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，着眼于获得针对各种模型不足的推理程序。在统计学中，“稳健性”是指一个程序在其推导的基础假设被违反时保持其有效性的能力。这个概念在实验研究中尤其重要，因为实验人员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，机器学习社区也认识到，他们所谓的“主动学习”在某种程度上是实验设计的同义词，同时也需要对该领域的处理方式进行强化。***我在这一领域的工作是从对相当普遍的问题的研究演变而来的，例如设计拟合几个参数的线性响应函数，当真正的响应实际上是这个拟合响应的一个邻域的未知成员时，通过对其他形式的错误规范（对异方差的鲁棒性，或依赖性等）的研究以及对特定应用领域的研究。这些应用领域导致了空间设计方面的问题，例如，环境监测站的位置，在面对不确定的相邻站之间的相关结构的歧视，例如，设计的问题，以便允许人们选择两种特定的和方便的方法来模拟药物反应，虽然承认两者都不一定非常准确，但在剂量反应方面，例如设计以预测药物的最低有效剂量或医疗水平，通常需要逻辑或概率分析，同时认识到这些联系可能是不适当的。预计在下一任总干事任期内，将对所有这些设计方法进行扩展和进一步探索。我想解决的一些特殊问题包括：***(I)分类问题中主动学习的鲁棒抽样方案这将与来自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，通过“智能”采样方案，在分析大量数据之前对其进行采样。导致这个项目的想法是在我之前的DG领导下的一个项目中开发的，在那里它们被应用于回归模型。***(ii)在一般和可能指定错误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，并应导致诸如空间设计的改进。***(iii)临床试验设计的稳健性这将解决在临床试验分析中使用预后因素时，对因素/反应关系的错误说明会极大地影响结果的问题。

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.