A new hierarchical ranking aggregation method

International audienceThe purpose of ranking aggregation (or fusion) is to combine multiple rankings to a consensus one. In the ranking aggregation, some of the items’ preference orders are easy to distinguish, however, some others’ are not. To specifically compare the ambiguous items, i.e., the items whose aggregated preference orders are difficult to distinguish, is helpful for ranking aggregation. In this paper, a new hierarchical ranking aggregation method is proposed. The items whose preference orders are easy to distinguish are first divided into different ranking levels (i.e., the ordered items subsets), and the ambiguous items are put into the same ranking level. The items in high ranking levels are ranked higher than the items in low ranking levels in the aggregated ranking. Then the items in the same ranking level are further compared and divided into multiple ranking sub-levels. The aggregated ranking is generated hierarchically by dividing the same ranking levels’ (or sub-levels’) items into sub-levels until each sub-level only includes one item. Furthermore, we discuss the way of using the insertion sort method for merging the adjacent levels’ rankings to improve the quality of the aggregated ranking. The experiments and simulations show that our new hierarchical methods perform well in ranking aggregation

Stable Feature Selection for Biomarker Discovery

Feature selection techniques have been used as the workhorse in biomarker discovery applications for a long time. Surprisingly, the stability of feature selection with respect to sampling variations has long been under-considered. It is only until recently that this issue has received more and more attention. In this article, we review existing stable feature selection methods for biomarker discovery using a generic hierarchal framework. We have two objectives: (1) providing an overview on this new yet fast growing topic for a convenient reference; (2) categorizing existing methods under an expandable framework for future research and development

Hierarchical Knowledge-Gradient for Sequential Sampling

We consider the problem of selecting the best of a finite but very large set of alternatives. Each alternative may be characterized by a multi-dimensional vector and has independent normal rewards. This problem arises in various settings such as (i) ranking and selection, (ii) simulation optimization where the unknown mean of each alternative is estimated with stochastic simulation output, and (iii) approximate dynamic programming where we need to estimate values based on Monte-Carlo simulation. We use a Bayesian probability model for the unknown reward of each alternative and follow a fully sequential sampling policy called the knowledge-gradient policy. This policy myopically optimizes the expected increment in the value of sampling information in each time period. Because the number of alternatives is large, we propose a hierarchical aggregation technique that uses the common features shared by alternatives to learn about many alternatives from even a single measurement, thus greatly reducing the measurement effort required. We demonstrate how this hierarchical knowledge-gradient policy can be applied to efficiently maximize a continuous function and prove that this policy finds a globally optimal alternative in the limit