Statistical treatment of signal power measurements under identification of the distant radiator antenna directional pattern

Antennas ◽  
2021 ◽  
Author(s):  
P. P. Krutskikh ◽  
V. G. Radzievskiy
Keyword(s):  
Gradient Descent ◽  
Radiation Power ◽  
Statistical Treatment ◽  
Average Power ◽  
Approximation Procedure ◽  
Gradient Descent Method ◽  
Linear Type ◽  
Gaussian Form ◽  
Gradient Descent Algorithm ◽  
Transmitting Antenna

Based on the use of the least squares method and the fastest gradient descent algorithm, the procedure for approximation of measurements of the radiation power of the transmitting antenna has been developed. This procedure involves an average power pattern of a linear type antenna with random amplitude and phase deviations on the assumptions of their normal distribution, consistency of average amplitude and phase dispersion along the antenna, Gaussian form of the correlation coefficient of deviations. As an approximation quality criterion, the minimum of the sum of the squared deviations of radiation power estimates at points of measurement from theoretical values of a random function that determines the shape of the radiation pattern is used. Given the nonlinearity of the function, the numerical approximation procedure based on the fastest gradient descent method has been proposed. The direction of descent at the next iteration is selected on the basis of the current value of the gradient of the criterion function. The criterion for the completion of the process is the achievement of a stationary, in a statistical sense, area of the function.

scholarly journals Implicit Stochastic Gradient Descent Method for Cross-Domain Recommendation System

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2510
Author(s):  
Nam D. Vo ◽  
Minsung Hong ◽  
Jason J. Jung
Keyword(s):  
Gradient Descent ◽  
Recommendation System ◽  
Computation Time ◽  
Descent Method ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Gradient Descent Method ◽  
Target Domain ◽  
Cross Domain ◽  
Gradient Descent Algorithm

The previous recommendation system applied the matrix factorization collaborative filtering (MFCF) technique to only single domains. Due to data sparsity, this approach has a limitation in overcoming the cold-start problem. Thus, in this study, we focus on discovering latent features from domains to understand the relationships between domains (called domain coherence). This approach uses potential knowledge of the source domain to improve the quality of the target domain recommendation. In this paper, we consider applying MFCF to multiple domains. Mainly, by adopting the implicit stochastic gradient descent algorithm to optimize the objective function for prediction, multiple matrices from different domains are consolidated inside the cross-domain recommendation system (CDRS). Additionally, we design a conceptual framework for CDRS, which applies to different industrial scenarios for recommenders across domains. Moreover, an experiment is devised to validate the proposed method. By using a real-world dataset gathered from Amazon Food and MovieLens, experimental results show that the proposed method improves 15.2% and 19.7% in terms of computation time and MSE over other methods on a utility matrix. Notably, a much lower convergence value of the loss function has been obtained from the experiment. Furthermore, a critical analysis of the obtained results shows that there is a dynamic balance between prediction accuracy and computational complexity.

scholarly journals LOSS FUNCTIONS AND DESCENT METHOD

2021 ◽  
Vol 55 (1 (254)) ◽  
pp. 29-35
Author(s):  
Hovhannes Z. Zohrabyan ◽  
Victor K. Ohanyan
Keyword(s):  
Gradient Descent ◽  
Descent Method ◽  
Loss Functions ◽  
Gradient Descent Method ◽  
Descent Algorithm ◽  
Minimal Error ◽  
Poisson Distributions ◽  
Gradient Descent Algorithm ◽  
Bayesian Estimators

In this paper, we showed that it is possible to use gradient descent method to get minimal error values of loss functions close to their Bayesian estimators. We calculated Bayesian estimators mathematically for different loss functions and tested them using gradient descent algorithm. This algorithm, working on Normal and Poisson distributions showed that it is possible to find minimal error values without having Bayesian estimators. Using Python, we tested the theory on loss functions with known Bayesian estimators as well as another loss functions, getting results proving the theory.

scholarly journals Online Supervised Learning with Distributed Features over Multiagent System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xibin An ◽  
Bing He ◽  
Chen Hu ◽  
Bingqi Liu
Keyword(s):  
Machine Learning ◽  
Gradient Descent ◽  
Machine Learning Algorithms ◽  
Global Minimizer ◽  
Consensus Method ◽  
Model Parameters ◽  
Gradient Descent Method ◽  
Global Features ◽  
Gradient Descent Algorithm ◽  
Distributed Machine Learning

Most current online distributed machine learning algorithms have been studied in a data-parallel architecture among agents in networks. We study online distributed machine learning from a different perspective, where the features about the same samples are observed by multiple agents that wish to collaborate but do not exchange the raw data with each other. We propose a distributed feature online gradient descent algorithm and prove that local solution converges to the global minimizer with a sublinear rate O 2 T . Our algorithm does not require exchange of the primal data or even the model parameters between agents. Firstly, we design an auxiliary variable, which implies the information of the global features, and estimate at each agent by dynamic consensus method. Then, local parameters are updated by online gradient descent method based on local data stream. Simulations illustrate the performance of the proposed algorithm.

scholarly journals Online Gradient Descent for Kernel-Based Maximum Correntropy Criterion

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 644
Author(s):  
Baobin Wang ◽  
Ting Hu
Keyword(s):  
Gradient Descent ◽  
Reproducing Kernel ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Theoretical Understanding ◽  
Scaling Parameter ◽  
Rigorous Error Bounds ◽  
Gradient Descent Algorithm ◽  
Kernel Hilbert Spaces ◽  
Maximum Correntropy Criterion

In the framework of statistical learning, we study the online gradient descent algorithm generated by the correntropy-induced losses in Reproducing kernel Hilbert spaces (RKHS). As a generalized correlation measurement, correntropy has been widely applied in practice, owing to its prominent merits on robustness. Although the online gradient descent method is an efficient way to deal with the maximum correntropy criterion (MCC) in non-parameter estimation, there has been no consistency in analysis or rigorous error bounds. We provide a theoretical understanding of the online algorithm for MCC, and show that, with a suitable chosen scaling parameter, its convergence rate can be min–max optimal (up to a logarithmic factor) in the regression analysis. Our results show that the scaling parameter plays an essential role in both robustness and consistency.

scholarly journals Revisiting the dynamic interactions between economic growth and environmental pollution in Italy: evidence from a gradient descent algorithm

2021 ◽  
Author(s):  
Marco Mele ◽  
Cosimo Magazzino ◽  
Nicolas Schneider ◽  
Floriana Nicolai
Keyword(s):  
Economic Growth ◽  
Gradient Descent ◽  
Statistical Data ◽  
Stochastic Gradient Descent ◽  
Policy Recommendations ◽  
Dynamic Interactions ◽  
Gradient Descent Algorithm ◽  
The Relationship ◽  
Main Strand ◽  
Yearly Data

AbstractAlthough the literature on the relationship between economic growth and CO2 emissions is extensive, the use of machine learning (ML) tools remains seminal. In this paper, we assess this nexus for Italy using innovative algorithms, with yearly data for the 1960–2017 period. We develop three distinct models: the batch gradient descent (BGD), the stochastic gradient descent (SGD), and the multilayer perceptron (MLP). Despite the phase of low Italian economic growth, results reveal that CO2 emissions increased in the predicting model. Compared to the observed statistical data, the algorithm shows a correlation between low growth and higher CO2 increase, which contradicts the main strand of literature. Based on this outcome, adequate policy recommendations are provided.

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