preprint · arXiv (Cornell University) · 2019

Testing that a Local Optimum of the Likelihood is Globally Optimum using\n Reparameterized Embeddings

J.W. LeBlanc, Brian J. Thelen, Alfred O. Hero

Cited by 0Open access

Abstract

Many mathematical imaging problems are posed as non-convex optimization\nproblems. When numerically tractable global optimization procedures are not\navailable, one is often interested in testing ex post facto whether or not a\nlocally convergent algorithm has found the globally optimal solution. When the\nproblem is formulated in terms of maximizing the likelihood function under a\nstatistical model for the measurements, one can construct a statistical test\nthat a local maximum is in fact the global maximum. A one-sided test is\nproposed for the case that the statistical model is a member of the generalized\nlocation family of probability distributions, a condition often satisfied in\nimaging and other inverse problems. We propose a general method for improving\nthe accuracy of the test by reparameterizing the likelihood function to embed\nits domain into a higher dimensional parameter space. We show that the proposed\nglobal maximum testing method results in improved accuracy and reduced\ncomputation for a physically-motivated joint-inverse problem arising in\ncamera-blur estimation.\n

Cite this paper

APA 7

LeBlanc, J., Thelen, B. J., & Hero, A. O. (2019). Testing that a Local Optimum of the Likelihood is Globally Optimum using\n Reparameterized Embeddings. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1906.00101

MLA 9

LeBlanc, J.W., et al. “Testing that a Local Optimum of the Likelihood is Globally Optimum using\n Reparameterized Embeddings.” arXiv (Cornell University), 2019, https://doi.org/10.48550/arxiv.1906.00101.

Chicago

LeBlanc, J.W., Brian J. Thelen, and Alfred O. Hero. 2019. “Testing that a Local Optimum of the Likelihood is Globally Optimum using\n Reparameterized Embeddings.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1906.00101.

Harvard

LeBlanc, J., Thelen, B.J. and Hero, A.O. (2019) ‘Testing that a Local Optimum of the Likelihood is Globally Optimum using\n Reparameterized Embeddings’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1906.00101.

BibTeX

@misc{leblanc2019testing,
  title = {{Testing that a Local Optimum of the Likelihood is Globally Optimum using\n Reparameterized Embeddings}},
  author = {LeBlanc, J.W. and Thelen, Brian J. and Hero, Alfred O.},
  journal = {arXiv (Cornell University)},
  year = {2019},
  doi = {10.48550/arxiv.1906.00101}
}

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