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Federated learning promises an elegant solution for learning global models across distributed and privacy-protected datasets. However, challenges related to skewed data distribution, limited computational and communication resources, data poisoning, and free riding clients affect the performance of federated learning. Selection of the best clients for each round of learning is critical in alleviating these problems. We propose a novel sampling method named the irrelevance sampling technique. Our method is founded on defining a novel irrelevance score that incorporates the client characteristics in a single floating value, which can elegantly classify the client into three numerical sign defined pools for easy sampling. It is a computationally inexpensive, intuitive and privacy preserving sampling technique that selects a subset of clients based on quality and quantity of data on edge devices. It achieves 50–80% faster convergence even in highly skewed data distribution in the presence of free riders based on lack of data and severe class imbalance under both Independent and Identically Distributed (IID) and Non-IID conditions. It shows good performance on practical application datasets. [ABSTRACT FROM AUTHOR]

In the literature there are several methods for comparing two convergent iterative processes for the same problem. In this note we have in view mostly the one introduced by Berinde in (Fixed Point Theory Appl. 2:97–105, 2004) because it seems to be very successful. In fact, if IP1 and IP2 are two iterative processes converging to the same element, then IP1 is faster than IP2 in the sense of Berinde. The aim of this note is to prove this almost obvious assertion and to discuss briefly several papers that cite the mentioned Berinde's paper and use his method for comparing iterative processes. [ABSTRACT FROM AUTHOR]

Normally, genetic algorithm (GA) does not guarantee global optimum for all optimization problems. Crossover operators play a crucial part in the convergence of GAs to a solution. Hence, if crossover is designed to pass on genes that highly contribute to the fitness of individuals, to subsequent generations, the convergence can be obtained faster while obtaining the best possible solution for the given initial population. In this paper, we propose two new crossover operators called the dominance and co-dominance crossover operators, based on the dominance and co-dominance principles of human genetics, respectively, to achieve this in case of applications using integer and real encoding. The dominance crossover operator is designed such that the child obtains a gene (feature) from a parent whose value for a particular gene (feature) is dominant than its value in the other parent. On the other hand, the co-dominance crossover operator is designed such that a child obtains two values for the same gene from both the parents in case both alleles (gene values) are equally dominant. These crossover operators were designed to get the optimal solution in less number of generations without sacrificing the performance of GA. The experiments conducted on test functions and two different problems, namely clustering (Reuters-21578 dataset) and learning to rank (LETOR dataset), emphasize that global optimum in fewer number of generations is obtained using our proposed crossover operators. [ABSTRACT FROM AUTHOR]

Expert systems routinely use conditional reasoning. Conditionally specified statistical models offer several advantages over joint models; one is that Gibbs sampling can be used to generate realizations of the model. As a result, full conditional specification for multiple imputation is gaining popularity because it is flexible and computationally straightforward. However, it would be restrictive to require that every regression/classification must involve all of the variables. Feature selection often removes some variables from the set of predictors, thus making the regression local. A mixture of full and local conditionals is referred to as a partially collapsed Gibbs sampler, which often achieves faster convergence due to reduced conditioning. However, its implementation requires choosing a correct scan order. Using an invalid scan order will bring about an incorrect transition kernel, which leads to the wrong stationary distribution. We prove a necessary and sufficient condition for Gibbs sampling to correctly sample the joint distribution. We propose an algorithm that identifies all of the valid scan orders for a given conditional model. A forward search algorithm is discussed. Checking compatibility among conditionals of different localities is also discussed. [ABSTRACT FROM AUTHOR]

In this study, a new optimal control law associated with sliding mode control is developed based on basis of the Bolza-Meyer criterion. The salient characteristic of the proposed controller is to have gains adjustability, where the gain values can be larger than one. This leads to enhancing control system performances with a given cost function. It should be pointed out that conventional optimal controllers usually have constant gains of one or less than one, and hence the control system performances such as the requirement on convergence speed may not be satisfactory. After formulating the proposed optimal control law for polynomial time-varying control systems, computer simulations are carried out to validate the benefits of the proposed approach. Firstly, as an illustrative example, three crucial index values including control gain index, main input control index and the state index are investigated. Secondly, the proposed controller is applied to a vehicle seat suspension system with magneto-rheological damper to evaluate vibration control performances. In simulation studies, a comparison between the proposed approach and a state-of-the-art optimal controller is undertaken to demonstrate additional benefits such as less power and faster convergence of the proposed optimal controller. • The Meyer term is designed with a chosen constant to reduce control energy. • The critical issue of definite symmetry matrices of the Hamilton-Jacobi-Bellman with values larger than one is thoroughly solved to provide both high performances and robustness. • The Bolza-Meyer method is used along with a modification of the Meyer term to simplify the control structure. [ABSTRACT FROM AUTHOR]