Multiple surrogates: how cross-validation errors can help us to obtain the best predictor
Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Viana, Felipe A. C. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2009 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2008 |
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| Übergeordnetes Werk: |
Enthalten in: Structural and multidisciplinary optimization - Berlin : Springer, 1989, 39(2009), 4 vom: 08. Jan., Seite 439-457 |
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| Übergeordnetes Werk: |
volume:39 ; year:2009 ; number:4 ; day:08 ; month:01 ; pages:439-457 |
| Links: |
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| DOI / URN: |
10.1007/s00158-008-0338-0 |
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| Katalog-ID: |
SPR001311751 |
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| 100 | 1 | |a Viana, Felipe A. C. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Multiple surrogates: how cross-validation errors can help us to obtain the best predictor |
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| 520 | |a Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. | ||
| 650 | 4 | |a Multiple surrogate models |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Weighted average surrogates |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Cross-validation errors |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Prediction sum of squares |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Haftka, Raphael T. |4 aut | |
| 700 | 1 | |a Steffen, Valder |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Structural and multidisciplinary optimization |d Berlin : Springer, 1989 |g 39(2009), 4 vom: 08. Jan., Seite 439-457 |w (DE-627)271602503 |w (DE-600)1481279-4 |x 1615-1488 |7 nnns |
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10.1007/s00158-008-0338-0 doi (DE-627)SPR001311751 (SPR)s00158-008-0338-0-e DE-627 ger DE-627 rakwb eng Viana, Felipe A. C. verfasserin aut Multiple surrogates: how cross-validation errors can help us to obtain the best predictor 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. Multiple surrogate models (dpeaa)DE-He213 Weighted average surrogates (dpeaa)DE-He213 Cross-validation errors (dpeaa)DE-He213 Prediction sum of squares (dpeaa)DE-He213 Haftka, Raphael T. aut Steffen, Valder aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 39(2009), 4 vom: 08. Jan., Seite 439-457 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:39 year:2009 number:4 day:08 month:01 pages:439-457 https://dx.doi.org/10.1007/s00158-008-0338-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2009 4 08 01 439-457 |
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10.1007/s00158-008-0338-0 doi (DE-627)SPR001311751 (SPR)s00158-008-0338-0-e DE-627 ger DE-627 rakwb eng Viana, Felipe A. C. verfasserin aut Multiple surrogates: how cross-validation errors can help us to obtain the best predictor 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. Multiple surrogate models (dpeaa)DE-He213 Weighted average surrogates (dpeaa)DE-He213 Cross-validation errors (dpeaa)DE-He213 Prediction sum of squares (dpeaa)DE-He213 Haftka, Raphael T. aut Steffen, Valder aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 39(2009), 4 vom: 08. Jan., Seite 439-457 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:39 year:2009 number:4 day:08 month:01 pages:439-457 https://dx.doi.org/10.1007/s00158-008-0338-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2009 4 08 01 439-457 |
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10.1007/s00158-008-0338-0 doi (DE-627)SPR001311751 (SPR)s00158-008-0338-0-e DE-627 ger DE-627 rakwb eng Viana, Felipe A. C. verfasserin aut Multiple surrogates: how cross-validation errors can help us to obtain the best predictor 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. Multiple surrogate models (dpeaa)DE-He213 Weighted average surrogates (dpeaa)DE-He213 Cross-validation errors (dpeaa)DE-He213 Prediction sum of squares (dpeaa)DE-He213 Haftka, Raphael T. aut Steffen, Valder aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 39(2009), 4 vom: 08. Jan., Seite 439-457 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:39 year:2009 number:4 day:08 month:01 pages:439-457 https://dx.doi.org/10.1007/s00158-008-0338-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2009 4 08 01 439-457 |
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10.1007/s00158-008-0338-0 doi (DE-627)SPR001311751 (SPR)s00158-008-0338-0-e DE-627 ger DE-627 rakwb eng Viana, Felipe A. C. verfasserin aut Multiple surrogates: how cross-validation errors can help us to obtain the best predictor 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. Multiple surrogate models (dpeaa)DE-He213 Weighted average surrogates (dpeaa)DE-He213 Cross-validation errors (dpeaa)DE-He213 Prediction sum of squares (dpeaa)DE-He213 Haftka, Raphael T. aut Steffen, Valder aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 39(2009), 4 vom: 08. Jan., Seite 439-457 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:39 year:2009 number:4 day:08 month:01 pages:439-457 https://dx.doi.org/10.1007/s00158-008-0338-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2009 4 08 01 439-457 |
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10.1007/s00158-008-0338-0 doi (DE-627)SPR001311751 (SPR)s00158-008-0338-0-e DE-627 ger DE-627 rakwb eng Viana, Felipe A. C. verfasserin aut Multiple surrogates: how cross-validation errors can help us to obtain the best predictor 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. Multiple surrogate models (dpeaa)DE-He213 Weighted average surrogates (dpeaa)DE-He213 Cross-validation errors (dpeaa)DE-He213 Prediction sum of squares (dpeaa)DE-He213 Haftka, Raphael T. aut Steffen, Valder aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 39(2009), 4 vom: 08. Jan., Seite 439-457 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:39 year:2009 number:4 day:08 month:01 pages:439-457 https://dx.doi.org/10.1007/s00158-008-0338-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2009 4 08 01 439-457 |
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Enthalten in Structural and multidisciplinary optimization 39(2009), 4 vom: 08. Jan., Seite 439-457 volume:39 year:2009 number:4 day:08 month:01 pages:439-457 |
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Viana, Felipe A. C. @@aut@@ Haftka, Raphael T. @@aut@@ Steffen, Valder @@aut@@ |
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Viana, Felipe A. C. |
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Viana, Felipe A. C. misc Multiple surrogate models misc Weighted average surrogates misc Cross-validation errors misc Prediction sum of squares Multiple surrogates: how cross-validation errors can help us to obtain the best predictor |
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Multiple surrogates: how cross-validation errors can help us to obtain the best predictor Multiple surrogate models (dpeaa)DE-He213 Weighted average surrogates (dpeaa)DE-He213 Cross-validation errors (dpeaa)DE-He213 Prediction sum of squares (dpeaa)DE-He213 |
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multiple surrogates: how cross-validation errors can help us to obtain the best predictor |
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Multiple surrogates: how cross-validation errors can help us to obtain the best predictor |
| abstract |
Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. © Springer-Verlag 2008 |
| abstractGer |
Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. © Springer-Verlag 2008 |
| abstract_unstemmed |
Abstract Surrogate models are commonly used to replace expensive simulations of engineering problems. Frequently, a single surrogate is chosen based on past experience. This approach has generated a collection of papers comparing the performance of individual surrogates. Previous work has also shown that fitting multiple surrogates and picking one based on cross-validation errors (PRESS in particular) is a good strategy, and that cross-validation errors may also be used to create a weighted surrogate. In this paper, we discussed how PRESS (obtained either from the leave-one-out or from the k-fold strategies) is employed to estimate the RMS error, and whether to use the best PRESS solution or a weighted surrogate when a single surrogate is needed. We also studied the minimization of the integrated square error as a way to compute the weights of the weighted average surrogate. We found that it pays to generate a large set of different surrogates and then use PRESS as a criterion for selection. We found that (1) in general, PRESS is good for filtering out inaccurate surrogates; and (2) with sufficient number of points, PRESS may identify the best surrogate of the set. Hence the use of cross-validation errors for choosing a surrogate and for calculating the weights of weighted surrogates becomes more attractive in high dimensions (when a large number of points is naturally required). However, it appears that the potential gains from using weighted surrogates diminish substantially in high dimensions. We also examined the utility of using all the surrogates for forming the weighted surrogates versus using a subset of the most accurate ones. This decision is shown to depend on the weighting scheme. Finally, we also found that PRESS as obtained through the k-fold strategy successfully estimates the RMSE. © Springer-Verlag 2008 |
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| title_short |
Multiple surrogates: how cross-validation errors can help us to obtain the best predictor |
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https://dx.doi.org/10.1007/s00158-008-0338-0 |
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Haftka, Raphael T. Steffen, Valder |
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10.1007/s00158-008-0338-0 |
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2024-07-03T21:42:41.130Z |
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| score |
7.401101 |