)允许连续变量和分类变量；以及(5)支持线性回归、Logistic回归(预测二元结果)、生存分析和其他类型的回归。这个项目基于最小角度回归，它统一并提供了许多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稳健性方面都是有限的。这个项目的结果应该是更健壮和更广泛适用的软件。该软件将广泛应用于医疗诊断、癌症检测、微阵列中的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可行性，通过在三个关键方向扩展最小角度的工作-分类预测，逻辑回归，和一个数值精确的实施。第二阶段的目标包括扩展到其他类型的解释变量(如多项式或样条函数，以及变量之间的相互作用)，扩展到生存和其他其他回归模型，以及处理缺失数据和海量数据集。该软件将使医学研究人员能够在高维情况下获得较高的预测精度，并获得稳定和可解释的结果。根据协变量预测结果，确定哪些协变量对结果影响最大，以及调整协变量的治疗效果估计，这些都是生物统计学中最重要的问题。当可能的特征比样本更多时，预测和特征选择尤其困难；基因微阵列和蛋白质质谱仪就是这种情况的极端例子，每个样本产生数千到数百万次测量。LARS擅长于特征选择；拟议的软件应该使医学研究人员能够在高维情况下获得稳定和可解释的模型，并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.