Timezone: »
Poster
Quantized Random Projections and Non-Linear Estimation of Cosine Similarity
Ping Li · Michael Mitzenmacher · Martin Slawski
Random projections constitute a simple, yet effective technique for dimensionality reduction with applications in learning and search problems. In the present paper, we consider the problem of estimating cosine similarities when the projected data undergo scalar quantization to $b$ bits. We here argue that the maximum likelihood estimator (MLE) is a principled approach to deal with the non-linearity resulting from quantization, and subsequently study its computational and statistical properties. A specific focus is on the on the trade-off between bit depth and the number of projections given a fixed budget of bits for storage or transmission. Along the way, we also touch upon the existence of a qualitative counterpart to the Johnson-Lindenstrauss lemma in the presence of quantization.
Author Information
Ping Li (Baidu Research USA)
Michael Mitzenmacher (Harvard University)
Martin Slawski (George Mason University)
More from the Same Authors
-
2021 Poster: DRIVE: One-bit Distributed Mean Estimation »
Shay Vargaftik · Ran Ben-Basat · Amit Portnoy · Gal Mendelson · Yaniv Ben-Itzhak · Michael Mitzenmacher -
2018 Poster: A Model for Learned Bloom Filters and Optimizing by Sandwiching »
Michael Mitzenmacher -
2018 Poster: A Bayesian Nonparametric View on Count-Min Sketch »
Diana Cai · Michael Mitzenmacher · Ryan Adams -
2017 Poster: Partial Hard Thresholding: Towards A Principled Analysis of Support Recovery »
Jie Shen · Ping Li -
2017 Poster: Simple strategies for recovering inner products from coarsely quantized random projections »
Ping Li · Martin Slawski -
2016 Poster: Exact Recovery of Hard Thresholding Pursuit »
Xiaotong Yuan · Ping Li · Tong Zhang -
2016 Poster: Learning Additive Exponential Family Graphical Models via $\ell_{2,1}$-norm Regularized M-Estimation »
Xiaotong Yuan · Ping Li · Tong Zhang · Qingshan Liu · Guangcan Liu -
2015 Poster: b-bit Marginal Regression »
Martin Slawski · Ping Li -
2015 Spotlight: b-bit Marginal Regression »
Martin Slawski · Ping Li -
2015 Poster: Regularization-Free Estimation in Trace Regression with Symmetric Positive Semidefinite Matrices »
Martin Slawski · Ping Li · Matthias Hein -
2014 Poster: Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS) »
Anshumali Shrivastava · Ping Li -
2014 Poster: Recovery of Coherent Data via Low-Rank Dictionary Pursuit »
Guangcan Liu · Ping Li -
2014 Poster: Online Optimization for Max-Norm Regularization »
Jie Shen · Huan Xu · Ping Li -
2014 Spotlight: Recovery of Coherent Data via Low-Rank Dictionary Pursuit »
Guangcan Liu · Ping Li -
2014 Oral: Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS) »
Anshumali Shrivastava · Ping Li -
2013 Poster: Beyond Pairwise: Provably Fast Algorithms for Approximate $k$-Way Similarity Search »
Anshumali Shrivastava · Ping Li -
2013 Poster: Sign Cauchy Projections and Chi-Square Kernel »
Ping Li · Gennady Samorodnitsk · John Hopcroft -
2013 Poster: Matrix factorization with binary components »
Martin Slawski · Matthias Hein · Pavlo Lutsik -
2013 Spotlight: Matrix factorization with binary components »
Martin Slawski · Matthias Hein · Pavlo Lutsik -
2012 Poster: Entropy Estimations Using Correlated Symmetric Stable Random Projections »
Ping Li · Cun-Hui Zhang -
2012 Poster: One Permutation Hashing »
Ping Li · Art B Owen · Cun-Hui Zhang -
2011 Poster: Sparse recovery by thresholded non-negative least squares »
Martin Slawski · Matthias Hein -
2011 Poster: Hashing Algorithms for Large-Scale Learning »
Ping Li · Anshumali Shrivastava · Joshua L Moore · Arnd C König -
2010 Spotlight: b-Bit Minwise Hashing for Estimating Three-Way Similarities »
Ping Li · Arnd C König · Wenhao Gui -
2010 Poster: b-Bit Minwise Hashing for Estimating Three-Way Similarities »
Ping Li · Arnd C König · Wenhao Gui -
2008 Poster: One sketch for all: Theory and Application of Conditional Random Sampling »
Ping Li · Kenneth W Church · Trevor Hastie -
2008 Spotlight: One sketch for all: Theory and Application of Conditional Random Sampling »
Ping Li · Kenneth W Church · Trevor Hastie -
2007 Spotlight: McRank: Learning to Rank Using Multiple Classification and Gradient Boosting »
Ping Li · Chris J Burges · Qiang Wu -
2007 Poster: McRank: Learning to Rank Using Multiple Classification and Gradient Boosting »
Ping Li · Chris J Burges · Qiang Wu -
2007 Poster: A Unified Near-Optimal Estimator For Dimension Reduction in $l_\alpha$ ($0<\alpha\leq 2$) Using Sta »
Ping Li · Trevor Hastie -
2006 Poster: Conditional Random Sampling: A Sketch-based Sampling Technique for Sparse Data »
Ping Li · Kenneth W Church · Trevor Hastie