Pairwise comparison

About: Pairwise comparison is a research topic. Over the lifetime, 6804 publications have been published within this topic receiving 174081 citations.

Shortest Paths in Probabilistic Graphs

Abstract: This paper considers the problem of finding shortest-path probability distributions in graphs whose branches are weighted with random lengths, examines the consequences of various assumptions concerning the nature of the available statistical information, and gives an exact method for computing the probability distribution, as well as methods based on hypothesis testing and statistical estimation. It presents Monte Carlo results and, based on these results, it develops an efficient method of hypothesis testing. Finally, it discusses briefly the pairwise comparison of paths.

Simplicial closure and higher-order link prediction

Abstract: Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once-for example, communication within a group rather than person to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental difference from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

Deriving weights from pairwise comparison matrices

Abstract: We study the problem of deriving weights from pairwise comparisons. Properties of acceptable solutions are analysed, including immunity to rank reversals, independence of description of the problem, independence of scale inversion, left-right eigenvector asymmetry, uniqueness, independence of order of operations and inter-level consistency, preservation of the algebraic structure of the problem, extensibility to the additive case, related optimization models and related error measures. We derive the geometric mean from two simple axioms and establish that it is the only acceptable solution to this problem.

Is network meta-analysis as valid as standard pairwise meta-analysis? It all depends on the distribution of effect modifiers

Abstract: Background In the last decade, network meta-analysis of randomized controlled trials has been introduced as an extension of pairwise meta-analysis. The advantage of network meta-analysis over standard pairwise meta-analysis is that it facilitates indirect comparisons of multiple interventions that have not been studied in a head-to-head fashion. Although assumptions underlying pairwise meta-analyses are well understood, those concerning network meta-analyses are perceived to be more complex and prone to misinterpretation. Discussion In this paper, we aim to provide a basic explanation when network meta-analysis is as valid as pairwise meta-analysis. We focus on the primary role of effect modifiers, which are study and patient characteristics associated with treatment effects. Because network meta-analysis includes different trials comparing different interventions, the distribution of effect modifiers cannot only vary across studies for a particular comparison (as with standard pairwise meta-analysis, causing heterogeneity), but also between comparisons (causing inconsistency). If there is an imbalance in the distribution of effect modifiers between different types of direct comparisons, the related indirect comparisons will be biased. If it can be assumed that this is not the case, network meta-analysis is as valid as pairwise meta-analysis. Summary The validity of network meta-analysis is based on the underlying assumption that there is no imbalance in the distribution of effect modifiers across the different types of direct treatment comparisons, regardless of the structure of the evidence network.

Improving pairwise learning for item recommendation from implicit feedback

Abstract: Pairwise algorithms are popular for learning recommender systems from implicit feedback. For each user, or more generally context, they try to discriminate between a small set of selected items and the large set of remaining (irrelevant) items. Learning is typically based on stochastic gradient descent (SGD) with uniformly drawn pairs. In this work, we show that convergence of such SGD learning algorithms slows down considerably if the item popularity has a tailed distribution. We propose a non-uniform item sampler to overcome this problem. The proposed sampler is context-dependent and oversamples informative pairs to speed up convergence. An efficient implementation with constant amortized runtime costs is developed. Furthermore, it is shown how the proposed learning algorithm can be applied to a large class of recommender models. The properties of the new learning algorithm are studied empirically on two real-world recommender system problems. The experiments indicate that the proposed adaptive sampler improves the state-of-the art learning algorithm largely in convergence without negative effects on prediction quality or iteration runtime.