In the context of learning to rank for information retrieval [15], we study a general class of “DCG-like” ranking loss functions which include DCG [13] and approximate ERR [6] as specific cases. We then study the Bayes optimal ranking function for this class, which is a function of the conditional distribution of graded document relevance levels. Our main contribution is a novel class of rankin...

Network security analysis based on attack graphs has been applied extensively in recent years. The ranking of nodes in an attack graph is an important step towards analyzing network security. This paper proposes an alternative attack graph ranking scheme based on a recent approach to machine learning in a structured graph domain, namely, Graph Neural Networks (GNNs). Evidence is presented in th...

The problem of ranking, in which the goal is to learn a real-valued ranking function that induces a ranking or ordering over an instance space, has recently gained attention in machine learning. We define a model of learnability for ranking functions in a particular setting of the ranking problem known as the bipartite ranking problem, and derive a number of results in this model. Our first mai...

The quality of the ranking function is an important factor that determines the quality of the Information Retrieval system. Each document is assigned a score by the ranking function; the score indicates the likelihood of relevance of the document given a query. In the vector space model, the ranking function is defined by a mathematic expression such as: ∑ ∈ = q t d q score ) , ( tf(t in d) * i...

Many machine learning technologies such as support vector machines, boosting, and neural networks have been applied to the ranking problem in information retrieval. However, since originally the methods were not developed for this task, their loss functions do not directly link to the criteria used in the evaluation of ranking. Specifically, the loss functions are defined on the level of docume...

Many machine learning technologies such as Support Vector Machines, Boosting, and Neural Networks have been applied to the ranking problem in information retrieval. However, since originally the methods were not developed for this task, their loss functions do not directly link to the criteria used in the evaluation of ranking. Specifically, the loss functions are defined on the level of docume...

The exchangeability assumption as defined in this paper on ranking functions seems intuitively natural, and indeed, specific ranking functions previously proposed in the literature are all exchangeable. While pointwise ranking functions are vacuously exchangeable, we now discuss two specifically listwise ranking functions previously proposed by [22] and [26] in light of our representation theor...

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting. In fuzzy decision making problems fuzzy numbers must be ranked before an action is taken by a decision maker. Chen and Li have proposed on “Representation, ranking, and distance of fuzzy number with exponential membership function using grade mean integration method" by ranking index for ranking expon...

Measuring the relative compositionality of Multi-word Expressions (MWEs) is crucial to Natural Language Processing. Various collocation based measures have been proposed to compute the relative compositionality of MWEs. In this paper, we define novel measures (both collocation based and context based measures) to measure the relative compositionality of MWEs of V-N type. We show that the correl...