Monotonicity of the Ratio of the Power and Second Seiffert Means with Applications

We present the necessary and sufficient condition for the monotonicity of the ratio of the power and second Seiffert means. As applications, we get the sharp upper and lower bounds for the second Seiffert mean in terms of the power mean

A separation of some Seiffert-type means by power means

Consider the identric mean $\mathcal{I}$, the logarithmic mean $\mathcal{L,}$ two trigonometric means defined by H. J. Seiffert and denoted by $\mathcal{P}$ and $\mathcal{T,}$ and the hyperbolic mean $\mathcal{M}$ defined by E. Neuman and J. Sándor. There are a number of known inequalities between these means and some power means $\mathcal{A}_{p}.$ We add to these inequalities some new results obtaining the following chain of inequalities\[\mathcal{A}_{0}<\mathcal{L}<\mathcal{A}_{1/3}<\mathcal{P<A}_{2/3}<\mathcal{I}<\mathcal{A}_{3/3}<\mathcal{M}<\mathcal{A}_{4/3}<\mathcal{T}<\mathcal{A}_{5/3}.\

A Nice Separation of Some Seiffert-Type Means by Power Means

Seiffert has defined two well-known trigonometric means denoted by and . In a similar way it was defined by Carlson the logarithmic mean ℒ as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean ℳ. There are more known inequalities between the means ,, and ℒ and some power means . We add to these inequalities two new results obtaining the following nice chain of inequalities 0<ℒ<1/2<<1<ℳ<3/2<<2, where the power means are evenly spaced with respect to their order

Augmented Cross-Selling Through Explainable AI—A Case From Energy Retailing

The advance of Machine Learning (ML) has led to a strong interest in this technology to support decision making. While complex ML models provide predictions that are often more accurate than those of traditional tools, such models often hide the reasoning behind the prediction from their users, which can lead to lower adoption and lack of insight. Motivated by this tension, research has put forth Explainable Artificial Intelligence (XAI) techniques that uncover patterns discovered by ML. Despite the high hopes in both ML and XAI, there is little empirical evidence of the benefits to traditional businesses. To this end, we analyze data on 220,185 customers of an energy retailer, predict cross-purchases with up to 86% correctness (AUC), and show that the XAI method SHAP provides explanations that hold for actual buyers. We further outline implications for research in information systems, XAI, and relationship marketing

Optimizing Weights And Biases in MLP Using Whale Optimization Algorithm

Artificial Neural Networks are intelligent and non-parametric mathematical models inspired by the human nervous system. They have been widely studied and applied for classification, pattern recognition and forecasting problems. The main challenge of training an Artificial Neural network is its learning process, the nonlinear nature and the unknown best set of main controlling parameters (weights and biases). When the Artificial Neural Networks are trained using the conventional training algorithm, they get caught in the local optima stagnation and slow convergence speed; this makes the stochastic optimization algorithm a definitive alternative to alleviate the drawbacks. This thesis proposes an algorithm based on the recently proposed Whale Optimization Algorithm(WOA). The algorithm has proven to solve a wide range of optimization problems and outperform existing algorithms. The successful implementation of this algorithm motivated our attempts to benchmark its performance in training feed-forward neural networks. We have taken a set of 20 datasets with different difficulty levels and tested the proposed WOA-MLP based trainer. Further, the results are verified by comparing WOA-MLP with the back propagation algorithms and six evolutionary techniques. The results have proved that the proposed trainer can outperform the current algorithms on the majority of datasets in terms of local optima avoidance and convergence speed

Implications of a wavelength dependent PSF for weak lensing measurements

The convolution of galaxy images by the point-spread function (PSF) is the dominant source of bias for weak gravitational lensing studies, and an accurate estimate of the PSF is required to obtain unbiased shape measurements. The PSF estimate for a galaxy depends on its spectral energy distribution (SED), because the instrumental PSF is generally a function of the wavelength. In this paper we explore various approaches to determine the resulting `effective' PSF using broad-band data. Considering the Euclid mission as a reference, we find that standard SED template fitting methods result in biases that depend on source redshift, although this may be remedied if the algorithms can be optimised for this purpose. Using a machine-learning algorithm we show that, at least in principle, the required accuracy can be achieved with the current survey parameters. It is also possible to account for the correlations between photometric redshift and PSF estimates that arise from the use of the same photometry. We explore the impact of errors in photometric calibration, errors in the assumed wavelength dependence of the PSF model and limitations of the adopted template libraries. Our results indicate that the required accuracy for Euclid can be achieved using the data that are planned to determine photometric redshifts