Publication: Efficient Derivative Codes through Automatic Differentiation and Interface Contraction: An Application in Biostatistics
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Efficient Derivative Codes through Automatic Differentiation and Interface Contraction: An Application in Biostatistics

- Article in a journal -
 

Author(s)
Paul D. Hovland , Christian H. Bischof , Donna Spiegelman , Mario Casella

Published in
SIAM Journal on Scientific Computing

Year
1997

Abstract
Developing code for computing the first- and higher-order derivatives of a function by hand can be very time consuming and is prone to errors. Automatic dierentiation has proven capable of producing derivative codes with very little eort on the part of the user. Automatic dierentiation avoids the truncation errors characteristic of divided dierence approximations. However, the derivative code produced by automatic dierentiation can be signicantly less ecient than one produced by hand. This shortcoming may be overcome by utilizing insight into the high-level structure of a computation. This paper focuses on how to take advantage of the fact that the number of variables passed between subroutines frequently is small compared with the number of variables with respect to which one wishes to dierentiate. Such an interface contraction, coupled with the associativity of the chain rule for differentiation, allows one to apply automatic differentiation in a more judicious fashion, resulting in much more ecient code for the computation of derivatives. A case study involving the ADIFOR (Automatic Dierentiation of Fortran) tool and a program for maximizing a logistic-normal likelihood function developed from a problem in nutritional epidemiology is examined, and performance figures are presented.

AD Tools
ADIFOR

AD Theory and Techniques
Interface Contraction

Related Applications
- Interface Contraction in Biostatistics

BibTeX
@ARTICLE{
         Hovland1997EDC,
       AUTHOR = "Paul D. Hovland and Christian H. Bischof and Donna Spiegelman and Mario Casella",
       TITLE = "Efficient Derivative Codes through Automatic Differentiation and Interface
         Contraction: {A}n Application in Biostatistics",
       JOURNAL = "{SIAM} Journal on Scientific Computing",
       PAGES = "1056--1066",
       REFERRED = "[Bischof1996UEw], [Bischof1996HAt], [Christianson1996SSU].",
       COMMENT = "Also appeared as Mathematics and Computer Science Division, Argonne National
         Laboratory, Preprint MCS--P491--0195, 1995.",
       ad_theotech = "Interface Contraction",
       VOLUME = "18",
       NUMBER = "4",
       YEAR = "1997",
       keywords = "automatic differentiation; computational differentiation; interface contraction;
         log-likelihood functions; derivatives; ADIFOR",
       url = "http://link.aip.org/link/?SCE/18/1056/1",
       doi = "10.1137/S1064827595281800",
       ad_tools = "ADIFOR",
       abstract = "Developing code for computing the first- and higher-order derivatives of a function
         by hand can be very time consuming and is prone to errors. Automatic dierentiation has proven
         capable of producing derivative codes with very little eort on the part of the user. Automatic
         dierentiation avoids the truncation errors characteristic of divided dierence approximations.
         However, the derivative code produced by automatic dierentiation can be signicantly less ecient than
         one produced by hand. This shortcoming may be overcome by utilizing insight into the high-level
         structure of a computation. This paper focuses on how to take advantage of the fact that the number
         of variables passed between subroutines frequently is small compared with the number of variables
         with respect to which one wishes to dierentiate. Such an interface contraction, coupled with the
         associativity of the chain rule for differentiation, allows one to apply automatic differentiation
         in a more judicious fashion, resulting in much more ecient code for the computation of derivatives.
         A case study involving the ADIFOR (Automatic Dierentiation of Fortran) tool and a program for
         maximizing a logistic-normal likelihood function developed from a problem in nutritional
         epidemiology is examined, and performance figures are presented."
}


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