Martingale Control of mFDR in Variable Selection

该项目的研究人员开发了在建立统计模型时控制从多个来源选择预测特征的方法。伪变量个数的一个鞅表示提供了基本的理论支持。这个鞅定义了一个框架，用于测试可能无限的假设序列。这种表示导致了用于流特征选择的方法，该方法控制错误发现的预期数量(MFDR)。这个项目中将要开发的扩展概括了研究人员先前的工作，将他们的结果扩展到多个潜在特征流，同时保持了鞅表示。尽管作者之前的工作是在高噪声、低信号环境下，其中几乎没有特征是可预测的(几乎是黑色环境)，但这一提议的进步将他们的方法推入了以许多具有更高信噪比的预测特征为特征的问题。这一建议设想用一个与模型的拟合优度直接相关的方法来取代原来的鞅。研究人员计划使用这个修正的鞅来证明一个结合了多个特征来源的基于拍卖的系统满足mFDR条件。研究人员开发了新的方法来建立组合并从多个信息来源学习的预测统计模型。预测统计模型是由数据构建的经验规则，它基于其他特征的值预测观察的特定特征，即响应。构建这些模型的挑战是识别能够产生预测性洞察力的特征。虽然越来越多的数据是统计模型的基本输入，但大量特征的存在会导致过度拟合的问题。当人们将特征之间的随机重合与可重现的模式混淆时，就会发生过度拟合。现代数据挖掘产生了如此多的特征，以至于很难区分真实的和想象的联想。研究人员提出了一个在通用建模范例的背景下进行这些区分的系统。作为一个实用的试验台，研究人员将使用应用统计学的主要方法-回归分析来分析经典的计算语言学问题。鉴于在语言学方面的经验，回归模型的任何缺陷都会突出出来。这将鼓励回归方面的创新，在保持其简单性的同时，与语言学中的手工方法竞争。这些创新应该扩展到其他应用，包括功能磁共振成像、遗传学和更一般的数据挖掘。

The investigators in this project develop methods that control the selection of predictive features from multiple sources when building statistical models. A martingale representation of the number of spurious variables provides the underlying theoretic support. This martingale defines a framework for testing a possibly infinite sequence of hypotheses. This representation leads to methods for streaming feature selection that control the expected number of false discoveries (mFDR). Extensions to be developed in this project generalize prior work of the investigators, extending their results to multiple streams of potential features while maintaining the martingale representation. Whereas the previous work of the authors was in the high-noise, low-signal setting in which few features are predictive (the nearly black setting), advances in this proposal push their methods into problems characterized by many predictive features with higher signal-to-noise ratios. This proposal envisions replacing the original martingale by one directly related to the goodness of fit of the model. The investigators plan to use this revised martingale to show that an auction-based system that combines several sources of features satisfies the mFDR condition.The investigators develop novel methods for building predictive statistical models that combine and learn from multiple sources of information. A predictive statistical model is an empirical rule constructed from data that predicts a specific characteristic of observations, the response, based on the values of other characteristics. The challenge of building these models is to identify characteristics that yield predictive insights. While ever larger amounts of data are an essential input to a statistical model, the presence of vast numbers of characteristics lead to the problem of over-fitting. Over-fitting occurs when one confuses a random coincidence among characteristics with a reproducible pattern. Modern data mining produces such a plethora of characteristics that it becomes difficult to distinguish real from imaginary associations. The investigators propose a system that makes these distinctions in the context of a common modeling paradigm. As a practical testbed, the investigators will analyze classic computational linguistic problems using regression analysis, the workhorse method of applied statistics. Given the extent of experience in linguistics, any deficiencies of a regression model will stand out. This will encourage innovations in regression that maintain their simplicity while competing with handcrafted methods in linguistics. These innovations should extend to other applications including fMRI, genetics, and more general data mining.