Robust Methods in Statistics and Machine Learning

统计和机器学习中的稳健方法

• 批准号: RGPIN-2019-04417
• 负责人: Wiens, Douglas
• 金额: $ 2.19万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758367
• 关键词: Robust; Methods; Statistics; Machine; Learning

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.

我打算继续研究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之处的稳健推理程序。在统计学中，“稳健性”是指当其推导所依据的假设被违反时，程序保持其有效性的能力。这个概念在实验研究中尤其重要，实验者可能对生成数据的随机机制的结构只有模糊的了解。近年来，机器学习社区也认识到，他们所说的“主动学习”在某种程度上与实验设计同义，随之而来的是对该领域的研究方式进行强化的需要。我在这一领域的工作是从对相当普遍的问题的研究发展而来的，例如设计在多个参数中拟合线性响应函数，而真实响应实际上是该拟合响应的邻域的未知成员，通过对其他形式的错误指定（异方差性或依赖性等的鲁棒性）的研究，以及特定的应用领域。这些应用领域导致了空间设计中的问题，例如，在邻近站之间的相关结构不确定的情况下环境监测站的放置问题，在区分中，例如设计问题，以便允许人们在两种特定且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，在剂量反应中，例如设计问题，以便预测药物的最小有效剂量 或医疗水平，通常需要进行逻辑或概率分析，同时认识到这些链接可能不合适。预计在下一任总干事的任期内，将对所有这些设计方法进行扩展和进一步尝试。我想解决的一些特定问题（其中包括）是：（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，在分析大量数据之前，使用“智能”采样方案对大量数据进行采样。这个项目的想法是在我之前的总负责人领导下的一个项目中提出的，它们被应用于回归模型。 (ii) 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，并且应该会导致例如空间设计的改进。 (iii) 临床试验设计的稳健性这将解决以下问题：当在临床试验分析中采用预后因素时，因素/反应关系中的错误指定可能会极大地使结果产生偏差。