Robust Methods in Statistics and Machine Learning

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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.