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Multivariate Spearman’s rho for aggregating ranks using copulas
, 2014
"... We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks by the average value and generalise Spearman’s ρ to ext ..."
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We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks by the average value and generalise Spearman’s ρ to extreme ranks. Our main contribution is the derivation of a nonparametric estimator for rank aggregation based on multivariate extensions of Spearman’s ρ, which measures correlation between a set of ranked lists. Multivariate Spearman’s ρ is defined using copulas, and we show that the geometric mean of normalised ranks maximises multivariate correlation. Motivated by this, we propose a weighted geometric mean approach for learning to rank which has a closed form least squares solution. When only the best or worst elements of a ranked list are known, we impute the missing ranks by the average value, allowing us to apply Spearman’s ρ. Finally, we demonstrate good performance on the rank aggregation benchmarks MQ2007 and MQ2008. 1.
Monotone Closure of Relaxed Constraints in Submodular Optimization: Connections Between Minimization and Maximization: Extended Version
"... It is becoming increasingly evident that many machine learning problems may be reduced to some form of submodular optimization. Previous work addresses generic discrete approaches and specific relaxations. In this work, we take a generic view from a relaxation perspective. We show a relaxation fo ..."
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It is becoming increasingly evident that many machine learning problems may be reduced to some form of submodular optimization. Previous work addresses generic discrete approaches and specific relaxations. In this work, we take a generic view from a relaxation perspective. We show a relaxation formulation and simple rounding strategy that, based on the monotone closure of relaxed constraints, reveals analogies between minimization and maximization problems, and includes known results as special cases and extends to a wider range of settings. Our resulting approximation factors match the corresponding integrality gaps. The results in this paper complement, in a sense explained in the paper, related discrete gradient based methods [30], and are particularly useful given the ever increasing need for efficient submodular optimization methods in very largescale machine learning. For submodular maximization, a number of relaxation approaches have been proposed. A critical challenge for the practical applicability of these techniques, however, is the complexity of evaluating the multilinear extension. We show that this extension can be efficiently evaluated for a number of useful submodular functions, thus making these otherwise impractical algorithms viable for many realworld machine learning problems. 1
AGeneral Truthfulness Characterizations Via Convex Analysis
"... We present a model of truthful elicitation which generalizes and extends mechanisms, scoring rules, and a number of related settings that do not quite qualify as one or the other. Our main result is a characterization theorem, yielding characterizations for all of these settings, including a new cha ..."
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We present a model of truthful elicitation which generalizes and extends mechanisms, scoring rules, and a number of related settings that do not quite qualify as one or the other. Our main result is a characterization theorem, yielding characterizations for all of these settings, including a new characterization of scoring rules for nonconvex sets of distributions. We generalize this model to eliciting some property of the agent’s private information, and provide the first general characterization for this setting. We also show how this yields a new proof of a result in mechanism design due to Saks and Yu. 1.
Systems biology HyDRA: gene prioritization via hybrid distancescore rank aggregation
"... Summary: Gene prioritization refers to a family of computational techniques for inferring disease genes through a set of training genes and carefully chosen similarity criteria. Test genes are scored based on their average similarity to the training set, and the rankings of genes under various simi ..."
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Summary: Gene prioritization refers to a family of computational techniques for inferring disease genes through a set of training genes and carefully chosen similarity criteria. Test genes are scored based on their average similarity to the training set, and the rankings of genes under various similarity criteria are aggregated via statistical methods. The contributions of our work are threefold: (i) first, based on the realization that there is no unique way to define an optimal aggregate for rankings, we investigate the predictive quality of a number of new aggregation methods and known fusion techniques from machine learning and social choice theory. Within this context, we quantify the influence of the number of training genes and similarity criteria on the diagnostic quality of the aggregate and perform indepth crossvalidation studies; (ii) second, we propose a new approach to genomic data aggregation, termed HyDRA (Hybrid Distancescore Rank Aggregation), which combines the advantages of scorebased and combinatorial aggregation techniques. We also propose incorporating a new topversusbottom (TvB) weighting feature into the hybrid schemes. The TvB feature ensures that aggregates are more reliable at the top of the list, rather than at the bottom, since only top candidates are tested experimentally; (iii) third, we propose an iterative pro