3 research outputs found
On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions
The implementation of global optimization algorithms, using the arithmetic of
infinity, is considered. A relatively simple version of implementation is
proposed for the algorithms that possess the introduced property of strong
homogeneity. It is shown that the P-algorithm and the one-step Bayesian
algorithm are strongly homogeneous.Comment: 11 pages, 1 figur
Phase-type survival trees and mixed distribution survival trees for clustering patients' hospital length of stay
Clinical investigators, health professionals and managers are often interested in developing criteria for clustering patients into clinically meaningful groups according to their expected
length of stay. In this paper, we propose two novel types of survival trees; phase-type survival trees
and mixed distribution survival trees, which extend previous work on exponential survival trees.
The trees are used to cluster the patients with respect to length of stay where partitioning is based
on covariates such as gender, age at the time of admission and primary diagnosis code. Likelihood
ratio tests are used to determine optimal partitions. The approach is illustrated using nationwide
data available from the English Hospital Episode Statistics (HES) database on stroke-related patients, aged 65 years and over, who were discharged from English hospitals over a 1-year period.peer-reviewe
Stochastic algorithms for solving structured low-rank approximation problems
In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. We demonstrate that finding optimal solutions of this problem is very hard. For example, we argue that if HSLRA is considered as a problem of estimating parameters of damped sinusoids, then the associated optimization problem is basically unsolvable. We discuss what is known as the orthogonality condition, which solutions to the HSLRA problem should satisfy, and describe how any approximation may be corrected to achieve this orthogonality. Unlike many other methods described in the literature the family of algorithms we propose has the property of guaranteed convergence