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确实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，但目前的技术水平仅限于具有连续变量或二元变量的线性回归，并且使用数值不稳定的计算。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。 第一阶段的工作将通过在三个关键方向上扩展最小角度工作来证明可行性-分类预测、逻辑回归和数值精确实现。第二阶段将把工作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)，以及生存和其他额外的回归模型。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。

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 to 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 the state of the art is limited to linear regression with continuous or binary variables, and uses numerically-unstable calculations. 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 will demonstrate feasibility by extending least angle work in three key directions-categorical predictors, logistic regression, and a numerically-accurate implementation. Phase II will extend the work to other types of explanatory variables (e.g. polynomial or spline functions, and interactions between variables), and to survival and other additional regression models. This proposed software will enable medical researchers to obtain high prediction accuracy, and obtain stable and interpretable results, in high-dimensional situations.