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HodgeRank with Information Maximization for Crowdsourced Pairwise Ranking Aggregation

arXiv.org Machine Learning

Recently, crowdsourcing has emerged as an effective paradigm for human-powered large scale problem solving in various domains. However, task requester usually has a limited amount of budget, thus it is desirable to have a policy to wisely allocate the budget to achieve better quality. In this paper, we study the principle of information maximization for active sampling strategies in the framework of HodgeRank, an approach based on Hodge Decomposition of pairwise ranking data with multiple workers. The principle exhibits two scenarios of active sampling: Fisher information maximization that leads to unsupervised sampling based on a sequential maximization of graph algebraic connectivity without considering labels; and Bayesian information maximization that selects samples with the largest information gain from prior to posterior, which gives a supervised sampling involving the labels collected. Experiments show that the proposed methods boost the sampling efficiency as compared to traditional sampling schemes and are thus valuable to practical crowdsourcing experiments.


Hybrid-MST: A Hybrid Active Sampling Strategy for Pairwise Preference Aggregation

Neural Information Processing Systems

In this paper we present a hybrid active sampling strategy for pairwise preference aggregation, which aims at recovering the underlying rating of the test candidates from sparse and noisy pairwise labelling. Our method employs Bayesian optimization framework and Bradley-Terry model to construct the utility function, then to obtain the Expected Information Gain (EIG) of each pair. For computational efficiency, Gaussian-Hermite quadrature is used for estimation of EIG. In this work, a hybrid active sampling strategy is proposed, either using Global Maximum (GM) EIG sampling or Minimum Spanning Tree (MST) sampling in each trial, which is determined by the test budget. The proposed method has been validated on both simulated and real-world datasets, where it shows higher preference aggregation ability than the state-of-the-art methods.


Hybrid-MST: A Hybrid Active Sampling Strategy for Pairwise Preference Aggregation

Neural Information Processing Systems

In this paper we present a hybrid active sampling strategy for pairwise preference aggregation, which aims at recovering the underlying rating of the test candidates from sparse and noisy pairwise labeling. Our method employs Bayesian optimization framework and Bradley-Terry model to construct the utility function, then to obtain the Expected Information Gain (EIG) of each pair. For computational efficiency, Gaussian-Hermite quadrature is used for estimation of EIG. In this work, a hybrid active sampling strategy is proposed, either using Global Maximum (GM) EIG sampling or Minimum Spanning Tree (MST) sampling in each trial, which is determined by the test budget. The proposed method has been validated on both simulated and real-world datasets, where it shows higher preference aggregation ability than the state-of-the-art methods.


Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs

arXiv.org Machine Learning

Crowdsourcing platforms are now extensively used for conducting subjective pairwise comparison studies. In this setting, a pairwise comparison dataset is typically gathered via random sampling, either \emph{with} or \emph{without} replacement. In this paper, we use tools from random graph theory to analyze these two random sampling methods for the HodgeRank estimator. Using the Fiedler value of the graph as a measurement for estimator stability (informativeness), we provide a new estimate of the Fiedler value for these two random graph models. In the asymptotic limit as the number of vertices tends to infinity, we prove the validity of the estimate. Based on our findings, for a small number of items to be compared, we recommend a two-stage sampling strategy where a greedy sampling method is used initially and random sampling \emph{without} replacement is used in the second stage. When a large number of items is to be compared, we recommend random sampling with replacement as this is computationally inexpensive and trivially parallelizable. Experiments on synthetic and real-world datasets support our analysis.


Hybrid-MST: A Hybrid Active Sampling Strategy for Pairwise Preference Aggregation

arXiv.org Machine Learning

In this paper we present a hybrid active sampling strategy for pairwise preference aggregation, which aims at recovering the underlying rating of the test candidates from sparse and noisy pairwise labelling. Our method employs Bayesian optimization framework and Bradley-Terry model to construct the utility function, then to obtain the Expected Information Gain (EIG) of each pair. For computational efficiency, Gaussian-Hermite quadrature is used for estimation of EIG. In this work, a hybrid active sampling strategy is proposed, either using Global Maximum (GM) EIG sampling or Minimum Spanning Tree (MST) sampling in each trial, which is determined by the test budget. The proposed method has been validated on both simulated and real-world datasets, where it shows higher preference aggregation ability than the state-of-the-art methods.