Optimal %$L_2%$-norm empirical importance weights for the change of probability measure

Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Amaral, Sergio [verfasserIn] Allaire, Douglas [verfasserIn] Willcox, Karen [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	Change of measure Empirical measure Radon–Nikodym theorem Importance weight Density ratio Quadratic program

Übergeordnetes Werk:	Enthalten in: Statistics and computing - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991, 27(2016), 3 vom: 14. März, Seite 625-643
Übergeordnetes Werk:	volume:27 ; year:2016 ; number:3 ; day:14 ; month:03 ; pages:625-643

Links:	Volltext

DOI / URN:	10.1007/s11222-016-9644-3

Katalog-ID:	SPR017850959

Internformat


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520			\|a Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches.
650		4	\|a Change of measure \|7 (dpeaa)DE-He213
650		4	\|a Empirical measure \|7 (dpeaa)DE-He213
650		4	\|a Radon–Nikodym theorem \|7 (dpeaa)DE-He213
650		4	\|a Importance weight \|7 (dpeaa)DE-He213
650		4	\|a Density ratio \|7 (dpeaa)DE-He213
650		4	\|a Quadratic program \|7 (dpeaa)DE-He213
700	1		\|a Allaire, Douglas \|e verfasserin \|4 aut
700	1		\|a Willcox, Karen \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Statistics and computing \|d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 \|g 27(2016), 3 vom: 14. März, Seite 625-643 \|w (DE-627)31529888X \|w (DE-600)2017741-0 \|x 1573-1375 \|7 nnns
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856	4	0	\|u https://dx.doi.org/10.1007/s11222-016-9644-3 \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_101
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
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912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
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912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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952			\|d 27 \|j 2016 \|e 3 \|b 14 \|c 03 \|h 625-643

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author_variant	s a sa d a da k w kw
matchkey_str	article:15731375:2016----::pial2ommiiaipracwihsotehnef
hierarchy_sort_str	2016
bklnumber	31.73 54.76
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allfields	10.1007/s11222-016-9644-3 doi (DE-627)SPR017850959 (SPR)s11222-016-9644-3-e DE-627 ger DE-627 rakwb eng 004 620 ASE 31.73 bkl 54.76 bkl Amaral, Sergio verfasserin aut Optimal %$L_2%$-norm empirical importance weights for the change of probability measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches. Change of measure (dpeaa)DE-He213 Empirical measure (dpeaa)DE-He213 Radon–Nikodym theorem (dpeaa)DE-He213 Importance weight (dpeaa)DE-He213 Density ratio (dpeaa)DE-He213 Quadratic program (dpeaa)DE-He213 Allaire, Douglas verfasserin aut Willcox, Karen verfasserin aut Enthalten in Statistics and computing Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 27(2016), 3 vom: 14. März, Seite 625-643 (DE-627)31529888X (DE-600)2017741-0 1573-1375 nnns volume:27 year:2016 number:3 day:14 month:03 pages:625-643 https://dx.doi.org/10.1007/s11222-016-9644-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE 54.76 ASE AR 27 2016 3 14 03 625-643
spelling	10.1007/s11222-016-9644-3 doi (DE-627)SPR017850959 (SPR)s11222-016-9644-3-e DE-627 ger DE-627 rakwb eng 004 620 ASE 31.73 bkl 54.76 bkl Amaral, Sergio verfasserin aut Optimal %$L_2%$-norm empirical importance weights for the change of probability measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches. Change of measure (dpeaa)DE-He213 Empirical measure (dpeaa)DE-He213 Radon–Nikodym theorem (dpeaa)DE-He213 Importance weight (dpeaa)DE-He213 Density ratio (dpeaa)DE-He213 Quadratic program (dpeaa)DE-He213 Allaire, Douglas verfasserin aut Willcox, Karen verfasserin aut Enthalten in Statistics and computing Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 27(2016), 3 vom: 14. März, Seite 625-643 (DE-627)31529888X (DE-600)2017741-0 1573-1375 nnns volume:27 year:2016 number:3 day:14 month:03 pages:625-643 https://dx.doi.org/10.1007/s11222-016-9644-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE 54.76 ASE AR 27 2016 3 14 03 625-643
allfields_unstemmed	10.1007/s11222-016-9644-3 doi (DE-627)SPR017850959 (SPR)s11222-016-9644-3-e DE-627 ger DE-627 rakwb eng 004 620 ASE 31.73 bkl 54.76 bkl Amaral, Sergio verfasserin aut Optimal %$L_2%$-norm empirical importance weights for the change of probability measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches. Change of measure (dpeaa)DE-He213 Empirical measure (dpeaa)DE-He213 Radon–Nikodym theorem (dpeaa)DE-He213 Importance weight (dpeaa)DE-He213 Density ratio (dpeaa)DE-He213 Quadratic program (dpeaa)DE-He213 Allaire, Douglas verfasserin aut Willcox, Karen verfasserin aut Enthalten in Statistics and computing Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 27(2016), 3 vom: 14. März, Seite 625-643 (DE-627)31529888X (DE-600)2017741-0 1573-1375 nnns volume:27 year:2016 number:3 day:14 month:03 pages:625-643 https://dx.doi.org/10.1007/s11222-016-9644-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE 54.76 ASE AR 27 2016 3 14 03 625-643
allfieldsGer	10.1007/s11222-016-9644-3 doi (DE-627)SPR017850959 (SPR)s11222-016-9644-3-e DE-627 ger DE-627 rakwb eng 004 620 ASE 31.73 bkl 54.76 bkl Amaral, Sergio verfasserin aut Optimal %$L_2%$-norm empirical importance weights for the change of probability measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches. Change of measure (dpeaa)DE-He213 Empirical measure (dpeaa)DE-He213 Radon–Nikodym theorem (dpeaa)DE-He213 Importance weight (dpeaa)DE-He213 Density ratio (dpeaa)DE-He213 Quadratic program (dpeaa)DE-He213 Allaire, Douglas verfasserin aut Willcox, Karen verfasserin aut Enthalten in Statistics and computing Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 27(2016), 3 vom: 14. März, Seite 625-643 (DE-627)31529888X (DE-600)2017741-0 1573-1375 nnns volume:27 year:2016 number:3 day:14 month:03 pages:625-643 https://dx.doi.org/10.1007/s11222-016-9644-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE 54.76 ASE AR 27 2016 3 14 03 625-643
allfieldsSound	10.1007/s11222-016-9644-3 doi (DE-627)SPR017850959 (SPR)s11222-016-9644-3-e DE-627 ger DE-627 rakwb eng 004 620 ASE 31.73 bkl 54.76 bkl Amaral, Sergio verfasserin aut Optimal %$L_2%$-norm empirical importance weights for the change of probability measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches. Change of measure (dpeaa)DE-He213 Empirical measure (dpeaa)DE-He213 Radon–Nikodym theorem (dpeaa)DE-He213 Importance weight (dpeaa)DE-He213 Density ratio (dpeaa)DE-He213 Quadratic program (dpeaa)DE-He213 Allaire, Douglas verfasserin aut Willcox, Karen verfasserin aut Enthalten in Statistics and computing Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 27(2016), 3 vom: 14. März, Seite 625-643 (DE-627)31529888X (DE-600)2017741-0 1573-1375 nnns volume:27 year:2016 number:3 day:14 month:03 pages:625-643 https://dx.doi.org/10.1007/s11222-016-9644-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.73 ASE 54.76 ASE AR 27 2016 3 14 03 625-643
language	English
source	Enthalten in Statistics and computing 27(2016), 3 vom: 14. März, Seite 625-643 volume:27 year:2016 number:3 day:14 month:03 pages:625-643
sourceStr	Enthalten in Statistics and computing 27(2016), 3 vom: 14. März, Seite 625-643 volume:27 year:2016 number:3 day:14 month:03 pages:625-643
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Change of measure Empirical measure Radon–Nikodym theorem Importance weight Density ratio Quadratic program
dewey-raw	004
isfreeaccess_bool	false
container_title	Statistics and computing
authorswithroles_txt_mv	Amaral, Sergio @@aut@@ Allaire, Douglas @@aut@@ Willcox, Karen @@aut@@
publishDateDaySort_date	2016-03-14T00:00:00Z
hierarchy_top_id	31529888X
dewey-sort	14
id	SPR017850959
language_de	englisch
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author	Amaral, Sergio
spellingShingle	Amaral, Sergio ddc 004 bkl 31.73 bkl 54.76 misc Change of measure misc Empirical measure misc Radon–Nikodym theorem misc Importance weight misc Density ratio misc Quadratic program Optimal %$L_2%$-norm empirical importance weights for the change of probability measure
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topic_title	004 620 ASE 31.73 bkl 54.76 bkl Optimal %$L_2%$-norm empirical importance weights for the change of probability measure Change of measure (dpeaa)DE-He213 Empirical measure (dpeaa)DE-He213 Radon–Nikodym theorem (dpeaa)DE-He213 Importance weight (dpeaa)DE-He213 Density ratio (dpeaa)DE-He213 Quadratic program (dpeaa)DE-He213
topic	ddc 004 bkl 31.73 bkl 54.76 misc Change of measure misc Empirical measure misc Radon–Nikodym theorem misc Importance weight misc Density ratio misc Quadratic program
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title	Optimal %$L_2%$-norm empirical importance weights for the change of probability measure
ctrlnum	(DE-627)SPR017850959 (SPR)s11222-016-9644-3-e
title_full	Optimal %$L_2%$-norm empirical importance weights for the change of probability measure
author_sort	Amaral, Sergio
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title_sort	optimal %$l_2%$-norm empirical importance weights for the change of probability measure
title_auth	Optimal %$L_2%$-norm empirical importance weights for the change of probability measure
abstract	Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches.
abstractGer	Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches.
abstract_unstemmed	Abstract This work proposes an optimization formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. This work considers the specific case in which the proposal distribution from which the random samples are generated is unknown; that is, we have available the samples but no explicit description of their underlying distribution. In this setting, the Radon–Nikodym theorem provides a valid but indeterminable solution to the task, since the distribution from which the random samples are generated is inaccessible. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The core idea is to compute importance weights associated with the random samples, such that the distance between the weighted proposal empirical distribution function and the desired target distribution function is minimized. The distance metric selected for this work is the %$L_2%$-norm and the importance weights are constrained to define a probability measure. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program. This problem can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem is shown to result in a weighted proposal empirical distribution function that converges to the target distribution function in the %$L_1%$-norm, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches.
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container_issue	3
title_short	Optimal %$L_2%$-norm empirical importance weights for the change of probability measure
url	https://dx.doi.org/10.1007/s11222-016-9644-3
remote_bool	true
author2	Allaire, Douglas Willcox, Karen
author2Str	Allaire, Douglas Willcox, Karen
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doi_str	10.1007/s11222-016-9644-3
up_date	2024-07-03T15:38:18.697Z
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score	7.4016733

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Optimal %$L_2%$-norm empirical importance weights for the change of probability measure

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