Flexible Statistical Modeling

科学、医学和商业领域的大量数据，以及计算技术的现状，为我们提供了前所未有的统计建模机会。例如，使用基因组标记，我们能够建立强大的乳腺癌、心脏病或中风风险预测模型。我们可以预测信用卡违约或欺诈性保险索赔的风险。预测模型能够根据客户过去的行为和偏好以及他们喜欢的客户的行为和偏好向客户推荐电影或音乐。利用多个动植物物种目击地点的数据，我们可以建立一个地理区域的分布图。有了大量的数据，有必要以自动的方式建立这些模型；这个项目的目标是确保结果产品保持可解释。广义可加模型既可解释，又具有一定的功能，但最初旨在用于相对较小的预测变量集。这个项目将使用凸优化的方法来自动建立这样的模型，可能使用数千个变量。该方法将自动省略不相关的变量，并为所有保留的变量选择所需的非线性量。凸方法也将被用来在矩阵完成问题中结合边信息，以及我们传统上使用低阶表示法的各种多变量方法。生态学家经常很难将来自多个物种和不同采样方案的数据结合起来。该项目将提供一个统一的框架，使用非齐次泊松过程模型来组合这些数据，并产生高质量的分布。

The abundance of data in science, medicine and commerce, and the current state of computing technologies gives us opportunities in statistical modeling never seen before. We are able to build powerful predictive models for the risk of breast cancer, heart disease or stroke, for example, using genomic markers. We can predict the risk of credit-card default or fraudulent insurance claims. Predictive models are able to recommend movies or music to a customer, based on their past behavior and preferences and that of customers like them. Using data on locations of sightings of multiple animal or plant species, we can build distribution maps over a geographical domain. With large amounts of data, it becomes necessary that these models are built in an automatic way; the goal of this project is to ensure that the resulting products remain interpretable.Generalized additive models are both interpretable and somewhat powerful, but were originally intended for a relatively small set of predictor variables. This project will use methods in convex optimization to automatically build such models using potentially thousands of variables. The method will automatically omit irrelevant variables, as well as select the amount of nonlinearity needed for all those retained. Convex methods will also be used to incorporate side information in matrix completion problems, as well as a variety of multivariate methods where we have traditionally worked with low-rank representations. Ecologists often struggle with combining data from multiple species and different sampling schemes. This project will provide a unified framework using inhomogeneous Poisson process models for combining these data, and producing high-quality distribution.