Mathematical Sciences: Flexible Regression and Classification

提案：DMS 9504495 PI：特雷弗Hastie机构：斯坦福大学标题：灵活回归和分类 摘要： 该研究涉及几个研究方向，有一个共同的主题：将广泛接受但有限的统计工具推向更冒险的方向，同时保留其一些有吸引力的功能，如模型的可解释性。 具体而言，研究涉及：a）非参数扩展的逻辑回归多类反应，包括添加剂，投影寻踪和基础扩展技术，以及类似于Fisher的LDA的秩降低模型; B）用于基选择的新的自适应算法，类似于Friedman的MARS模型，其使用自然惩罚准则来同时选择变量并收缩它们的系数; c）用于局部地调整最近邻距离度量以对抗维数灾难的技术。 数据分析和建模中的许多重要问题都集中在预测上。一些重要的例子包括 计算机辅助疾病诊断（例如，阅读数字乳房X光照片）、心脏病风险评估、自动阅读手写数字（例如，信封上的邮政编码）、语音识别，仅举几例。这项研究是关于以自然的方式丰富现有的成熟统计模型工具箱，以解决其中一些更复杂的情况。通常，新的外来技术，如神经网络，是“黑盒子”，似乎产生良好的结果，但不提供分析师一个可解释的模型，诊断或类似的反馈，让他们相信盒子产生了合理的结果。 通过发展竞争性和防御性，统计可以在这些重要的预测和数据分析问题中发挥积极作用 模型 这项研究就是通过 创造了一个融合的经典技术和新的技术，允许模型探索。

Proposal: DMS 9504495 PI: Trevor Hastie Institution: Stanford University Title: Flexible Regression and Classification Abstract: The research concerns several research directions with a common theme: to push widely accepted but limited statistical tools in more adventurous directions, while retaining some of their attractive features, such as model interpretability. Specifically, the research involves the development of: a) nonparametric extensions of logistic regression for multiclass responses, including additive, projection pursuit and basis expansion techniques, as well as rank reduced models similar to Fisher's LDA; b) a new adaptive algorithm for basis selection, similar to Friedman's MARS model, which uses a natural penalized criterion to simultaneously select variables and shrinks their coefficients; c) a technique for locally adapting the nearest neighbor distance metric to combat the curse of dimensionality. Many important problems in data analysis and modeling focus on prediction. Some important examples include computer assisted diagnosis of disease (e.g. reading digital mammograms), heart disease risk assessment, automatic reading of handwritten digits (e.g. zip-codes on envelopes), speech recognition, to name a few. This research is about enriching the current toolbox of well established statistical models in a natural way to address some of these more complex scenarios. Often new exotic techniques, such as neural networks, are ``black boxes'' that appear to produce good results, but do not provide the analyst with an interpretable model, diagnostics or similar feedback to give them confidence that the box has produced sensible results. Statistics can play an active role in these important prediction and data analysis problems through the development competitive and defensible models. This research does just that by creating a blend between the well understood classical techniques and the new techniques that allow for model exploration.