Cited By
View all- Hovland P(2024)Jacobian sparsity detection using Bloom filtersOptimization Methods and Software10.1080/10556788.2023.2285486(1-13)Online publication date: 10-Oct-2024
Efficient detection of hessian matrix sparsity pattern
Pages 151 - 154
Abstract
Evaluation of the Hessian matrix of a scalar function is a subproblem in many numerical optimization algorithms. For large-scale problems often the Hessian matrix is sparse and structured, and it is preferable to exploit such information when available. Using symmetry in the second derivative values of the components it is possible to detect the sparsity pattern of the Hessian via products of the Hessian matrix with specially chosen direction vectors. We use graph coloring methods and employ efficient sparse data structures to implement the sparsity pattern detection algorithms. Results from preliminary numerical testings are highly promising.
References
[1]
ADMAT, http://www.cayugaresearch.com (accessed May 15, 2016).
[2]
R. G. Carter. Fast Numerical Determination of Symmetric Sparsity Patterns. Tech. report MCS- P326--0992, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1992.
[3]
T. F. Coleman and J. J. Moré. Estimation of sparse Jacobian matrices and graph coloring problems. SIAM J. Numer. Anal., 20(1):187--209, 1983.
[4]
A. R. Curtis, M. J. D. Powell, and J. K. Reid. On the estimation of sparse Jacobian matrices. J. Inst. Math. Appl., 13:117--119, 1974.
[5]
The Matrix Market Project. http://math.nist.gov/MatrixMarket/ (accessed May 15, 2016).
[6]
A. H. Gebremedhin, F. Manne, and A. Pothen. What Color is your Jacobian? Graph Coloring for Computing Derivatives. SIAM Rev., 47(4):629--705, 2005.
[7]
A. Griewank and C. Mitev. Detecting Jacobian sparsity patterns by Bayesian probing. Math. Prog., 93(1):1--25, 2002.
[8]
M. Hasan, S. Hossain, A. I. Khan, N. H. Mithila, and A. H. Suny. DSJM: A Software Toolkit for Direct Determination of Sparse Jacobian Matrices. To appear in the Springer Lecture Notes in Computer Science LNCS 9725, ICMS 2016, Berlin.
[9]
S. A. Forth. An Efficient Overloaded Implementation of Forward Mode Automatic Differentiation in MATLAB. ACM Transactions on Mathematical Software, 32(2):195--222, 2006.
[10]
A. Walther and A. Griewank. Getting started with ADOL-C. In U. Naumann and O. Schenk Eds., Combinatorial Scientific Computing. Chapman-Hall CRC Computational Science, Chapter 7, 181--202, 2012.
Recommendations
Hessian Matrix vs. Gauss-Newton Hessian Matrix
In this paper, we investigate how the Gauss-Newton Hessian matrix affects the basin of convergence in Newton-type methods. Although the Newton algorithm is theoretically superior to the Gauss-Newton algorithm and the Levenberg-Marquardt (LM) method as ...
An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems
AbstractThe sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse group ...
High-dimensional interactions detection with sparse principal Hessian matrix
In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to combinatorial ...
Comments
Information & Contributors
Information
Published In
Copyright © 2017 Authors.
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 22 February 2017
Published in SIGSAM-CCA Volume 50, Issue 4
Check for updates
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 129Total Downloads
- Downloads (Last 12 months)4
- Downloads (Last 6 weeks)1
Reflects downloads up to 26 Jan 2025
Other Metrics
Citations
Cited By
View all- Hovland P(2024)Jacobian sparsity detection using Bloom filtersOptimization Methods and Software10.1080/10556788.2023.2285486(1-13)Online publication date: 10-Oct-2024
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in