GNNRank: Learning Global Rankings from Pairwise Comparisons via Directed Graph Neural Networks
University of Oxford（牛津大学）；Amazon Web Services AI Shanghai Lablet（亚马逊云科技AI上海实验室）；The Alan Turing Institute（阿兰·图灵研究所）；Shanghai Jiao Tong University（上海交通大学）；Shanghai AI Laboratory（上海人工智能实验室）
Yixuan He, Quan Gan, David Wipf, Gesine Reinert, Junchi Yan, Mihai Cucuringu
备注：
ICML 2022 spotlight; 32 pages (9 pages for main text)
Recovering global rankings from pairwise comparisons has wide applications from time synchronization to sports team ranking. Pairwise comparisons corresponding to matches in a competition can be construed as edges in a directed graph (digraph), whose nodes represent e.g. competitors with an unknown rank. In this paper, we introduce neural networks into the ranking recovery problem by proposing the so-called GNNRank, a trainable GNN-based framework with digraph embedding. Moreover, new objectives are devised to encode ranking upsets/violations. The framework involves a ranking score estimation approach, and adds an inductive bias by unfolding the Fiedler vector computation of the graph constructed from a learnable similarity matrix. Experimental results on extensive data sets show that our methods attain competitive and often superior performance against baselines, as well as showing promising transfer ability. Codes and preprocessed data are at: \url{https://github.com/SherylHYX/GNNRank}.
We present pairwise fairness metrics for ranking models and regression models that form analogues of statistical fairness notions such as equal opportunity, equal accuracy, and statistical parity. Our pairwise formulation supports both discrete protected groups, and continuous protected attributes. We show that the resulting training problems can be efficiently and effectively solved using existing constrained optimization and robust optimization techniques developed for fair classification. Experiments illustrate the broad applicability and trade-offs of these methods.
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise comparisons. We are interested in natural situations in which relationships among the objects may allow for ranking using far fewer pairwise comparisons. Specifically, we assume that the objects can be embedded into a $d$-dimensional Euclidean space and that the rankings reflect their relative distances from a common reference point in $R^d$. We show that under thi…
In this paper we consider the collaborative ranking setting: a pool of users each provides a small number of pairwise preferences between $d$ possible items; from these we need to predict preferences of the users for items they have not yet seen. We do so by fitting a rank $r$ score matrix to the pairwise data, and provide two main contributions: (a) we show that an algorithm based on convex optimization provides good generalization guarantees once each user provides as few as $O(r\log^2 d)$ pairwise comparisons -- essentially matching the sample complexity required in the related matrix compl…
We consider the problem of recovering the rank of a set of $n$ items based on noisy pairwise comparisons. We assume the SST class as the family of generative models. Our analysis gave sharp information theoretic upper and lower bound for the exact requirement, which matches exactly in the parametric limit. Our tight analysis on the algorithm induced by the moment method gave better constant in Minimax optimal rate than ~\citet{shah2017simple} and contribute to their open problem. The strategy we used in this work to obtain information theoretic bounds is based on combinatorial arguments and is…
Ohio State University（俄亥俄州立大学）；Iowa State University（爱荷华州立大学）
This paper explores the adaptive (active) PAC (probably approximately correct) top-$k$ ranking (i.e., top-$k$ item selection) and total ranking problems from $l$-wise ($l\geq 2$) comparisons under the multinomial logit (MNL) model. By adaptively choosing sets to query and observing the noisy output of the most favored item of each query, we want to design ranking algorithms that recover the top-$k$ or total ranking using as few queries as possible. For the PAC top-$k$ ranking problem, we derive a lower bound on the sample complexity (aka number of queries), and propose an algorithm that is sam…
We study the problem of ranking from crowdsourced pairwise comparisons. Answers to pairwise tasks are known to be affected by the position of items on the screen, however, previous models for aggregation of pairwise comparisons do not focus on modeling such kind of biases. We introduce a new aggregation model factorBT for pairwise comparisons, which accounts for certain factors of pairwise tasks that are known to be irrelevant to the result of comparisons but may affect workers' answers due to perceptual reasons. By modeling biases that influence workers, factorBT is able to reduce the effect …
University of California Irvine（加州大学欧文分校）；Xerox Research Centre India（施乐印度研究中心）
We study the problem of ranking a set of items from nonactively chosen pairwise preferences where each item has feature information with it. We propose and characterize a very broad class of preference matrices giving rise to the Feature Low Rank (FLR) model, which subsumes several models ranging from the classic Bradley-Terry-Luce (BTL) (Bradley and Terry 1952) and Thurstone (Thurstone 1927) models to the recently proposed blade-chest (Chen and Joachims 2016) and generic low-rank preference (Rajkumar and Agarwal 2016) models. We use the technique of matrix completion in the presence of side i…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder this matrix and construct a ranking. We first show that this spectral seriation algorithm recovers the true ranking when all pairwise comparisons are observed and consistent with a total order. We then show that ranking reconstruction is still exact when some pairwise comparisons …
Center for the Study of Complex Systems, University of Michigan（密歇根大学复杂系统研究中心）
The task of ranking individuals or teams, based on a set of comparisons between pairs, arises in various contexts, including sporting competitions and the analysis of dominance hierarchies among animals and humans. Given data on which competitors beat which others, the challenge is to rank the competitors from best to worst. Here we study the problem of computing rankings when there are multiple, potentially conflicting modes of comparison, such as multiple types of dominance behaviors among animals. We assume that we do not know a priori what information each behavior conveys about the rankin…
Rice University（莱斯大学）；University of California, Berkeley（加州大学伯克利分校）
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the top-k items as the most prominent special case. The score of a given item is defined as the probability that it beats a randomly chosen other item. Finding an exact ranking typically requires a prohibitively large number of comparisons, but in practice, approximate rankings are often adequate. Accordingly, we study the problem of finding approximate rankings …
CNRS & Ecole Normale Supérieure（法国国家科学研究中心与巴黎高等师范学院）；University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）；INRIA Lille-Nord Europe（法国国家信息与自动化研究所里尔-北欧中心）
Given a measurement graph $G= (V,E)$ and an unknown signal $r \in \mathbb{R}^n$, we investigate algorithms for recovering $r$ from pairwise measurements of the form $r_i - r_j$; $\{i,j\} \in E$. This problem arises in a variety of applications, such as ranking teams in sports data and time synchronization of distributed networks. Framed in the context of ranking, the task is to recover the ranking of $n$ teams (induced by $r$) given a small subset of noisy pairwise rank offsets. We propose a simple SVD-based algorithmic pipeline for both the problem of time synchronization and ranking. We prov…
Learning to rank is an effective recommendation approach since its introduction around 2010. Famous algorithms such as Bayesian Personalized Ranking and Collaborative Less is More Filtering have left deep impact in both academia and industry. However, most learning to rank approaches focus on improving technical accuracy metrics such as AUC, MRR and NDCG. Other evaluation metrics of recommender systems like fairness have been largely overlooked until in recent years. In this paper, we propose a new learning to rank algorithm named Pareto Pairwise Ranking. We are inspired by the idea of Bayesia…
Recommender systems are one of the most pervasive applications of machine learning in industry, with many services using them to match users to products or information. As such it is important to ask: what are the possible fairness risks, how can we quantify them, and how should we address them? In this paper we offer a set of novel metrics for evaluating algorithmic fairness concerns in recommender systems. In particular we show how measuring fairness based on pairwise comparisons from randomized experiments provides a tractable means to reason about fairness in rankings from recommender syst…
We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items into sets of pre-specified sizes according to their scores. This notion of ranking includes as special cases the identification of the top-k items and the total ordering of the items. We first analyze a sequential ranking algorithm that counts the number of comparisons won, and uses these counts to decide whether to stop, or to compare another pair of items, ch…
We introduce deep learning models to the two most important stages in product search at JD.com, one of the largest e-commerce platforms in the world. Specifically, we outline the design of a deep learning system that retrieves semantically relevant items to a query within milliseconds, and a pairwise deep re-ranking system, which learns subtle user preferences. Compared to traditional search systems, the proposed approaches are better at semantic retrieval and personalized ranking, achieving significant improvements.
Automatic Readability Assessment (ARA), the task of assigning a reading level to a text, is traditionally treated as a classification problem in NLP research. In this paper, we propose the first neural, pairwise ranking approach to ARA and compare it with existing classification, regression, and (non-neural) ranking methods. We establish the performance of our model by conducting experiments with three English, one French and one Spanish datasets. We demonstrate that our approach performs well in monolingual single/cross corpus testing scenarios and achieves a zero-shot cross-lingual ranking a…
Graduate School of Information Sciences, Tohoku University（东北大学信息科学研究科）；RIKEN Center for AIP（理化学研究所人工智能研究中心）
Owing to the advancement of deep learning, artificial systems are now rival to humans in several pattern recognition tasks, such as visual recognition of object categories. However, this is only the case with the tasks for which correct answers exist independent of human perception. There is another type of tasks for which what to predict is human perception itself, in which there are often individual differences. Then, there are no longer single "correct" answers to predict, which makes evaluation of artificial systems difficult. In this paper, focusing on pairwise ranking tasks sensitive to …
The problem of bipartite ranking, where instances are labeled positive or negative and the goal is to learn a scoring function that minimizes the probability of mis-ranking a pair of positive and negative instances (or equivalently, that maximizes the area under the ROC curve), has been widely studied in recent years. A dominant theoretical and algorithmic framework for the problem has been to reduce bipartite ranking to pairwise classification; in particular, it is well known that the bipartite ranking regret can be formulated as a pairwise classification regret, which in turn can be upper bo…
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in data analysis (e.g., ranking teams in sports data), computer vision, and machine learning. We formulate the above problem of ranking with incomplete noisy information as an instance of the group synchronization problem over the group SO(2) of planar rotations, whose usefulness has been demonstrated in numerous applications in recent years. Its least squares s…
Listwise ranking losses have been widely studied in recommender systems. However, new paradigms of content consumption present new challenges for ranking methods. In this work we contribute an analysis of learning to rank for personalized mobile push notifications and discuss the unique challenges this presents compared to traditional ranking problems. To address these challenges, we introduce a novel ranking loss based on weighting the pairwise loss between candidates by the expected regret incurred for misordering the pair. We demonstrate that the proposed method can outperform prior methods…
INESCTEC；LIACS；HasLab, INESC TEC, Departamento de Informática, Universidade do Minho（Minho大学信息学院HasLab, INESC TEC）；DCC - Faculdade de Ciencias, Universidade do Porto（波尔图大学科学学院DCC）；LIACS, Leiden, Netherlands（莱顿大学LIACS）
In this paper we investigate two variants of association rules for preference data, Label Ranking Association Rules and Pairwise Association Rules. Label Ranking Association Rules (LRAR) are the equivalent of Class Association Rules (CAR) for the Label Ranking task. In CAR, the consequent is a single class, to which the example is expected to belong to. In LRAR, the consequent is a ranking of the labels. The generation of LRAR requires special support and confidence measures to assess the similarity of rankings. In this work, we carry out a sensitivity analysis of these similarity-based measur…
This report describes our PromptShots submissions to a shared task on Evaluating the Rationales of Amateur Investors (ERAI). We participated in both pairwise comparison and unsupervised ranking tasks. For pairwise comparison, we employed instruction-based models based on T5-small and OpenAI InstructGPT language models. Surprisingly, we observed OpenAI InstructGPT language model few-shot trained on Chinese data works best in our submissions, ranking 3rd on the maximal loss (ML) pairwise accuracy. This model works better than training on the Google translated English data by a large margin, wher…
We consider data in the form of pairwise comparisons of n items, with the goal of precisely identifying the top k items for some value of k < n, or alternatively, recovering a ranking of all the items. We analyze the Copeland counting algorithm that ranks the items in order of the number of pairwise comparisons won, and show it has three attractive features: (a) its computational efficiency leads to speed-ups of several orders of magnitude in computation time as compared to prior work; (b) it is robust in that theoretical guarantees impose no conditions on the underlying matrix of pairwise-com…
Ranking a set of objects involves establishing an order allowing for comparisons between any pair of objects in the set. Oftentimes, due to the unavailability of a ground truth of ranked orders, researchers resort to obtaining judgments from multiple annotators followed by inferring the ground truth based on the collective knowledge of the crowd. However, the aggregation is often ad-hoc and involves imposing stringent assumptions in inferring the ground truth (e.g. majority vote). In this work, we propose Expectation-Maximization (EM) based algorithms that rely on the judgments from multiple a…
We propose a topic modeling approach to the prediction of preferences in pairwise comparisons. We develop a new generative model for pairwise comparisons that accounts for multiple shared latent rankings that are prevalent in a population of users. This new model also captures inconsistent user behavior in a natural way. We show how the estimation of latent rankings in the new generative model can be formally reduced to the estimation of topics in a statistically equivalent topic modeling problem. We leverage recent advances in the topic modeling literature to develop an algorithm that can lea…
Top-K Pairwise Ranking: Bridging the Gap Among Ranking-Based Measures for Multi-Label Classification
IIE, Chinese Academy of Sciences（中国科学院自动化研究所）；SCS, University of Chinese Academy of Sciences（中国科学院大学计算机科学与技术学院）；IIP, ICT, Chinese Academy of Sciences（中国科学院计算技术研究所）；SCST, University of Chinese Academy of Sciences（中国科学院大学计算机科学与技术学院）；Alibaba Group（阿里巴巴集团）；SCST, Shenzhen Campus of Sun Yat-sen University（中山大学深圳校区计算机科学与技术学院）；BDKM, University of Chinese Academy of Sciences（中国科学院大学大数据与知识管理实验室）
We present an attention-based ranking framework for learning to order sentences given a paragraph. Our framework is built on a bidirectional sentence encoder and a self-attention based transformer network to obtain an input order invariant representation of paragraphs. Moreover, it allows seamless training using a variety of ranking based loss functions, such as pointwise, pairwise, and listwise ranking. We apply our framework on two tasks: Sentence Ordering and Order Discrimination. Our framework outperforms various state-of-the-art methods on these tasks on a variety of evaluation metrics. W…
New York University（纽约大学）；University of Iowa（爱荷华大学）
Rank aggregation based on pairwise comparisons over a set of items has a wide range of applications. Although considerable research has been devoted to the development of rank aggregation algorithms, one basic question is how to efficiently collect a large amount of high-quality pairwise comparisons for the ranking purpose. Because of the advent of many crowdsourcing services, a crowd of workers are often hired to conduct pairwise comparisons with a small monetary reward for each pair they compare. Since different workers have different levels of reliability and different pairs have different …
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Massachusetts Institute of Technology（麻省理工学院）
Ranking by pairwise comparisons has shown improved reliability over ordinal classification. However, as the annotations of pairwise comparisons scale quadratically, this becomes less practical when the dataset is large. We propose a method for reducing the number of pairwise comparisons required to rank by a quantitative metric, demonstrating the effectiveness of the approach in ranking medical images by image quality in this proof of concept study. Using the medical image annotation software that we developed, we actively subsample pairwise comparisons using a sorting algorithm with a human r…
KAIST（韩国科学技术院）；Electronics and Telecommunications Research Institute（电子与电信研究所）；UIUC（伊利诺伊大学厄巴纳-香槟分校）
We explore the top-$K$ rank aggregation problem. Suppose a collection of items is compared in pairs repeatedly, and we aim to recover a consistent ordering that focuses on the top-$K$ ranked items based on partially revealed preference information. We investigate the Bradley-Terry-Luce model in which one ranks items according to their perceived utilities modeled as noisy observations of their underlying true utilities. Our main contributions are two-fold. First, in a general comparison model where item pairs to compare are given a priori, we attain an upper and lower bound on the sample size f…
This paper studies the problem of finding the exact ranking from noisy comparisons. A comparison over a set of $m$ items produces a noisy outcome about the most preferred item, and reveals some information about the ranking. By repeatedly and adaptively choosing items to compare, we want to fully rank the items with a certain confidence, and use as few comparisons as possible. Different from most previous works, in this paper, we have three main novelties: (i) compared to prior works, our upper bounds (algorithms) and lower bounds on the sample complexity (aka number of comparisons) require th…
University of Science and Technology of China（中国科学技术大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Most recommender systems optimize the model on observed interaction data, which is affected by the previous exposure mechanism and exhibits many biases like popularity bias. The loss functions, such as the mostly used pointwise Binary Cross-Entropy and pairwise Bayesian Personalized Ranking, are not designed to consider the biases in observed data. As a result, the model optimized on the loss would inherit the data biases, or even worse, amplify the biases. For example, a few popular items take up more and more exposure opportunities, severely hurting the recommendation quality on niche items …
University of Utah（犹他大学）；University of Twente（特文特大学）；University of California（加利福尼亚大学）
Given a graph where vertices represent alternatives and arcs represent pairwise comparison data, the statistical ranking problem is to find a potential function, defined on the vertices, such that the gradient of the potential function agrees with the pairwise comparisons. Our goal in this paper is to develop a method for collecting data for which the least squares estimator for the ranking problem has maximal Fisher information. Our approach, based on experimental design, is to view data collection as a bi-level optimization problem where the inner problem is the ranking problem and the outer…
Indian Institute of Science, Bangalore（印度科学学院，班加罗尔）；Google Inc., Mountain View（谷歌公司，山景城）
We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $Ω(n^2)$ for the purpose. We analyze the problem with an additional structure of relational graph $G([n],E)$ over the $n$ items added with an assumption of \emph{locality}: Neighboring items are similar in their rankings. Noting the preferential nature of the data, we choose to embed not the graph, but, its \emph{strong product} to capture the pairwise node relationships. Further…
Fair ranking problems arise in many decision-making processes that often necessitate a trade-off between accuracy and fairness. Many existing studies have proposed correction methods such as adding fairness constraints to a ranking model's loss. However, the challenge of correcting the data bias for fair ranking remains, and the trade-off of the ranking models leaves room for improvement. In this paper, we propose a fair ranking framework that evaluates the order of training data in a pairwise manner as well as various fairness measurements in ranking. This study is the first proposal of a pre…
Recent work in recommender systems has emphasized the importance of fairness, with a particular interest in bias and transparency, in addition to predictive accuracy. In this paper, we focus on the state of the art pairwise ranking model, Bayesian Personalized Ranking (BPR), which has previously been found to outperform pointwise models in predictive accuracy, while also being able to handle implicit feedback. Specifically, we address two limitations of BPR: (1) BPR is a black box model that does not explain its outputs, thus limiting the user's trust in the recommendations, and the analyst's …
Google（谷歌）；University of Michigan（密歇根大学）；University of Washington（华盛顿大学）；Yale University（耶鲁大学）
Given a number of pairwise preferences of items, a common task is to rank all the items. Examples include pairwise movie ratings, New Yorker cartoon caption contests, and many other consumer preferences tasks. What these settings have in common is two-fold: a scarcity of data (it may be costly to get comparisons for all the pairs of items) and additional feature information about the items (e.g., movie genre, director, and cast). In this paper we modify a popular and well studied method, RankCentrality for rank aggregation to account for few comparisons and that incorporates additional feature…
Learning from implicit feedback is challenging because of the difficult nature of the one-class problem: we can observe only positive examples. Most conventional methods use a pairwise ranking approach and negative samplers to cope with the one-class problem. However, such methods have two main drawbacks particularly in large-scale applications; (1) the pairwise approach is severely inefficient due to the quadratic computational cost; and (2) even recent model-based samplers (e.g. IRGAN) cannot achieve practical efficiency due to the training of an extra model. In this paper, we propose a lear…
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；Qatar Computing Research Institute（卡塔尔计算研究所）
Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Result…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Brandeis University（布兰迪斯大学）；Sun Yat-Sen University（中山大学）；Yahoo Research（雅虎研究院）；University of Notre Dame（圣母大学）
Pairwise ranking models have been widely used to address recommendation problems. The basic idea is to learn the rank of users' preferred items through separating items into \emph{positive} samples if user-item interactions exist, and \emph{negative} samples otherwise. Due to the limited number of observable interactions, pairwise ranking models face serious \emph{class-imbalance} issues. Our theoretical analysis shows that current sampling-based methods cause the vertex-level imbalance problem, which makes the norm of learned item embeddings towards infinite after a certain training iteration…
Gene expression datasets are usually of high dimensionality and therefore require efficient and effective methods for identifying the relative importance of their attributes. Due to the huge size of the search space of the possible solutions, the attribute subset evaluation feature selection methods tend to be not applicable, so in these scenarios feature ranking methods are used. Most of the feature ranking methods described in the literature are univariate methods, so they do not detect interactions between factors. In this paper we propose two new multivariate feature ranking methods based …
