Shape constraint inference: Open problems and new directions

University Of California-Davis, Davis CA

Investigators

Abstract

The international conference on "Shape constraint inference: Open problems and new directions" will take place October 5 - 9, 2015, at the Lorentz Center, Leiden, The Netherlands. The topic of this conference is the study of the performance of a certain category of statistical methodologies. These methodologies distinguish themselves from related methods by their goal to explicitly incorporate a certain type of structural prior knowledge about the target object. Many examples of practical importance exist, for instance, in finance, economics, genomics and medicine. A simple example is given by the reasonable statement that older cars tend to have a higher risk of failure. Thus when predicting the risk of failure of a car at different ages, the statistical methodology should explicitly use this prior knowledge. Ideally this should be achieved without imposing any further constraints that are difficult to justify in practice. The structural assumption just described, i.e. being increasing over time, is classical. Modern statistical challenges are much more complex. For instance, the object of interest might not just be influenced by one factor ("age" in the above example), but by a large number of factors, and the influence of these factors might differ. While some of them might increase the risk, some others might decrease it, for instance. There are many other important types of structural constraints for which statistical methodology needs to be developed. It is of crucial importance to gain a thorough understanding for the behavior of these methods. Answering questions such as "When do these methods work, and when do they not work?" is crucial. There are also computational challenges associated with the development of these methodologies that need to be tackled. The conference will provide a forum to advance this field of statistics. Participants will consist of both senior and more junior researchers, as well as postdocs and PhD students. Special emphasis will be given to increase female participation. Shape and order constraints can be considered as a way to regularize an underlying problem in a more explicit and verifiable way, which in particular is useful in multi and high-dimensional situations. Despite the intuitive appeal often inherent in shape constraint methods, their analysis and the computations involved tend to be challenging. Thus tackling such problems in complex situations (e.g. high-dimensional) often requires novel ideas. Recent promising advances exist and they will guide the organization of this conference. Moreover, the connection of shape constrained inference to related geometrically motivated statistical approaches, including the investigation of modality and of related ideas from topological data analysis (persistent homology) deserve being explored in more depth. The conference will serve as a catalyzer for further developments in these fields, including novel developments for shape constraint estimation in high-dimensional situations, computational and methodological ideas for log-concave estimation in multivariate settings, distributional results for multivariate order restricted non-parametric maximum likelihood estimators, and more.