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，以期获得针对各种模型不足的稳健的推理程序。在统计学中，“稳健性”是指当一个程序的推导依据的假设被违反时，该程序保持其有效性的能力。这一概念在实验研究中尤其重要，因为实验者对产生数据的随机机制的结构可能只有一个模糊的了解。近年来，机器学习界也认识到，他们所知的“主动学习”在某种程度上是实验设计的同义词，随之而来的是对处理该领域的方法的粗暴的需要。*我在这一领域的工作是从对非常普遍的问题的调查中发展而来的，例如，通过调查其他形式的错误描述(对异方差或相关性等的健壮性)，当真实的响应实际上是该拟合的响应的邻域中的未知成员时，设计以几个参数线性的响应函数。并延伸到特定的应用领域。这些应用领域导致了空间设计方面的问题，例如，在对相邻监测站之间的相关结构进行区分时面临不确定的环境监测站的布置问题，例如，设计使人能够在两种对药理反应进行建模的具体和方便的方法之间进行选择的问题，同时承认，这两种方法都不一定非常准确，而且在剂量反应方面也不一定非常准确，例如，设计用于预测一种药物的最低有效剂量或一种医疗水平的方法，通常需要进行逻辑分析或概率分析，同时认识到这些联系可能是不适当的。所有这些设计方法的扩展和进一步尝试都有望在下一任DG的任期内完成。我想要解决的一些具体问题(其中包括)是：*(I)在分类问题中主动学习的稳健抽样方案这将与西班牙潘普洛纳的同事一起进行。主动学习是一种机器学习技术，在对大量数据进行分析之前，可以使用“智能”抽样方案对其进行采样。这个项目的想法是在我之前的DG领导下的一个项目中发展出来的，在那里它们被应用到回归模型中。*(Ii)在一般和可能错误指定的依赖结构下设计的稳健性这将与来自科威特的一位同事一起进行，例如，应该导致改进的空间设计。*(Iii)临床试验设计的稳健性这将解决这样一个问题，即当在临床试验的分析中使用预测因素时，因素/反应关系中的错误指定可能会极大地影响结果。

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.