Shape constraint inference: Open problems and new directions

关于“形状约束推理：开放问题和新方向”的国际会议将于2015年10月5日至9日在荷兰莱顿的洛伦兹中心举行。本次会议的主题是研究某类统计方法的性能。这些方法与相关方法的区别在于它们的目标是明确地结合关于目标对象的某种类型的结构先验知识。例如，在金融、经济、基因组学和医学领域，有许多具有实际重要性的例子。一个简单的例子是合理的说法，即旧汽车往往有更高的风险失败。因此，在预测汽车在不同年龄段的故障风险时，统计方法应该明确使用这种先验知识。理想的情况是，在实现这一目标时，不应施加任何在实践中难以证明合理的进一步限制。刚才所描述的结构性假设，即随着时间的推移而增加，是经典的。现代统计挑战要复杂得多。例如，感兴趣的对象可能不仅受一个因素（上述示例中的“年龄”）的影响，而是受大量因素的影响，并且这些因素的影响可能不同。例如，其中一些可能会增加风险，而另一些可能会降低风险。还有许多其他重要类型的结构性制约因素需要制定统计方法。深入了解这些方法的行为是至关重要的。提出诸如“这些方法何时有效，何时无效？“至关重要。还有与这些方法的发展相关的计算挑战需要解决。会议将为推动这一统计领域的发展提供一个论坛。参与者将包括高级和初级研究人员，以及博士后和博士生。形状和顺序约束可以被认为是一种以更明确和可验证的方式规范基本问题的方法，这在多维和高维情况下特别有用。尽管形状约束方法具有直观的吸引力，但其分析和计算往往具有挑战性。因此，在复杂的情况下（例如高维）解决这些问题通常需要新颖的想法。最近取得了一些有希望的进展，这些进展将指导这次会议的组织工作。此外，连接形状约束推理相关的几何动机的统计方法，包括调查的方式和相关的想法，从拓扑数据分析（持久同源性）值得更深入地探讨。该会议将作为这些领域进一步发展的催化剂，包括高维情况下形状约束估计的新发展，多变量设置中对数凹估计的计算和方法思想，多变量顺序限制非参数最大似然估计的分布结果等等。

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.