Pierangelo Lombardo

Pierangelo Lombardo

A relevant problem in statistics is defining the correlation of two rankings of a list of items. Kendall's tau and Spearman's rho are two well established correlation coefficients, characterized by a symmetric form that ensures zero expected value between two pairs of rankings randomly chosen with uniform probability. However, in recent years, several weighted versions of the original Spearman and Kendall coefficients have emerged that take into account the greater importance of top ranks compared to low ranks, which is common in many contexts. The weighting schemes break the symmetry, causing a non-zero expected value between two random rankings. This issue is very relevant, as it undermines the concept of uncorrelation between rankings. In this paper, we address this problem by proposing a standardization function $g(x)$ that maps a correlation ranking coefficient $Γ$ in a standard form $g(Γ)$ that has zero expected value, while maintaining the relevant statistical properties of $Γ$.

Pierangelo Lombardo, Alessio Boiardi, Luca Colombo et al.

The growth of domain-specific applications of semantic models, boosted by the recent achievements of unsupervised embedding learning algorithms, demands domain-specific evaluation datasets. In many cases, content-based recommenders being a prime example, these models are required to rank words or texts according to their semantic relatedness to a given concept, with particular focus on top ranks. In this work, we give a threefold contribution to address these requirements: (i) we define a protocol for the construction, based on adaptive pairwise comparisons, of a relatedness-based evaluation dataset tailored on the available resources and optimized to be particularly accurate in top-rank evaluation; (ii) we define appropriate metrics, extensions of well-known ranking correlation coefficients, to evaluate a semantic model via the aforementioned dataset by taking into account the greater significance of top ranks. Finally, (iii) we define a stochastic transitivity model to simulate semantic-driven pairwise comparisons, which confirms the effectiveness of the proposed dataset construction protocol.