Robust Methods in Statistics and Machine Learning

我打算继续调查与实验研究设计有关的问题，以期获得对各种模型不足具有鲁棒性的推理程序。在统计学中，“鲁棒性”指的是一个过程在其推导的假设被违反时保持其有效性的能力。这一概念在实验研究中尤其重要，因为实验者可能对产生数据的随机机制的结构只有模糊的认识。近年来，机器学习界也认识到，他们所知道的“主动学习”在某种程度上是实验设计的代名词，同时需要对该领域的处理方式进行鲁棒化。我在这一领域的工作已经从调查相当普遍的问题，例如设计，以适应响应函数线性的几个参数，当真正的反应实际上是一个未知的成员，一个邻居，这个拟合的反应，通过调查其他形式的误指定（鲁棒性对异方差，或依赖等）。并应用于特定的应用领域。这些应用领域导致了空间设计方面的问题-例如，在相邻监测站之间的相关结构不确定的情况下如何安置环境监测站-歧视方面的问题-例如，如何设计以便在两种特定和方便的药理反应建模方法之间进行选择的问题，虽然承认两者都不一定非常准确-而且在剂量反应方面-例如，为了预测药物的最低有效剂量或医疗水平而进行设计，这通常需要逻辑或概率单位分析，但也认识到这些联系可能不适当。预计在下一任总干事任期内，所有这些设计方法都将得到推广和进一步尝试。我想解决的一些特殊问题（除其他外）是：（一）在分类问题中主动学习的鲁棒抽样方案这是与西班牙潘普洛纳的同事一起进行的。主动学习是一种机器学习技术，其中“智能”采样方案用于在分析之前对大量数据进行采样。导致这个项目的想法是在我以前的总干事的一个项目中开发的，在那里它们被应用于回归模型。 (ii)在一般和可能错误指定的依赖结构下设计的鲁棒性。科威特，并应导致，例如，改进空间设计。(iii)临床试验设计的稳健性这将解决这样的问题，即当在临床试验分析中采用预后因素时，因素/响应关系中的错误指定可能会极大地偏倚结果。

I intend to continue my investigations into problems related to the design of experimental studies, with an eye to obtaining inferential procedures which are robust against various model inadequacies. In Statistics, 'robustness' refers to the ability of a procedure to retain its validity when the assumptions underlying its derivation are violated. This notion is particularly important in experimental studies, where the experimenter may have only a vague knowledge of the structure of the stochastic mechanism generating the data. In recent years it has also been recognized within the Machine Learning community that what they know as 'active learning' is somewhat synonymous with experimental design, with an accompanying need for a robustification of the ways in which the field is approached. My work in this area has evolved from investigations of quite general problems, for instance designing to fit a response function linear in several parameters, when the true response is in fact an unknown member of a neighbourhood of this fitted response, through investigations of other forms of misspecification (robustness against heteroscedasticity, or dependence, etc.) and on to particular fields of application. These fields of application have led to problems in spatial design - for instance, the placement of environmental monitoring stations in the face of uncertainly about the correlation structure between neighbouring stations - in discrimination - for instance the problem of designing so as to allow one to choose between two particular and convenient methods of modelling pharmacological reactions, while admitting that neither is necessarily very accurate - and in dose response - for instance designing so as to predict a minimum effective dose of a drug or level of a medical treatment, something typically calling for a logistic or probit analysis, while recognizing that these links might be inappropriate. Extensions and further forays into all of these approaches to design are anticipated within the tenure of the next DG. Some particular problems (among others) that I would like to address are: (i) Robust sampling schemes for active learning in classification problems This is to be carried out with colleagues from Pamplona, Spain. Active learning is a machine learning technique whereby 'intelligent' sampling schemes are used to sample huge amounts of data prior to their being analyzed. The ideas leading to this project were developed in a project under my previous DG, where they were applied to regression models. (ii) Robustness of design under general and possibly misspecified dependence structures This will be carried out with a colleague from U. Kuwait, and should lead to, for instance, improved spatial designs. (iii) Robustness of design for clinical trials This will address the problem that, when prognostic factors are employed in the analysis of clinical trials, misspecifications in the factor/response relationships  can greatly bias the results.