Robustness of Design

我打算继续调查与实验研究设计相关的问题，着眼于获得针对各种模型不足的健壮的推理程序。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反应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”在很大程度上是实验设计的同义词，随之而来的是需要对该领域的方法进行粗暴的改革。我在这一领域的工作是从对非常普遍的问题的调查发展而来的，例如，通过调查其他形式的误指定(异方差、相关性等)，设计拟合响应函数，而实际响应实际上是该拟合响应的邻域中的未知成员。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，在面临邻近站点之间相关结构的不确定性的情况下设置环境监测站的问题，在区分方面--例如设计问题，使人们能够在两种具体和方便的药理反应建模方法之间进行选择，同时承认这两种方法都不一定非常准确，并且在剂量反应方面--例如设计以便预测一种药物的最低有效剂量或一种医疗的水平，这种情况通常需要进行逻辑分析或概率分析，同时认识到这两种分析都可能有偏差。对所有这些设计方法的扩展和进一步尝试是可以预期的。我想要解决的一些具体问题(除其他许多问题外)：(I)文献中关于稳健设计方法和稳健估计和预测方法的结合存在差距。几年前，我开始了一项关于设计稳健性的调查，当时M-估计将成为预期的估计方法。目前，分位数回归估计正在流行，但到目前为止还没有相应的健壮设计策略来使其“完全健壮”。这将是我未来几年进一步研究的重点。(Ii)临床试验的设计--这是设计中特别重要的一个领域，因为医生往往执着于长期存在的与各种协变量的反应有关的“经典”模型。设计者主要关注的是治疗和协变量组之间的“平衡”，很少考虑效率。同样，将新来的患者分配到治疗组的典型方法往往没有考虑到可能的异方差，或者使用其有效性可能受到严重质疑的方差函数。因此，显然需要更健壮的方法；静态和顺序设计策略都可以考虑。(Iii)在机器学习中，近年来有几个研究人员借鉴了我介绍的一些技术，并将它们改造为主动学习的应用。他们特别是通过我提出的模拟退火法应用了这些技术。这种算法非常适合于小规模问题，但对于在某些应用中被建模和采样的海量数据集则不太合适。我打算研究更有效的算法来处理这类问题。(4)我打算把我的工作扩展到计算机实验领域。

I intend to continue my investigations into problems related to the design of experimental studies, with an eye to obtaining inferential procedures that 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 response generating the data. In recent years it has also been recognized within the Machine Learning community that what they know as 'active learning' is largely 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 when the true response is in fact an unknown member of a neighbourhood of this fitted response, through investigations of other forms of misspecification (heteroscedasticity, 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 uncertainty 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 both of these analyses might be biased. Extensions and further forays into all of these approaches to design are anticipated. Some particular problems (among many others) that I would like to address:(i) There is a gap in the literature as regards the combination of robust methods of designs and robust methods of estimation and prediction. Some years ago I initiated an investigation into robustness of design when M-estimation was to be the intended method of estimation. Currently, quantile regression estimation is coming into vogue, but so far without correspondingly robust design strategies to make it 'fully robust'. This will be a further focus of my research in the next few years.(ii) Designs for Clinical Trials – this is an area of particular importance in design, given that medical practitioners tend to be wedded to longstanding 'classical' models relating response to various covariates. The designers are primarily concerned with 'balance' across treatment and covariate groups, with little thought being given to efficiency. As well, typical methods of assigning incoming patients to treatment groups often fail to take possible heteroscedasticity into account, or employ variance functions whose validity may be seriously in doubt. There is then a clear need for more robust approaches; both static and sequential design strategies may be considered.(iii) In Machine Learning, several researchers have in recent years borrowed some of the techniques introduced by me and adapted them as applications of 'active learning'. They have in particular applied these techniques via a simulated annealing algorithm proposed by me. Such algorithms are quite appropriate for small scale problems, but less so for the massive data sets being modelled and sampled in some applications. I intend to study more efficient algorithms for dealing with such problems.(iv) I intend to extend my work to the field of Computer Experimentation.