Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights
Abstract Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental re...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Pébay, Philippe [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg (outside the USA) 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Computational statistics - Springer Berlin Heidelberg, 1992, 31(2016), 4 vom: 29. März, Seite 1305-1325 |
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| Übergeordnetes Werk: |
volume:31 ; year:2016 ; number:4 ; day:29 ; month:03 ; pages:1305-1325 |
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10.1007/s00180-015-0637-z |
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| 520 | |a Abstract Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application. | ||
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10.1007/s00180-015-0637-z doi (DE-627)OLC2070885097 (DE-He213)s00180-015-0637-z-p DE-627 ger DE-627 rakwb eng 510 004 VZ Pébay, Philippe verfasserin aut Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg (outside the USA) 2016 Abstract Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application. Descriptive statistics Statistical moments Parallel computing Large data analysis Terriberry, Timothy B. aut Kolla, Hemanth aut Bennett, Janine aut Enthalten in Computational statistics Springer Berlin Heidelberg, 1992 31(2016), 4 vom: 29. März, Seite 1305-1325 (DE-627)131054694 (DE-600)1104678-8 (DE-576)028053559 0943-4062 nnns volume:31 year:2016 number:4 day:29 month:03 pages:1305-1325 https://doi.org/10.1007/s00180-015-0637-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 AR 31 2016 4 29 03 1305-1325 |
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10.1007/s00180-015-0637-z doi (DE-627)OLC2070885097 (DE-He213)s00180-015-0637-z-p DE-627 ger DE-627 rakwb eng 510 004 VZ Pébay, Philippe verfasserin aut Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg (outside the USA) 2016 Abstract Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application. Descriptive statistics Statistical moments Parallel computing Large data analysis Terriberry, Timothy B. aut Kolla, Hemanth aut Bennett, Janine aut Enthalten in Computational statistics Springer Berlin Heidelberg, 1992 31(2016), 4 vom: 29. März, Seite 1305-1325 (DE-627)131054694 (DE-600)1104678-8 (DE-576)028053559 0943-4062 nnns volume:31 year:2016 number:4 day:29 month:03 pages:1305-1325 https://doi.org/10.1007/s00180-015-0637-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 AR 31 2016 4 29 03 1305-1325 |
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10.1007/s00180-015-0637-z doi (DE-627)OLC2070885097 (DE-He213)s00180-015-0637-z-p DE-627 ger DE-627 rakwb eng 510 004 VZ Pébay, Philippe verfasserin aut Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg (outside the USA) 2016 Abstract Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application. Descriptive statistics Statistical moments Parallel computing Large data analysis Terriberry, Timothy B. aut Kolla, Hemanth aut Bennett, Janine aut Enthalten in Computational statistics Springer Berlin Heidelberg, 1992 31(2016), 4 vom: 29. März, Seite 1305-1325 (DE-627)131054694 (DE-600)1104678-8 (DE-576)028053559 0943-4062 nnns volume:31 year:2016 number:4 day:29 month:03 pages:1305-1325 https://doi.org/10.1007/s00180-015-0637-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_2088 AR 31 2016 4 29 03 1305-1325 |
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Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights |
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Abstract Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application. © Springer-Verlag Berlin Heidelberg (outside the USA) 2016 |
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Abstract Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application. © Springer-Verlag Berlin Heidelberg (outside the USA) 2016 |
| abstract_unstemmed |
Abstract Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application. © Springer-Verlag Berlin Heidelberg (outside the USA) 2016 |
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| title_short |
Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights |
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https://doi.org/10.1007/s00180-015-0637-z |
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Terriberry, Timothy B. Kolla, Hemanth Bennett, Janine |
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2024-07-04T02:30:34.605Z |
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