Timezone: »
A crucial technique for scaling kernel methods to very large data sets reaching or exceeding millions of instances is based on low-rank approximation of kernel matrices. We introduce a new family of algorithms based on mixtures of Nystrom approximations, ensemble Nystrom algorithms, that yield more accurate low-rank approximations than the standard Nystrom method. We give a detailed study of multiple variants of these algorithms based on simple averaging, an exponential weight method, or regression-based methods. We also present a theoretical analysis of these algorithms, including novel error bounds guaranteeing a better convergence rate than the standard Nystrom method. Finally, we report the results of extensive experiments with several data sets containing up to 1M points demonstrating the significant performance improvements gained over the standard Nystrom approximation.
Author Information
Sanjiv Kumar (Google Research)
Mehryar Mohri (Google Research & Courant Institute of Mathematical Sciences)
Ameet S Talwalkar (CMU)
More from the Same Authors
-
2020 Poster: Adapting to Misspecification in Contextual Bandits »
Dylan Foster · Claudio Gentile · Mehryar Mohri · Julian Zimmert -
2020 Poster: Why are Adaptive Methods Good for Attention Models? »
Jingzhao Zhang · Sai Praneeth Karimireddy · Andreas Veit · Seungyeon Kim · Sashank Reddi · Sanjiv Kumar · Suvrit Sra -
2020 Poster: Agnostic Learning with Multiple Objectives »
Corinna Cortes · Mehryar Mohri · Javier Gonzalvo · Dmitry Storcheus -
2020 Poster: Multi-Stage Influence Function »
Hongge Chen · Si Si · Yang Li · Ciprian Chelba · Sanjiv Kumar · Duane Boning · Cho-Jui Hsieh -
2020 Poster: O(n) Connections are Expressive Enough: Universal Approximability of Sparse Transformers »
Chulhee Yun · Yin-Wen Chang · Srinadh Bhojanapalli · Ankit Singh Rawat · Sashank Reddi · Sanjiv Kumar -
2020 Poster: Robust large-margin learning in hyperbolic space »
Melanie Weber · Manzil Zaheer · Ankit Singh Rawat · Aditya Menon · Sanjiv Kumar -
2020 Poster: Reinforcement Learning with Feedback Graphs »
Christoph Dann · Yishay Mansour · Mehryar Mohri · Ayush Sekhari · Karthik Sridharan -
2020 Poster: PAC-Bayes Learning Bounds for Sample-Dependent Priors »
Pranjal Awasthi · Satyen Kale · Stefani Karp · Mehryar Mohri -
2020 Poster: Learning discrete distributions: user vs item-level privacy »
Yuhan Liu · Ananda Theertha Suresh · Felix Xinnan Yu · Sanjiv Kumar · Michael D Riley -
2019 Poster: Breaking the Glass Ceiling for Embedding-Based Classifiers for Large Output Spaces »
Chuan Guo · Ali Mousavi · Xiang Wu · Daniel Holtmann-Rice · Satyen Kale · Sashank Reddi · Sanjiv Kumar -
2019 Poster: Learning GANs and Ensembles Using Discrepancy »
Ben Adlam · Corinna Cortes · Mehryar Mohri · Ningshan Zhang -
2019 Poster: Bandits with Feedback Graphs and Switching Costs »
Raman Arora · Teodor Vanislavov Marinov · Mehryar Mohri -
2019 Poster: Multilabel reductions: what is my loss optimising? »
Aditya Menon · Ankit Singh Rawat · Sashank Reddi · Sanjiv Kumar -
2019 Spotlight: Multilabel reductions: what is my loss optimising? »
Aditya Menon · Ankit Singh Rawat · Sashank Reddi · Sanjiv Kumar -
2019 Poster: Regularized Gradient Boosting »
Corinna Cortes · Mehryar Mohri · Dmitry Storcheus -
2019 Poster: Hypothesis Set Stability and Generalization »
Dylan Foster · Spencer Greenberg · Satyen Kale · Haipeng Luo · Mehryar Mohri · Karthik Sridharan -
2019 Poster: Sampled Softmax with Random Fourier Features »
Ankit Singh Rawat · Jiecao Chen · Felix Xinnan Yu · Ananda Theertha Suresh · Sanjiv Kumar -
2018 Poster: Policy Regret in Repeated Games »
Raman Arora · Michael Dinitz · Teodor Vanislavov Marinov · Mehryar Mohri -
2018 Poster: Efficient Gradient Computation for Structured Output Learning with Rational and Tropical Losses »
Corinna Cortes · Vitaly Kuznetsov · Mehryar Mohri · Dmitry Storcheus · Scott Yang -
2018 Poster: Adaptive Methods for Nonconvex Optimization »
Manzil Zaheer · Sashank Reddi · Devendra Sachan · Satyen Kale · Sanjiv Kumar -
2018 Poster: Algorithms and Theory for Multiple-Source Adaptation »
Judy Hoffman · Mehryar Mohri · Ningshan Zhang -
2018 Poster: cpSGD: Communication-efficient and differentially-private distributed SGD »
Naman Agarwal · Ananda Theertha Suresh · Felix Xinnan Yu · Sanjiv Kumar · Brendan McMahan -
2018 Spotlight: cpSGD: Communication-efficient and differentially-private distributed SGD »
Naman Agarwal · Ananda Theertha Suresh · Felix Xinnan Yu · Sanjiv Kumar · Brendan McMahan -
2017 Poster: Discriminative State Space Models »
Vitaly Kuznetsov · Mehryar Mohri -
2017 Poster: Online Learning with Transductive Regret »
Scott Yang · Mehryar Mohri -
2017 Poster: Multiscale Quantization for Fast Similarity Search »
Xiang Wu · Ruiqi Guo · Ananda Theertha Suresh · Sanjiv Kumar · Daniel Holtmann-Rice · David Simcha · Felix Yu -
2017 Poster: Parameter-Free Online Learning via Model Selection »
Dylan J Foster · Satyen Kale · Mehryar Mohri · Karthik Sridharan -
2017 Spotlight: Parameter-Free Online Learning via Model Selection »
Dylan J Foster · Satyen Kale · Mehryar Mohri · Karthik Sridharan -
2017 Spotlight: Online Learning with Transductive Regret »
Scott Yang · Mehryar Mohri -
2017 Poster: Variable Importance Using Decision Trees »
Jalil Kazemitabar · Arash Amini · Adam Bloniarz · Ameet S Talwalkar -
2017 Poster: Federated Multi-Task Learning »
Virginia Smith · Chao-Kai Chiang · Maziar Sanjabi · Ameet S Talwalkar -
2016 Poster: Structured Prediction Theory Based on Factor Graph Complexity »
Corinna Cortes · Vitaly Kuznetsov · Mehryar Mohri · Scott Yang -
2016 Poster: Orthogonal Random Features »
Felix Xinnan Yu · Ananda Theertha Suresh · Krzysztof M Choromanski · Daniel Holtmann-Rice · Sanjiv Kumar -
2016 Oral: Orthogonal Random Features »
Felix Xinnan Yu · Ananda Theertha Suresh · Krzysztof M Choromanski · Daniel Holtmann-Rice · Sanjiv Kumar -
2016 Poster: Boosting with Abstention »
Corinna Cortes · Giulia DeSalvo · Mehryar Mohri -
2016 Poster: Optimistic Bandit Convex Optimization »
Scott Yang · Mehryar Mohri -
2016 Poster: Yggdrasil: An Optimized System for Training Deep Decision Trees at Scale »
Firas Abuzaid · Joseph K Bradley · Feynman Liang · Andrew Feng · Lee Yang · Matei Zaharia · Ameet S Talwalkar -
2016 Tutorial: Theory and Algorithms for Forecasting Non-Stationary Time Series »
Vitaly Kuznetsov · Mehryar Mohri -
2015 Workshop: The 1st International Workshop "Feature Extraction: Modern Questions and Challenges" »
Dmitry Storcheus · Sanjiv Kumar · Afshin Rostamizadeh -
2015 Poster: Revenue Optimization against Strategic Buyers »
Mehryar Mohri · Andres Munoz -
2015 Poster: Spherical Random Features for Polynomial Kernels »
Jeffrey Pennington · Felix Yu · Sanjiv Kumar -
2015 Spotlight: Spherical Random Features for Polynomial Kernels »
Jeffrey Pennington · Felix Yu · Sanjiv Kumar -
2015 Poster: Structured Transforms for Small-Footprint Deep Learning »
Vikas Sindhwani · Tara Sainath · Sanjiv Kumar -
2015 Poster: Learning Theory and Algorithms for Forecasting Non-stationary Time Series »
Vitaly Kuznetsov · Mehryar Mohri -
2015 Spotlight: Structured Transforms for Small-Footprint Deep Learning »
Vikas Sindhwani · Tara Sainath · Sanjiv Kumar -
2015 Oral: Learning Theory and Algorithms for Forecasting Non-stationary Time Series »
Vitaly Kuznetsov · Mehryar Mohri -
2014 Workshop: Second Workshop on Transfer and Multi-Task Learning: Theory meets Practice »
Urun Dogan · Tatiana Tommasi · Yoshua Bengio · Francesco Orabona · Marius Kloft · Andres Munoz · Gunnar Rätsch · Hal Daumé III · Mehryar Mohri · Xuezhi Wang · Daniel Hernández-lobato · Song Liu · Thomas Unterthiner · Pascal Germain · Vinay P Namboodiri · Michael Goetz · Christopher Berlind · Sigurd Spieckermann · Marta Soare · Yujia Li · Vitaly Kuznetsov · Wenzhao Lian · Daniele Calandriello · Emilie Morvant -
2014 Workshop: Distributed Machine Learning and Matrix Computations »
Reza Zadeh · Ion Stoica · Ameet S Talwalkar -
2014 Workshop: NIPS Workshop on Transactional Machine Learning and E-Commerce »
David Parkes · David H Wolpert · Jennifer Wortman Vaughan · Jacob D Abernethy · Amos Storkey · Mark Reid · Ping Jin · Nihar Bhadresh Shah · Mehryar Mohri · Luis E Ortiz · Robin Hanson · Aaron Roth · Satyen Kale · Sebastien Lahaie -
2014 Poster: Optimal Regret Minimization in Posted-Price Auctions with Strategic Buyers »
Mehryar Mohri · Andres Munoz -
2014 Poster: Multi-Class Deep Boosting »
Vitaly Kuznetsov · Mehryar Mohri · Umar Syed -
2014 Session: Oral Session 8 »
Sanjiv Kumar -
2014 Spotlight: Optimal Regret Minimization in Posted-Price Auctions with Strategic Buyers »
Mehryar Mohri · Andres Munoz -
2014 Session: Oral Session 6 »
Mehryar Mohri -
2014 Poster: Discrete Graph Hashing »
Wei Liu · Cun Mu · Sanjiv Kumar · Shih-Fu Chang -
2014 Poster: Conditional Swap Regret and Conditional Correlated Equilibrium »
Mehryar Mohri · Scott Yang -
2014 Spotlight: Discrete Graph Hashing »
Wei Liu · Cun Mu · Sanjiv Kumar · Shih-Fu Chang -
2013 Poster: Learning Kernels Using Local Rademacher Complexity »
Corinna Cortes · Marius Kloft · Mehryar Mohri -
2013 Spotlight: Learning Kernels Using Local Rademacher Complexity »
Corinna Cortes · Marius Kloft · Mehryar Mohri -
2012 Poster: Accuracy at the Top »
Stephen Boyd · Corinna Cortes · Mehryar Mohri · Ana Radovanovic -
2012 Poster: Spectral Learning of General Weighted Automata via Constrained Matrix Completion »
Borja Balle · Mehryar Mohri -
2012 Oral: Spectral Learning of General Weighted Automata via Constrained Matrix Completion »
Borja Balle · Mehryar Mohri -
2012 Poster: Angular Quantization based Binary Codes for Fast Similarity Search »
Yunchao Gong · Sanjiv Kumar · Vishal Verma · Svetlana Lazebnik -
2011 Workshop: Sparse Representation and Low-rank Approximation »
Ameet S Talwalkar · Lester W Mackey · Mehryar Mohri · Michael W Mahoney · Francis Bach · Mike E davies · Remi Gribonval · Guillaume R Obozinski -
2011 Poster: Divide-and-Conquer Matrix Factorization »
Lester W Mackey · Ameet S Talwalkar · Michael Jordan -
2010 Workshop: Low-rank Methods for Large-scale Machine Learning »
Arthur Gretton · Michael W Mahoney · Mehryar Mohri · Ameet S Talwalkar -
2010 Poster: Learning Bounds for Importance Weighting »
Corinna Cortes · Yishay Mansour · Mehryar Mohri -
2009 Poster: Efficient Large-Scale Distributed Training of Conditional Maximum Entropy Models »
Gideon S Mann · Ryan McDonald · Mehryar Mohri · Nathan Silberman · Dan Walker -
2009 Spotlight: Efficient Large-Scale Distributed Training of Conditional Maximum Entropy Models »
Gideon S Mann · Ryan McDonald · Mehryar Mohri · Nathan Silberman · Dan Walker -
2009 Poster: Learning Non-Linear Combinations of Kernels »
Corinna Cortes · Mehryar Mohri · Afshin Rostamizadeh -
2009 Poster: Polynomial Semantic Indexing »
Bing Bai · Jason E Weston · David Grangier · Ronan Collobert · Kunihiko Sadamasa · Yanjun Qi · Corinna Cortes · Mehryar Mohri -
2008 Workshop: Kernel Learning: Automatic Selection of Optimal Kernels »
Corinna Cortes · Arthur Gretton · Gert Lanckriet · Mehryar Mohri · Afshin Rostamizadeh -
2008 Poster: Domain Adaptation with Multiple Sources »
Yishay Mansour · Mehryar Mohri · Afshin Rostamizadeh -
2008 Spotlight: Domain Adaptation with Multiple Sources »
Yishay Mansour · Mehryar Mohri · Afshin Rostamizadeh -
2008 Poster: Rademacher Complexity Bounds for Non-I.I.D. Processes »
Mehryar Mohri · Afshin Rostamizadeh -
2007 Poster: Stability Bounds for Non-i.i.d. Processes »
Mehryar Mohri · Afshin Rostamizadeh -
2006 Poster: On Transductive Regression »
Corinna Cortes · Mehryar Mohri