Browsing by Subject "Randomization"

Now showing 1 - 11 of 11

Open Access
Estimation of a change point in a hazard function based on censored data
(Springer New York LLC, 2003) Gijbels, I.; Gürler, Ü.
The hazard function plays an important role in reliability or survival studies since it describes the instantaneous risk of failure of items at a time point, given that they have not failed before. In some real life applications, abrupt changes in the hazard function are observed due to overhauls, major operations or specific maintenance activities. In such situations it is of interest to detect the location where such a change occurs and estimate the size of the change. In this paper we consider the problem of estimating a single change point in a piecewise constant hazard function when the observed variables are subject to random censoring. We suggest an estimation procedure that is based on certain structural properties and on least squares ideas. A simulation study is carried out to compare the performance of this estimator with two estimators available in the literature: an estimator based on a functional of the Nelson-Aalen estimator and a maximum likelihood estimator. The proposed least squares estimator turns out to be less biased than the other two estimators, but has a larger variance. We illustrate the estimation method on some real data sets.
Open Access
On the optimality of likelihood ratio test for prospect theory-based binary hypothesis testing
(Institute of Electrical and Electronics Engineers, 2018) Gezici, Sinan; Varshney, P. K.
In this letter, the optimality of the likelihood ratio test (LRT) is investigated for binary hypothesis testing problems in the presence of a behavioral decision-maker. By utilizing prospect theory, a behavioral decision-maker is modeled to cognitively distort probabilities and costs based on some weight and value functions, respectively. It is proved that the LRT may or may not be an optimal decision rule for prospect theory-based binary hypothesis testing, and conditions are derived to specify different scenarios. In addition, it is shown that when the LRT is an optimal decision rule, it corresponds to a randomized decision rule in some cases; i.e., nonrandomized LRTs may not be optimal. This is unlike Bayesian binary hypothesis testing, in which the optimal decision rule can always be expressed in the form of a nonrandomized LRT. Finally, it is proved that the optimal decision rule for prospect theory-based binary hypothesis testing can always be represented by a decision rule that randomizes at most two LRTs. Two examples are presented to corroborate the theoretical results.
Open Access
Optimal decision rules for simple hypothesis testing under general criterion involving error probabilities
(IEEE, 2020) Dulek, B.; Öztürk, Cüneyd; Gezici, Sinan
The problem of simple M-ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule can be characterized as a randomization among at most two deterministic decision rules, each of the form reminiscent to Bayes rule, if the boundary points corresponding to each rule have zero probability under each hypothesis. Otherwise, a randomization among at most M(M-1)+1 deterministic decision rules is sufficient. The form of the deterministic decision rules are explicitly specified. Likelihood ratios are shown to be sufficient statistics. Classical performance measures including Bayesian, minimax, Neyman-Pearson, generalized Neyman-Pearson, restricted Bayesian, and prospect theory based approaches are all covered under the proposed formulation. A numerical example is presented for prospect theory based binary hypothesis testing.
Open Access
Optimal detector randomization for multiuser communications systems
(IEEE, 2013) Tutay, M. E.; Gezici, Sinan; Arıkan, Orhan
Optimal detector randomization is studied for the downlink of a multiuser communications system, in which users can perform time-sharing among multiple detectors. A formulation is provided to obtain optimal signal amplitudes, detectors, and detector randomization factors. It is shown that the solution of this joint optimization problem can be calculated in two steps, resulting in significant reduction in computational complexity. It is proved that the optimal solution is achieved via randomization among at most min{K, Nd} detector sets, where K is the number of users and Nd is the number of detectors at each receiver. Lower and upper bounds are derived on the performance of optimal detector randomization, and it is proved that the optimal detector randomization approach can reduce the worst-case average probability of error of the optimal approach that employs a single detector for each user by up to K times. Various sufficient conditions are obtained for the improvability and nonimprovability via detector randomization. In the special case of equal crosscorrelations and noise powers, a simple solution is developed for the optimal detector randomization problem, and necessary and sufficient conditions are presented for the uniqueness of that solution. Numerical examples are provided to illustrate the improvements achieved via detector randomization.
Open Access
Optimal randomization of signal constellations on downlink of a multiuser DS-CDMA system
(IEEE, 2013-10) Tutay, M. E.; Gezici, Sinan; Arıkan, Orhan
In this study, the jointly optimal power control with signal constellation randomization is proposed for the downlink of a multiuser communications system. Unlike a conventional system in which a fixed signal constellation is employed for all the bits of a user (for given channel conditions and noise power), power control with signal constellation randomization involves randomization/time- sharing among different signal constellations for each user. A formulation is obtained for the problem of optimal power control with signal constellation randomization, and it is shown that the optimal solution can be represented by a randomization among (K+1) or fewer distinct signal constellations for each user, where K denotes the number of users. In addition to the original nonconvex formulation, an approximate solution based on convex relaxation is derived. Then, detailed performance analysis is presented when the receivers employ symmetric signaling and sign detectors. Specifically, the maximum asymptotical improvement ratio is shown to be equal to the number of users, and the conditions under which the maximum and minimum asymptotical improvement ratios are achieved are derived. Numerical examples are presented to investigate the theoretical results, and to illustrate performance improvements achieved via the proposed approach. © 2002-2012 IEEE.
Open Access
Optimal stochastic parameter design for estimation problems
(Institute of Electrical and Electronics Engineers, 2012) Soganci, H.; Gezici, Sinan; Arıkan, Orhan
In this study, the aim is to perform optimal stochastic parameter design in order to minimize the cost of a given estimator. Optimal probability distributions of signals corresponding to different parameters are obtained in the presence and absence of an average power constraint. It is shown that the optimal parameter design results in either a deterministic signal or a randomization between two different signal levels. In addition, sufficient conditions are obtained to specify the cases in which improvements over the deterministic parameter design can or cannot be achieved via the stochastic parameter design. Numerical examples are presented in order to provide illustrations of theoretical results.
Open Access
Optimal stochastic signaling for power-constrained binary communications systems
(IEEE, 2010) Goken, C.; Gezici, Sinan; Arıkan, Orhan
Optimal stochastic signaling is studied under second and fourth moment constraints for the detection of scalar-valued binary signals in additive noise channels. Sufficient conditions are obtained to specify when the use of stochastic signals instead of deterministic ones can or cannot improve the error performance of a given binary communications system. Also, statistical characterization of optimal signals is presented, and it is shown that an optimal stochastic signal can be represented by a randomization of at most three different signal levels. In addition, the power constraints achieved by optimal stochastic signals are specified under various conditions. Furthermore, two approaches for solving the optimal stochastic signaling problem are proposed; one based on particle swarm optimization (PSO) and the other based on convex relaxation of the original optimization problem. Finally, simulations are performed to investigate the theoretical results, and extensions of the results to M-ary communications systems and to other criteria than the average probability of error are discussed.
Open Access
Optimum Power Allocation for Average Power Constrained Jammers in the Presense of Non-Gaussian Noise
(Institute of Electrical and Electronics Engineers, 2012-08) Bayram, S.; Vanli, N. D.; Dulek, B.; Sezer, I.; Gezici, Sinan
We study the problem of determining the optimum power allocation policy for an average power constrained jammer operating over an arbitrary additive noise channel, where the aim is to minimize the detection probability of an instantaneously and fully adaptive receiver employing the Neyman-Pearson (NP) criterion. We show that the optimum jamming performance can be achieved via power randomization between at most two different power levels. We also provide sufficient conditions for the improvability and nonimprovability of the jamming performance via power randomization in comparison to a fixed power jamming scheme. Numerical examples are presented to illustrate theoretical results.
Open Access
Self-adaptive randomized and rank-based differential evolution for multimodal problems
(Springer, 2011-01-15) Urfalioglu, O.; Arıkan, Orhan
Differential Evolution (DE) is a widely used successful evolutionary algorithm (EA) based on a population of individuals, which is especially well suited to solve problems that have non-linear, multimodal cost functions. However, for a given population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitness of the population. This paper presents a novel extension of DE called Randomized and Rank-based Differential Evolution (R2DE) and its self-adaptive version SAR2DE to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the population fitness. In extensive experiments conducted with a wide range of complexity settings, we show that the proposed heuristics lead to an overall improvement in robustness and speed of convergence compared to several global optimization techniques, including DE, Opposition based Differential Evolution (ODE), DE with Random Scale Factor (DERSF) and the self-adaptive Cauchy distribution based DE (NSDE).
Open Access
Short-term dietary restriction in old zebrafish changes cell senescence mechanisms
(Elsevier, 2016-10) Arslan-Ergul, Ayca; Erbaba, Begun; Karoglu, Elif Tugce; Halim, Dilara Ozge; Adams, Michelle M.
Brain aging is marked by a decline in cognitive abilities and associated with neurodegenerative disorders. Recent studies have shown, neurogenesis continues into adulthood but is known to be decreasing during advancing age and these changes may contribute to cognitive alterations. Advances, which aim to promote better aging are of paramount importance. Dietary restriction (DR) is the only non-genetic intervention that reliably extends life- and health-span. Mechanisms of how and why DR and age affect neurogenesis are not well-understood, and have not been utilized much in the zebrafish, which has become a popular model to study brain aging and neurodegenerative disease due to widely available genetic tools. In this study we used young (8–8.5 months) and old (26–32.5 months) zebrafish as the model to investigate the effects of a short-term DR on actively proliferating cells. We successfully applied a 10-week DR to young and old fish, which resulted in a significant loss of body weight in both groups with no effect on normal age-related changes in body growth. We found that age decreased cell proliferation and increased senescence associated β-galactosidase, as well as shortened telomere lengths. In contrast, DR shortened telomere lengths only in young animals. Neither age nor DR changed the differentiation patterns of glial cells. Our results suggest that the potential effects of DR could be mediated by telomere regulation and whether these are beneficial or negative remains to be determined.
Open Access
Stochastic signal design on the downlink of a multiuser communications system
(IEEE, 2012-06) Tutay, Mehmet Emin; Gezici, Sinan; Arıkan, Orhan
Stochastic signal design is studied for the downlink of a multiuser communications system. First, a formulation is proposed for the joint design of optimal stochastic signals. Then, an approximate formulation, which can get arbitrarily close to the optimal solution, is obtained based on convex relaxation. In addition, when the receivers employ symmetric signaling and sign detectors, it is shown that the maximum asymptotical improvement ratio is equal to the number of users, and the conditions under which that maximum asymptotical improvement ratio is achieved are presented. Numerical examples are provided to explain the theoretical results. © 2012 IEEE.