In maximizing a non-linear function G(theta), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1-1 transformation on the variables theta...
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In maximizing a non-linear function G(theta), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1-1 transformation on the variables theta, so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihoodfunctions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.
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...
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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.
Linear sparse arrays with N physical sensors can resolve O(N-2) directions of arrival (DOAs) for uncorrelated sources. This attribute is associated with the difference coarray of size O(N-2). However, the number of so...
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ISBN:
(纸本)9798350344820;9798350344813
Linear sparse arrays with N physical sensors can resolve O(N-2) directions of arrival (DOAs) for uncorrelated sources. This attribute is associated with the difference coarray of size O(N-2). However, the number of sources is assumed to be known in many coarray-based DOA estimators. This paper proposes a Monte Carlo source enumerator (MCSE) for sparse arrays by maximizing the log-likelihood function (LLF). This LLF depends on an unbounded parameter space and a multiple integral, which are challenging for computation. This unbounded parameter space is replaced with a bounded space derived from coarse estimates and Cramer-Rao bounds. Next, the multiple integral is approximated with Monte Carlo methods. The MCSE applies to three scenarios: no sources, fewer sources than sensors, and more sources than sensors. Furthermore, some details in the MCSE can be computed in parallel. Numerical examples demonstrate the applicability of the MCSE to sparse arrays.
Nowadays, nuclear imaging is increasingly used for non-invasive diagnosis. The image modalities in nuclear imaging suffer of worse statistics, in comparison with computed tomography, since they are based on emission t...
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ISBN:
(纸本)9781479914920
Nowadays, nuclear imaging is increasingly used for non-invasive diagnosis. The image modalities in nuclear imaging suffer of worse statistics, in comparison with computed tomography, since they are based on emission transition tomography. Thus, precise reconstruction methods that can deal with incomplete or missing measurements are needed in order to improve the quality of nuclear images. In this paper we present a generalization of the state of the art EMML and ISRA algorithms for emission computed tomography reconstruction. The proposed method was tested and validated in comparison with the mentioned state of the art methods on a set of synthetic data. Better results (in terms of speed of convergence) were obtained for certain parameter settings.
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