Improving compressed matrix multiplication using control variate method
The seminal work by Pagh [1] proposed a matrix multiplication algorithm for real-valued squared matrices called Compressed Matrix Multiplication (CMM) having a sparse matrix output product. The algorithm is based on a popular sketching technique called Count-Sketch [2] and Fast Fourier Transform (FF...
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| Vydáno v: | Information processing letters Ročník 187; s. 106517 |
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Elsevier B.V
01.01.2025
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| ISSN: | 0020-0190, 1872-6119 |
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| Abstract | The seminal work by Pagh [1] proposed a matrix multiplication algorithm for real-valued squared matrices called Compressed Matrix Multiplication (CMM) having a sparse matrix output product. The algorithm is based on a popular sketching technique called Count-Sketch [2] and Fast Fourier Transform (FFT). For input square matrices A and B of order n and the product matrix AB with Frobenius norm ||AB||F, the algorithm offers an unbiased estimate for each entry, i.e., (AB)i,j of the product matrix AB with a variance bounded by ||AB||F2/b, where b is the compressed bucket size. Thus, the variance will eventually become high for a small bucket size. In this work, we address the high variance problem of CMM with the help of a simple and practical technique based on classical variance reduction methods in statistics. Our techniques rely on the Control Variate (CV) method. We suggest rigorous theoretical analysis for variance reduction and complement it via supporting empirical evidence.
•This work proposes an improvement to the compressed matrix multiplication (CMM) algorithm.•Our proposal, CV-CMM, is based on the control variate (CV) method.•Our proposal provides more accurate matrix product estimates compared to CMM. |
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| AbstractList | The seminal work by Pagh [1] proposed a matrix multiplication algorithm for real-valued squared matrices called Compressed Matrix Multiplication (CMM) having a sparse matrix output product. The algorithm is based on a popular sketching technique called Count-Sketch [2] and Fast Fourier Transform (FFT). For input square matrices A and B of order n and the product matrix AB with Frobenius norm ||AB||F, the algorithm offers an unbiased estimate for each entry, i.e., (AB)i,j of the product matrix AB with a variance bounded by ||AB||F2/b, where b is the compressed bucket size. Thus, the variance will eventually become high for a small bucket size. In this work, we address the high variance problem of CMM with the help of a simple and practical technique based on classical variance reduction methods in statistics. Our techniques rely on the Control Variate (CV) method. We suggest rigorous theoretical analysis for variance reduction and complement it via supporting empirical evidence.
•This work proposes an improvement to the compressed matrix multiplication (CMM) algorithm.•Our proposal, CV-CMM, is based on the control variate (CV) method.•Our proposal provides more accurate matrix product estimates compared to CMM. |
| ArticleNumber | 106517 |
| Author | Dubey, Punit Pankaj Verma, Bhisham Dev Thakur, Manoj Pratap, Rameshwar |
| Author_xml | – sequence: 1 givenname: Bhisham Dev surname: Verma fullname: Verma, Bhisham Dev email: bhishamdevverma@gmail.com organization: Indian Institute of Technology Mandi, Himachal Pradesh, India – sequence: 2 givenname: Punit Pankaj surname: Dubey fullname: Dubey, Punit Pankaj email: punitpankajdubey@gmail.com organization: Indian Institute of Technology Mandi, Himachal Pradesh, India – sequence: 3 givenname: Rameshwar surname: Pratap fullname: Pratap, Rameshwar email: rameshwar@cse.iith.ac.in organization: Indian Institute of Technology Hyderabad, Telangana, India – sequence: 4 givenname: Manoj surname: Thakur fullname: Thakur, Manoj email: manoj@iitmandi.ac.in organization: Indian Institute of Technology Mandi, Himachal Pradesh, India |
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| Cites_doi | 10.1145/1077464.1077466 10.1137/0909040 10.1016/0022-0000(81)90033-7 10.1006/jcss.1997.1545 10.1145/2220357.2220361 10.1007/BF02165411 10.1145/2493252.2493254 10.1016/0022-0000(79)90044-8 10.1145/3019134 10.1016/S0304-3975(03)00400-6 10.1137/15M1009718 10.1006/jagm.1998.0989 10.1137/S0097539704442684 10.1287/mnsc.27.3.322 10.1007/s10994-022-06166-z 10.1007/s10618-021-00764-6 |
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| Keywords | Control variate Sketching algorithms Matrix multiplication Count-Sketch |
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| References | Pham, Pagh (br0300) 2013 Amossen, Pagh (br0210) 2009 Kang (br0070) 2017 Le Gall (br0170) 2012 Coppersmith, Winograd (br0160) 1987 Cohen, Lewis (br0230) 1999; 30 Verma, Pratap, Thakur (br0100) 2022; 111 Wegman, Carter (br0270) 1981; 22 Alon, Matias, Szegedy (br0260) 1999; 58 Pagh (br0010) aug 2013; 5 Pratap, Kulkarni (br0130) 2021; vol. 161 Clarkson, Woodruff (br0290) 2017; 63 Kang, Hooker (br0060) 2017 Carter, Wegman (br0030) 1979; 18 Sarlos (br0250) 2006 Pătraşcu, Thorup (br0040) 2012; 59 Kang, Hooker (br0080) 2018 Pratap, Verma, Kulkarni (br0140) 2021 Bailey (br0180) 1988; 9 Kang (br0090) 2021; 35 Yuster, Zwick (br0190) 2005; 1 Weinberger, Dasgupta, Langford, Smola, Attenberg (br0280) 2009 Lavenberg, Welch (br0050) 1981; 27 Charikar, Chen, Farach-Colton (br0020) 2004; 312 Lingas (br0200) 2009 Kang, Kushnarev, Wong, Pratap, Yeo, Yijia (br0110) 2021; vol. 157 Strassen (br0150) 1969; 13 Drineas, Kannan, Mahoney (br0240) 2006; 36 Ghashami, Liberty, Phillips, Woodruff (br0220) 2016; 45 Chew, Kang (br0120) 2021 Bailey (10.1016/j.ipl.2024.106517_br0180) 1988; 9 Kang (10.1016/j.ipl.2024.106517_br0090) 2021; 35 Le Gall (10.1016/j.ipl.2024.106517_br0170) 2012 Drineas (10.1016/j.ipl.2024.106517_br0240) 2006; 36 Clarkson (10.1016/j.ipl.2024.106517_br0290) 2017; 63 Kang (10.1016/j.ipl.2024.106517_br0110) 2021; vol. 157 Yuster (10.1016/j.ipl.2024.106517_br0190) 2005; 1 Weinberger (10.1016/j.ipl.2024.106517_br0280) 2009 Kang (10.1016/j.ipl.2024.106517_br0060) 2017 Kang (10.1016/j.ipl.2024.106517_br0080) 2018 Kang (10.1016/j.ipl.2024.106517_br0070) 2017 Chew (10.1016/j.ipl.2024.106517_br0120) 2021 Ghashami (10.1016/j.ipl.2024.106517_br0220) 2016; 45 Carter (10.1016/j.ipl.2024.106517_br0030) 1979; 18 Sarlos (10.1016/j.ipl.2024.106517_br0250) 2006 Pratap (10.1016/j.ipl.2024.106517_br0140) 2021 Strassen (10.1016/j.ipl.2024.106517_br0150) 1969; 13 Coppersmith (10.1016/j.ipl.2024.106517_br0160) 1987 Lingas (10.1016/j.ipl.2024.106517_br0200) 2009 Wegman (10.1016/j.ipl.2024.106517_br0270) 1981; 22 Pratap (10.1016/j.ipl.2024.106517_br0130) 2021; vol. 161 Pătraşcu (10.1016/j.ipl.2024.106517_br0040) 2012; 59 Verma (10.1016/j.ipl.2024.106517_br0100) 2022; 111 Lavenberg (10.1016/j.ipl.2024.106517_br0050) 1981; 27 Alon (10.1016/j.ipl.2024.106517_br0260) 1999; 58 Pagh (10.1016/j.ipl.2024.106517_br0010) 2013; 5 Charikar (10.1016/j.ipl.2024.106517_br0020) 2004; 312 Cohen (10.1016/j.ipl.2024.106517_br0230) 1999; 30 Amossen (10.1016/j.ipl.2024.106517_br0210) 2009 Pham (10.1016/j.ipl.2024.106517_br0300) 2013 |
| References_xml | – volume: 13 start-page: 354 year: 1969 end-page: 356 ident: br0150 article-title: Gaussian elimination is not optimal publication-title: Numer. Math. – volume: 63 start-page: 1 year: 2017 end-page: 45 ident: br0290 article-title: Low-rank approximation and regression in input sparsity time publication-title: J. ACM – start-page: 1113 year: 2009 end-page: 1120 ident: br0280 article-title: Feature hashing for large scale multitask learning publication-title: Proceedings of the 26th Annual International Conference on Machine Learning – start-page: 514 year: 2012 end-page: 523 ident: br0170 article-title: Faster algorithms for rectangular matrix multiplication publication-title: 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science – volume: 35 start-page: 1622 year: 2021 end-page: 1653 ident: br0090 article-title: Correlations between random projections and the bivariate normal publication-title: Data Min. Knowl. Discov. – volume: vol. 161 start-page: 183 year: 2021 end-page: 193 ident: br0130 article-title: Variance reduction in frequency estimators via control variates method publication-title: Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence – start-page: 143 year: 2006 end-page: 152 ident: br0250 article-title: Improved approximation algorithms for large matrices via random projections publication-title: 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) – volume: 18 start-page: 143 year: 1979 end-page: 154 ident: br0030 article-title: Universal classes of hash functions publication-title: J. Comput. Syst. Sci. – volume: 1 start-page: 2 year: 2005 end-page: 13 ident: br0190 article-title: Fast sparse matrix multiplication publication-title: ACM Trans. Algorithms – volume: 5 year: aug 2013 ident: br0010 article-title: Compressed matrix multiplication publication-title: ACM Trans. Comput. Theory – volume: 312 start-page: 3 year: 2004 end-page: 15 ident: br0020 article-title: Finding frequent items in data streams publication-title: Theor. Comput. Sci. – start-page: 138 year: 2017 end-page: 147 ident: br0060 article-title: Random projections with control variates publication-title: International Conference on Pattern Recognition Applications and Methods, vol. 2 – start-page: 397 year: 2017 end-page: 405 ident: br0070 article-title: Using the multivariate normal to improve random projections publication-title: International Conference on Intelligent Data Engineering and Automated Learning – volume: 36 start-page: 132 year: 2006 end-page: 157 ident: br0240 article-title: Fast Monte Carlo algorithms for matrices I: approximating matrix multiplication publication-title: SIAM J. Comput. – start-page: 1 year: 2018 end-page: 20 ident: br0080 article-title: Control variates as a variance reduction technique for random projections publication-title: Pattern Recognition Applications and Methods: 6th International Conference – start-page: 468 year: 2021 end-page: 479 ident: br0120 article-title: Control variates for similarity search publication-title: Chinese Conference on Pattern Recognition and Computer Vision (PRCV) – start-page: 66 year: 2021 end-page: 76 ident: br0140 article-title: Improving tug-of-war sketch using control-variates method publication-title: SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21) – volume: 27 start-page: 322 year: 1981 end-page: 335 ident: br0050 article-title: A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations publication-title: Manag. Sci. – volume: 111 start-page: 2631 year: 2022 end-page: 2662 ident: br0100 article-title: Variance reduction in feature hashing using MLE and control variate method publication-title: Mach. Learn. – volume: 9 start-page: 603 year: 1988 end-page: 607 ident: br0180 article-title: Extra high speed matrix multiplication on the cray-2 publication-title: SIAM J. Sci. Stat. Comput. – start-page: 408 year: 2009 end-page: 419 ident: br0200 article-title: A fast output-sensitive algorithm for Boolean matrix multiplication publication-title: Algorithms - ESA 2009 – volume: 59 start-page: 1 year: 2012 end-page: 50 ident: br0040 article-title: The power of simple tabulation hashing publication-title: J. ACM – volume: 58 start-page: 137 year: 1999 end-page: 147 ident: br0260 article-title: The space complexity of approximating the frequency moments publication-title: J. Comput. Syst. Sci. – volume: vol. 157 start-page: 814 year: 2021 end-page: 829 ident: br0110 article-title: Improving hashing algorithms for similarity search via MLE and the control variates trick publication-title: Proceedings of the 13th Asian Conference on Machine Learning – start-page: 1 year: 1987 end-page: 6 ident: br0160 article-title: Matrix multiplication via arithmetic progressions publication-title: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing – volume: 22 start-page: 265 year: 1981 end-page: 279 ident: br0270 article-title: New hash functions and their use in authentication and set equality publication-title: J. Comput. Syst. Sci. – volume: 30 start-page: 211 year: 1999 end-page: 252 ident: br0230 article-title: Approximating matrix multiplication for pattern recognition tasks publication-title: J. Algorithms – start-page: 239 year: 2013 end-page: 247 ident: br0300 article-title: Fast and scalable polynomial kernels via explicit feature maps publication-title: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining – volume: 45 start-page: 1762 year: 2016 end-page: 1792 ident: br0220 article-title: Frequent directions: simple and deterministic matrix sketching publication-title: SIAM J. Comput. – start-page: 121 year: 2009 end-page: 126 ident: br0210 article-title: Faster join-projects and sparse matrix multiplications publication-title: Proceedings of the 12th International Conference on Database Theory – volume: 1 start-page: 2 issue: 1 year: 2005 ident: 10.1016/j.ipl.2024.106517_br0190 article-title: Fast sparse matrix multiplication publication-title: ACM Trans. Algorithms doi: 10.1145/1077464.1077466 – volume: vol. 161 start-page: 183 year: 2021 ident: 10.1016/j.ipl.2024.106517_br0130 article-title: Variance reduction in frequency estimators via control variates method – volume: 9 start-page: 603 issue: 3 year: 1988 ident: 10.1016/j.ipl.2024.106517_br0180 article-title: Extra high speed matrix multiplication on the cray-2 publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0909040 – start-page: 408 year: 2009 ident: 10.1016/j.ipl.2024.106517_br0200 article-title: A fast output-sensitive algorithm for Boolean matrix multiplication – volume: 22 start-page: 265 issue: 3 year: 1981 ident: 10.1016/j.ipl.2024.106517_br0270 article-title: New hash functions and their use in authentication and set equality publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(81)90033-7 – volume: 58 start-page: 137 issue: 1 year: 1999 ident: 10.1016/j.ipl.2024.106517_br0260 article-title: The space complexity of approximating the frequency moments publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.1997.1545 – volume: 59 start-page: 1 issue: 3 year: 2012 ident: 10.1016/j.ipl.2024.106517_br0040 article-title: The power of simple tabulation hashing publication-title: J. ACM doi: 10.1145/2220357.2220361 – start-page: 143 year: 2006 ident: 10.1016/j.ipl.2024.106517_br0250 article-title: Improved approximation algorithms for large matrices via random projections – volume: vol. 157 start-page: 814 year: 2021 ident: 10.1016/j.ipl.2024.106517_br0110 article-title: Improving hashing algorithms for similarity search via MLE and the control variates trick – start-page: 397 year: 2017 ident: 10.1016/j.ipl.2024.106517_br0070 article-title: Using the multivariate normal to improve random projections – volume: 13 start-page: 354 year: 1969 ident: 10.1016/j.ipl.2024.106517_br0150 article-title: Gaussian elimination is not optimal publication-title: Numer. Math. doi: 10.1007/BF02165411 – start-page: 1113 year: 2009 ident: 10.1016/j.ipl.2024.106517_br0280 article-title: Feature hashing for large scale multitask learning – start-page: 239 year: 2013 ident: 10.1016/j.ipl.2024.106517_br0300 article-title: Fast and scalable polynomial kernels via explicit feature maps – start-page: 138 year: 2017 ident: 10.1016/j.ipl.2024.106517_br0060 article-title: Random projections with control variates – volume: 5 issue: 3 year: 2013 ident: 10.1016/j.ipl.2024.106517_br0010 article-title: Compressed matrix multiplication publication-title: ACM Trans. Comput. Theory doi: 10.1145/2493252.2493254 – start-page: 514 year: 2012 ident: 10.1016/j.ipl.2024.106517_br0170 article-title: Faster algorithms for rectangular matrix multiplication – volume: 18 start-page: 143 issue: 2 year: 1979 ident: 10.1016/j.ipl.2024.106517_br0030 article-title: Universal classes of hash functions publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(79)90044-8 – start-page: 1 year: 2018 ident: 10.1016/j.ipl.2024.106517_br0080 article-title: Control variates as a variance reduction technique for random projections – start-page: 468 year: 2021 ident: 10.1016/j.ipl.2024.106517_br0120 article-title: Control variates for similarity search – volume: 63 start-page: 1 issue: 6 year: 2017 ident: 10.1016/j.ipl.2024.106517_br0290 article-title: Low-rank approximation and regression in input sparsity time publication-title: J. ACM doi: 10.1145/3019134 – start-page: 1 year: 1987 ident: 10.1016/j.ipl.2024.106517_br0160 article-title: Matrix multiplication via arithmetic progressions – volume: 312 start-page: 3 issue: 1 year: 2004 ident: 10.1016/j.ipl.2024.106517_br0020 article-title: Finding frequent items in data streams publication-title: Theor. Comput. Sci. doi: 10.1016/S0304-3975(03)00400-6 – volume: 45 start-page: 1762 issue: 5 year: 2016 ident: 10.1016/j.ipl.2024.106517_br0220 article-title: Frequent directions: simple and deterministic matrix sketching publication-title: SIAM J. Comput. doi: 10.1137/15M1009718 – volume: 30 start-page: 211 issue: 2 year: 1999 ident: 10.1016/j.ipl.2024.106517_br0230 article-title: Approximating matrix multiplication for pattern recognition tasks publication-title: J. Algorithms doi: 10.1006/jagm.1998.0989 – volume: 36 start-page: 132 issue: 1 year: 2006 ident: 10.1016/j.ipl.2024.106517_br0240 article-title: Fast Monte Carlo algorithms for matrices I: approximating matrix multiplication publication-title: SIAM J. Comput. doi: 10.1137/S0097539704442684 – volume: 27 start-page: 322 issue: 3 year: 1981 ident: 10.1016/j.ipl.2024.106517_br0050 article-title: A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations publication-title: Manag. Sci. doi: 10.1287/mnsc.27.3.322 – start-page: 66 year: 2021 ident: 10.1016/j.ipl.2024.106517_br0140 article-title: Improving tug-of-war sketch using control-variates method – volume: 111 start-page: 2631 issue: 7 year: 2022 ident: 10.1016/j.ipl.2024.106517_br0100 article-title: Variance reduction in feature hashing using MLE and control variate method publication-title: Mach. Learn. doi: 10.1007/s10994-022-06166-z – volume: 35 start-page: 1622 issue: 4 year: 2021 ident: 10.1016/j.ipl.2024.106517_br0090 article-title: Correlations between random projections and the bivariate normal publication-title: Data Min. Knowl. Discov. doi: 10.1007/s10618-021-00764-6 – start-page: 121 year: 2009 ident: 10.1016/j.ipl.2024.106517_br0210 article-title: Faster join-projects and sparse matrix multiplications |
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