Despite the growing interest in the interplay of machine learning and optimization, existing contributions remain scattered across the research board, and a comprehensive overview on such reciprocity still lacks at this stage. In this context, this paper visits one particular direction of interplay between learning-driven solutions and optimization, and further explicates the subject matter with a clear background and summarized theory. For instance, machine learning and its offsprings are trending because of their enhanced capabilities in automating analytical modeling. In this realm, learning-based techniques (supervised, unsupervised, and reinforcement) have grown to complement many of the optimization problems in testing and training. This paper overviews how machine learning-based techniques, namely deep neural networks, echo-state networks, reinforcement learning, and federated learning, can be used to solve complex and analytically intractable optimization problems, for which specific cases are examined in this paper. The paper particularly overviews when learning-based algorithms are useful at solving particular optimizing problems, especially those of random, dynamic, and mathematically complex nature. The paper then illustrates such applications by presenting particular use-cases in communications and signal processing including wireless scheduling, wireless offloading and resource management, power control, aerial base station placement, virtual reality, and vehicular networks. Lastly, the paper sheds light on some future research directions, where the dynamicity and randomness of the underlying optimization problems make deep learning-driven techniques a necessity, namely in sensing at the terahertz (THz) bands, cellular vehicle-to-everything, 6G communication networks, underwater optical networks, distributed optimization, and applications of emerging learning-based techniques.

Images can be broadly classified into two types: isotropic and anisotropic. Isotropic images contain largely rounded objects while anisotropics are made of flow-like structures. Regardless of the types, the acquisition process introduces noise. A standard approach is to use diffusion for image smoothing. Based on the category, either isotropic or anisotropic diffusion can be used. Fundamentally, diffusion process is an iterated one, starting with a poor quality image, and converging to a completely blurred mean-value image, with no significant structure left. Though the process starts by doing a desirable job of cleaning noise and filling gaps, called under-smoothing, it quickly passes into an over-smoothing phase where it starts destroying the important structure. One relevant concern is to find the boundary between the under-smoothing and over-smoothing regions. The spatial entropy change is found to be one such measure that may be helpful in providing important clues to describe that boundary, and thus provides a reasonable stopping rule for isotropic as well as anisotropic diffusion. Numerical experiments with real fingerprint data confirm the role of entropy-change in identification of a reasonable stopping point where most of the noise is diminished and blurring is just started. The proposed criterion is directly related to the blurring phenomena that is an increasing function of diffusion process. The proposed scheme is evaluated with the help of synthetic as well as the real images and compared with other state-of-the-art schemes using a qualitative measure. Diffusions of some challenging low-quality images from FVC2004 are also analyzed to provide a reasonable stopping rule using the proposed stopping rule.

Various modifications have been suggested in the past to extend Shannon entropy to continuous random variables. This article investigates these modifications, and suggests a new entropy measure with the name of average entropy (AE). AE is more general than Shannon entropy in the sense that its definition encompasses both continuous as well as discrete domains. It is additive, positive and attains zero only when the distribution is uniform. The main characteristic of the suggested measure lies in its consistency behavior. Many properties of AE, including its relationship with Kullback–Leibler information measure, are studied. Precise theorems about the vanishing of the conditional AE for both continuous and discrete distributions are provided. Toward the end, the measure is tested for its effectiveness in image segmentation. [Received March 2014. Revised June 2015.]

Typically, in accelerated life testing analysis, only probability distributions possessing shape parameters are used to fit the experimental data, and many distributions with no shape parameters have been excluded, including the fundamental ones like the normal distribution, even when they are good fitters to the data. This work shows that the coefficient of variation is a replacement for the shape parameter and allows using normal distributions in this context. The work focuses on the Arrhenius-normal model as a life-stress relationship for lithium-ion (Li-ion) batteries and precisely derives the estimating equations of its accelerating parameters. Real and simulated lives of Li-ion batteries are used to validate our results.

This paper proposes an overlapping-based test statistic for testing the equality of two exponential distributions with different scale and location parameters. The test statistic is defined as the maximum likelihood estimate of the Weitzman's overlapping coefficient, which estimates the agreement of two densities. The proposed test statistic is derived in closed form. Simulated critical points are generated for the proposed test statistic for various sample sizes and significance levels via Monte Carlo Simulations. Statistical powers of the proposed test are computed via simulation studies and compared to those of the existing Log likelihood ratio test.

Usually, researchers adopt Weibull distribution as the best fitting lifetime model of several electronics/ optoelectronics devices, including organic light-emitting diodes (OLEDs). They justify the adoption based on a few statistical goodness-of-fit (GoF) tests, which are not always applicable due to violating some of the assumptions of the tests. In this article, several standard and valid GoF tests show that the lognormal distribution is a better fitting model than the Weibull distribution for OLEDs and performs better when a censoring scheme is applied.