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

Details

• Personal Author:
  Bischof C ; Casella M ; Hovland P ; Spiegelman D
• Description:
  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 differentiation has proven capable of producing derivative codes with very little effort on the part of the user. Automatic differentiation avoids the truncation errors characteristic of divided difference approximations. However, the derivative code produced by automatic differentiation can be significantly less efficient 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 differentiate. 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 efficient code for the computation of derivatives. A case study involving the ADIFOR (Automatic Differentiation 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. [Description provided by NIOSH]
• Subjects:
  Antineoplastic Agents Occupational Exposure Occupational Health Risk Assessment Risk Factors Safety
• Keywords:
  ADIFOR Antineoplastic-agents Author Keywords: Automatic Differentiation Biostatistics Computational Differentiation Derivatives Interface Contraction Log-likelihood Functions Mathematical-models Occupational-exposure Risk-factors Statistical-analysis

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• ISSN:
  1064-8275
• Document Type:
  Text
• Funding:
  Grant
• Genre:
  Journal Article
• Place as Subject:
  Massachusetts ; OSHA Region 1
• CIO:
  National Institute for Occupational Safety and Health (NIOSH)
• Topic:
  Workplace Safety & Health
• Location:
  North America
• Volume:
  18
• Issue:
  4
• NIOSHTIC Number:
  nn:20024391
• Citation:
  SIAM J Sci Comput 1997 Jul-Aug; 18(4):1056-1066
• Contact Point Address:
  Computer Science Department, University of Illinois at Urbana-Champaign, 1304 W. Springfield Avenue, Urbana, IL 61801
• Email:
  hovland@uiuc.edu
• Federal Fiscal Year:
  1997
• NORA Priority Area:
  Grants Other
• Performing Organization:
  Harvard University, School of Public Health, Department of Epidemiology and Biostatistics, Boston, Massachusetts
• Peer Reviewed:
  True
• Start Date:
  19910701
• Source Full Name:
  SIAM Journal on Scientific Computing
• End Date:
  19950630
• Collection(s):
  National Institute for Occupational Safety and Health
• Main Document Checksum:
  urn:sha-512:931f0df985133fada545d1baa9b56027b254626e58e76631cd1e8fcd2131f45964109f59a655f2c473bd0d6944566d67292c8afa3af9f0bf71abb409a0940068
• Download URL:
  https://stacks.cdc.gov/view/cdc/196215/cdc_196215_DS1.pdf
• File Type:
  [PDF - 1.32 MB ]