Path Ranking with Attention to Type Hierarchies

The objective of the knowledge base completion problem is to infer missing information from existing facts in a knowledge base. Prior work has demonstrated the effectiveness of path-ranking based methods, which solve the problem by discovering observable patterns in knowledge graphs, consisting of nodes representing entities and edges representing relations. However, these patterns either lack accuracy because they rely solely on relations or cannot easily generalize due to the direct use of specific entity information. We introduce Attentive Path Ranking, a novel path pattern representation that leverages type hierarchies of entities to both avoid ambiguity and maintain generalization. Then, we present an end-to-end trained attention-based RNN model to discover the new path patterns from data. Experiments conducted on benchmark knowledge base completion datasets WN18RR and FB15k-237 demonstrate that the proposed model outperforms existing methods on the fact prediction task by statistically significant margins of 26% and 10%, respectively. Furthermore, quantitative and qualitative analyses show that the path patterns balance between generalization and discrimination.Comment: Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20

Antitrust Analysis for the Internet Upstream Market: a BGP Approach

In this paper we study concentration in the European Internet upstream access market. Measurement of market concentration depends on correctly defining the market, but this is not always possible as Antitrust authorities often lack reliable pricing and traffic data. We present an alternative approach based on the inference of the Internet Operators interconnection policies using micro-data sourced from their Border Gateway Protocol tables. Firstly we propose a price-independent algorithm for defining both the vertical and geographical relevant market boundaries, then we calculate market concentration indexes using two novel metrics. These assess, for each undertaking, both its role in terms of essential network facility and of wholesale market dominance. The results, applied to four leading Internet Exchange Points in London, Amsterdam, Frankfurt and Milan, show that some vertical segments of these markets are extremely competitive, while others are highly concentrated, putting them within the special attention category of the Merger Guidelines

Antitrust Analysis for the Internet Upstream Market: A BGP Approach

In this paper we study concentration in the European Internet upstream access market. The possibility of measuring market concentration depends on a correct definition of the market itself; however, this is not always possible, since, as it is the case of the Internet industry, very often Antitrust authorities lack reliable pricing and traffic data. This difficulty motivates our paper. We present an alternative approach based on the inference of the Internet Operators interconnection policies using micro-data sourced from their Border Gateway Protocol tables. We assess market concentration following a two step process: firstly we propose a price-independent algorithm for defining both the vertical and geographical relevant market boundaries, then we calculate market concentration indexes using two novel metrics. These assess, for each undertaking, both itsrole in terms of essential network facility and of wholesale market dominance. The results, applied to four leading Internet Exchange Points in London, Amsterdam, Frankfurt and Milan, show that some vertical segments of these markets are highly concentrated, while others are extremely competitive. According to the Merger Guidelines some of the estimated market concentration values would immediately fall within the special attention category.Technology and Industry, Other Topics

Evaluation Measures for Hierarchical Classification: a unified view and novel approaches

Hierarchical classification addresses the problem of classifying items into a hierarchy of classes. An important issue in hierarchical classification is the evaluation of different classification algorithms, which is complicated by the hierarchical relations among the classes. Several evaluation measures have been proposed for hierarchical classification using the hierarchy in different ways. This paper studies the problem of evaluation in hierarchical classification by analyzing and abstracting the key components of the existing performance measures. It also proposes two alternative generic views of hierarchical evaluation and introduces two corresponding novel measures. The proposed measures, along with the state-of-the art ones, are empirically tested on three large datasets from the domain of text classification. The empirical results illustrate the undesirable behavior of existing approaches and how the proposed methods overcome most of these methods across a range of cases.Comment: Submitted to journa

Tail universalities in rank distributions as an algebraic problem: the beta-like function

Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks etc., these fits usually fail at the tails. Some distributions have been proposed to solve the problem, but unfortunately they do not fit at the same time both ending tails. We show that many different data in rank laws, like in granular materials, codons, author impact in scientific journal, etc. are very well fitted by a beta-like function. Then we propose that such universality is due to the fact that a system made from many subsystems or choices, imply stretched exponential frequency-rank functions which qualitatively and quantitatively can be fitted with the proposed beta-like function distribution in the limit of many random variables. We prove this by transforming the problem into an algebraic one: finding the rank of successive products of a given set of numbers

Hierarchy measure for complex networks

Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and dynamics of complex systems has been the investigation of the networks associated with the above units (nodes) together with their relations (edges). Most complex systems have an inherently hierarchical organization and, correspondingly, the networks behind them also exhibit hierarchical features. Indeed, several papers have been devoted to describing this essential aspect of networks, however, without resulting in a widely accepted, converging concept concerning the quantitative characterization of the level of their hierarchy. Here we develop an approach and propose a quantity (measure) which is simple enough to be widely applicable, reveals a number of universal features of the organization of real-world networks and, as we demonstrate, is capable of capturing the essential features of the structure and the degree of hierarchy in a complex network. The measure we introduce is based on a generalization of the m-reach centrality, which we first extend to directed/partially directed graphs. Then, we define the global reaching centrality (GRC), which is the difference between the maximum and the average value of the generalized reach centralities over the network. We investigate the behavior of the GRC considering both a synthetic model with an adjustable level of hierarchy and real networks. Results for real networks show that our hierarchy measure is related to the controllability of the given system. We also propose a visualization procedure for large complex networks that can be used to obtain an overall qualitative picture about the nature of their hierarchical structure.Comment: 29 pages, 9 figures, 4 table