Timezone: »
The question of aggregating pairwise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR’s TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining ranking, finding ‘scores’ for each object (e.g. player’s rating) is of interest to understanding the intensity of the preferences. In this paper, we propose a novel iterative rank aggregation algorithm for discovering scores for objects from pairwise comparisons. The algorithm has a natural random walk interpretation over the graph of objects with edges present between two objects if they are compared; the scores turn out to be the stationary probability of this random walk. The algorithm is model independent. To establish the efficacy of our method, however, we consider the popular Bradley-Terry-Luce (BTL) model in which each object has an associated score which determines the probabilistic outcomes of pairwise comparisons between objects. We bound the finite sample error rates between the scores assumed by the BTL model and those estimated by our algorithm. This, in essence, leads to order-optimal dependence on the number of samples required to learn the scores well by our algorithm. Indeed, the experimental evaluation shows that our (model independent) algorithm performs as well as the Maximum Likelihood Estimator of the BTL model and outperforms a recently proposed algorithm by Ammar and Shah [1].
Author Information
Sahand N Negahban (University of California, Berkeley)
Sewoong Oh (University of Washington)
Devavrat Shah (Massachusetts Institute of Technology)
Devavrat Shah is a professor of Electrical Engineering & Computer Science and Director of Statistics and Data Science at MIT. He received PhD in Computer Science from Stanford. He received Erlang Prize from Applied Probability Society of INFORMS in 2010 and NeuIPS best paper award in 2008.
Related Events (a corresponding poster, oral, or spotlight)
-
2012 Poster: Iterative ranking from pair-wise comparisons »
Thu. Dec 6th 10:00 PM -- 08:00 AM Room Harrah’s Special Events Center 2nd Floor
More from the Same Authors
-
2021 Spotlight: Regulating algorithmic filtering on social media »
Sarah Cen · Devavrat Shah -
2021 : Regret, stability, and fairness in matching markets with bandit learners »
Sarah Cen · Devavrat Shah -
2021 : Regret, stability, and fairness in matching markets with bandit learners »
Sarah Cen · Devavrat Shah -
2022 : A Causal Inference Framework for Network Interference with Panel Data »
Sarah Cen · Anish Agarwal · Christina Yu · Devavrat Shah -
2022 : On counterfactual inference with unobserved confounding »
Abhin Shah · Raaz Dwivedi · Devavrat Shah · Gregory Wornell -
2023 Poster: Auditing for Human Expertise »
Rohan Alur · Loren Laine · Darrick Li · Manish Raghavan · Devavrat Shah · Dennis Shung -
2023 Poster: SAMoSSA: Multivariate Singular Spectrum Analysis with Stochastic Autoregressive Noise »
Abdullah Alomar · Munther Dahleh · Sean Mann · Devavrat Shah -
2021 Poster: A Computationally Efficient Method for Learning Exponential Family Distributions »
Abhin Shah · Devavrat Shah · Gregory Wornell -
2021 Poster: Regulating algorithmic filtering on social media »
Sarah Cen · Devavrat Shah -
2021 Poster: Change Point Detection via Multivariate Singular Spectrum Analysis »
Arwa Alanqary · Abdullah Alomar · Devavrat Shah -
2021 Poster: PerSim: Data-Efficient Offline Reinforcement Learning with Heterogeneous Agents via Personalized Simulators »
Anish Agarwal · Abdullah Alomar · Varkey Alumootil · Devavrat Shah · Dennis Shen · Zhi Xu · Cindy Yang -
2020 Poster: Estimation of Skill Distribution from a Tournament »
Ali Jadbabaie · Anuran Makur · Devavrat Shah -
2020 Spotlight: Estimation of Skill Distribution from a Tournament »
Ali Jadbabaie · Anuran Makur · Devavrat Shah -
2020 Poster: Sample Efficient Reinforcement Learning via Low-Rank Matrix Estimation »
Devavrat Shah · Dogyoon Song · Zhi Xu · Yuzhe Yang -
2020 Demonstration: tspDB: Time Series Predict DB »
Anish Agarwal · Abdullah Alomar · Devavrat Shah -
2019 Poster: On Robustness of Principal Component Regression »
Anish Agarwal · Devavrat Shah · Dennis Shen · Dogyoon Song -
2019 Oral: On Robustness of Principal Component Regression »
Anish Agarwal · Devavrat Shah · Dennis Shen · Dogyoon Song -
2019 Tutorial: Synthetic Control »
Alberto Abadie · Vishal Misra · Devavrat Shah -
2018 Poster: Q-learning with Nearest Neighbors »
Devavrat Shah · Qiaomin Xie -
2017 : New perspective from Blackwell's "comparisons of experiments" on generative adversarial networks »
Sewoong Oh -
2017 Workshop: Nearest Neighbors for Modern Applications with Massive Data: An Age-old Solution with New Challenges »
George H Chen · Devavrat Shah · Christina Lee -
2017 Poster: Optimal Sample Complexity of M-wise Data for Top-K Ranking »
Minje Jang · Sunghyun Kim · Changho Suh · Sewoong Oh -
2017 Poster: Thy Friend is My Friend: Iterative Collaborative Filtering for Sparse Matrix Estimation »
Christian Borgs · Jennifer Chayes · Christina Lee · Devavrat Shah -
2017 Poster: Estimating Mutual Information for Discrete-Continuous Mixtures »
Weihao Gao · Sreeram Kannan · Sewoong Oh · Pramod Viswanath -
2017 Poster: Matrix Norm Estimation from a Few Entries »
Ashish Khetan · Sewoong Oh -
2017 Spotlight: Estimating Mutual Information for Discrete-Continuous Mixtures »
Weihao Gao · Sreeram Kannan · Sewoong Oh · Pramod Viswanath -
2017 Spotlight: Matrix Norm Estimation from a Few Entries »
Ashish Khetan · Sewoong Oh -
2017 Poster: Discovering Potential Correlations via Hypercontractivity »
Hyeji Kim · Weihao Gao · Sreeram Kannan · Sewoong Oh · Pramod Viswanath -
2016 Poster: Breaking the Bandwidth Barrier: Geometrical Adaptive Entropy Estimation »
Weihao Gao · Sewoong Oh · Pramod Viswanath -
2016 Poster: Computational and Statistical Tradeoffs in Learning to Rank »
Ashish Khetan · Sewoong Oh -
2016 Poster: Blind Regression: Nonparametric Regression for Latent Variable Models via Collaborative Filtering »
Dogyoon Song · Christina Lee · Yihua Li · Devavrat Shah -
2016 Poster: Achieving budget-optimality with adaptive schemes in crowdsourcing »
Ashish Khetan · Sewoong Oh -
2015 Workshop: Non-convex Optimization for Machine Learning: Theory and Practice »
Anima Anandkumar · Niranjan Uma Naresh · Kamalika Chaudhuri · Percy Liang · Sewoong Oh -
2015 Poster: Secure Multi-party Differential Privacy »
Peter Kairouz · Sewoong Oh · Pramod Viswanath -
2015 Poster: Collaboratively Learning Preferences from Ordinal Data »
Sewoong Oh · Kiran Thekumparampil · Jiaming Xu -
2014 Workshop: Analysis of Rank Data: Confluence of Social Choice, Operations Research, and Machine Learning »
Shivani Agarwal · Hossein Azari Soufiani · Guy Bresler · Sewoong Oh · David Parkes · Arun Rajkumar · Devavrat Shah -
2014 Poster: Hardness of parameter estimation in graphical models »
Guy Bresler · David Gamarnik · Devavrat Shah -
2014 Poster: Provable Tensor Factorization with Missing Data »
Prateek Jain · Sewoong Oh -
2014 Poster: A Latent Source Model for Online Collaborative Filtering »
Guy Bresler · George H Chen · Devavrat Shah -
2014 Poster: Extremal Mechanisms for Local Differential Privacy »
Peter Kairouz · Sewoong Oh · Pramod Viswanath -
2014 Poster: Minimax-optimal Inference from Partial Rankings »
Bruce Hajek · Sewoong Oh · Jiaming Xu -
2014 Spotlight: A Latent Source Model for Online Collaborative Filtering »
Guy Bresler · George H Chen · Devavrat Shah -
2014 Poster: Learning Mixed Multinomial Logit Model from Ordinal Data »
Sewoong Oh · Devavrat Shah -
2014 Poster: Structure learning of antiferromagnetic Ising models »
Guy Bresler · David Gamarnik · Devavrat Shah -
2013 Workshop: Crowdsourcing: Theory, Algorithms and Applications »
Jennifer Wortman Vaughan · Greg Stoddard · Chien-Ju Ho · Adish Singla · Michael Bernstein · Devavrat Shah · Arpita Ghosh · Evgeniy Gabrilovich · Denny Zhou · Nikhil Devanur · Xi Chen · Alexander Ihler · Qiang Liu · Genevieve Patterson · Ashwinkumar Badanidiyuru Varadaraja · Hossein Azari Soufiani · Jacob Whitehill -
2013 Poster: A Latent Source Model for Nonparametric Time Series Classification »
George H Chen · Stanislav Nikolov · Devavrat Shah -
2013 Poster: Computing the Stationary Distribution Locally »
Christina Lee · Asuman Ozdaglar · Devavrat Shah -
2012 Poster: Stochastic optimization and sparse statistical recovery: Optimal algorithms for high dimensions »
Alekh Agarwal · Sahand N Negahban · Martin J Wainwright -
2011 Poster: Iterative Learning for Reliable Crowdsourcing Systems »
David R Karger · Sewoong Oh · Devavrat Shah -
2011 Oral: Iterative Learning for Reliable Crowdsourcing Systems »
David R Karger · Sewoong Oh · Devavrat Shah -
2010 Oral: Fast global convergence rates of gradient methods for high-dimensional statistical recovery »
Alekh Agarwal · Sahand N Negahban · Martin J Wainwright -
2010 Poster: Fast global convergence rates of gradient methods for high-dimensional statistical recovery »
Alekh Agarwal · Sahand N Negahban · Martin J Wainwright -
2009 Poster: A Data-Driven Approach to Modeling Choice »
Vivek Farias · Srikanth Jagabathula · Devavrat Shah -
2009 Spotlight: A Data-Driven Approach to Modeling Choice »
Vivek Farias · Srikanth Jagabathula · Devavrat Shah -
2009 Poster: Local Rules for Global MAP: When Do They Work ? »
Kyomin Jung · Pushmeet Kohli · Devavrat Shah -
2009 Poster: Matrix Completion from Noisy Entries »
Raghunandan Keshavan · Andrea Montanari · Sewoong Oh -
2009 Poster: A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers »
Sahand N Negahban · Pradeep Ravikumar · Martin J Wainwright · Bin Yu -
2009 Oral: A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers »
Sahand N Negahban · Pradeep Ravikumar · Martin J Wainwright · Bin Yu -
2008 Poster: Phase transitions for high-dimensional joint support recovery »
Sahand N Negahban · Martin J Wainwright -
2008 Poster: Inferring rankings under constrained sensing »
Srikanth Jagabathula · Devavrat Shah -
2008 Oral: Inferring rankings under constrained sensing »
Srikanth Jagabathula · Devavrat Shah -
2008 Spotlight: Phase transitions for high-dimensional joint support recovery »
Sahand N Negahban · Martin J Wainwright -
2007 Spotlight: Message Passing for Max-weight Independent Set »
Sujay Sanghavi · Devavrat Shah · Alan S Willsky -
2007 Poster: Message Passing for Max-weight Independent Set »
Sujay Sanghavi · Devavrat Shah · Alan S Willsky -
2007 Poster: Local Algorithms for Approximate Inference in Minor-Excluded Graphs »
Kyomin Jung · Devavrat Shah