scholarly journals Optimal Randomness for Stochastic Configuration Network (SCN) with Heavy-Tailed Distributions

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 56
Author(s):  
Haoyu Niu ◽  
Jiamin Wei ◽  
YangQuan Chen
Keyword(s):  
Research Work ◽  
Cauchy Distribution ◽  
Classification Model ◽  
Test Accuracy ◽  
Functional Link ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Improved Performance ◽  
Hidden Layer ◽  
Hidden Nodes

Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for single hidden layer feed-forward neural networks, such as Randomized Radial Basis Function (RBF) Networks and Random Vector Functional-link (RVFL), the SCN randomly assigns the input weights and biases of the hidden nodes in a supervisory mechanism. Since the parameters in the hidden layers are randomly generated in uniform distribution, hypothetically, there is optimal randomness. Heavy-tailed distribution has shown optimal randomness in an unknown environment for finding some targets. Therefore, in this research, the authors used heavy-tailed distributions to randomly initialize weights and biases to see if the new SCN models can achieve better performance than the original SCN. Heavy-tailed distributions, such as Lévy distribution, Cauchy distribution, and Weibull distribution, have been used. Since some mixed distributions show heavy-tailed properties, the mixed Gaussian and Laplace distributions were also studied in this research work. Experimental results showed improved performance for SCN with heavy-tailed distributions. For the regression model, SCN-Lévy, SCN-Mixture, SCN-Cauchy, and SCN-Weibull used less hidden nodes to achieve similar performance with SCN. For the classification model, SCN-Mixture, SCN-Lévy, and SCN-Cauchy have higher test accuracy of 91.5%, 91.7% and 92.4%, respectively. Both are higher than the test accuracy of the original SCN.

scholarly journals Means as Improper Integrals

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 284
Author(s):  
John Gray ◽  
Andrew Vogt
Keyword(s):  
Law Of Large Numbers ◽  
Cauchy Distribution ◽  
Cumulative Distribution ◽  
Tail Probabilities ◽  
Strong Law ◽  
Improper Integral ◽  
Heavy Tailed Distributions ◽  
Large Numbers ◽  
The Mean ◽  
Heavy Tailed

The aim of this work is to study generalizations of the notion of the mean. Kolmogorov proposed a generalization based on an improper integral with a decay rate for the tail probabilities. This weak or Kolmogorov mean relates to the weak law of large numbers in the same way that the ordinary mean relates to the strong law. We propose a further generalization, also based on an improper integral, called the doubly-weak mean, applicable to heavy-tailed distributions such as the Cauchy distribution and the other symmetric stable distributions. We also consider generalizations arising from Abel–Feynman-type mollifiers that damp the behavior at infinity and alternative formulations of the mean in terms of the cumulative distribution and the characteristic function.

scholarly journals Means as Improper Integrals

2019 ◽  
Author(s):  
John E. Gray ◽  
Andrew Vogt
Keyword(s):  
Law Of Large Numbers ◽  
Cauchy Distribution ◽  
Cumulative Distribution ◽  
Tail Probabilities ◽  
Strong Law ◽  
Improper Integral ◽  
Heavy Tailed Distributions ◽  
Large Numbers ◽  
The Mean ◽  
Heavy Tailed

The aim of this work is to study generalizations of the notion of mean. Kolmogorov proposed a generalization based on an improper integral with a decay rate for the tail probabilities. This weak or Kolmogorov mean relates to the Weak Law of Large Numbers in the same way that the ordinary mean relates to the Strong Law. We propose a further generalization, also based on an improper integral, called the doubly weak mean, applicable to heavy-tailed distributions such as the Cauchy distribution and the other symmetric stable distributions, We also consider generalizations arising from Abel-Feynman type mollifiers that damp the behavior at infinity and alternative formulations of the mean in terms of the cumulative distribution and the characteristic function.

Probability and Random Processes

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Random Processes ◽  
Distribution Functions ◽  
Basic Logic ◽  
Heavy Tailed Distributions ◽  
Random Components ◽  
Classical Distribution ◽  
Heavy Tailed ◽  
Basic Facts ◽  
Stochastic Events ◽  
Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

scholarly journals AI-based localization and classification of skin disease with erythema

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ha Min Son ◽  
Wooho Jeon ◽  
Jinhyun Kim ◽  
Chan Yeong Heo ◽  
Hye Jin Yoon ◽  
...  
Keyword(s):  
Neural Network ◽  
Skin Diseases ◽  
Classification Model ◽  
Screening Tests ◽  
Sensitivity Score ◽  
Common Skin ◽  
Novel Method ◽  
Improved Performance ◽  
High Level

AbstractAlthough computer-aided diagnosis (CAD) is used to improve the quality of diagnosis in various medical fields such as mammography and colonography, it is not used in dermatology, where noninvasive screening tests are performed only with the naked eye, and avoidable inaccuracies may exist. This study shows that CAD may also be a viable option in dermatology by presenting a novel method to sequentially combine accurate segmentation and classification models. Given an image of the skin, we decompose the image to normalize and extract high-level features. Using a neural network-based segmentation model to create a segmented map of the image, we then cluster sections of abnormal skin and pass this information to a classification model. We classify each cluster into different common skin diseases using another neural network model. Our segmentation model achieves better performance compared to previous studies, and also achieves a near-perfect sensitivity score in unfavorable conditions. Our classification model is more accurate than a baseline model trained without segmentation, while also being able to classify multiple diseases within a single image. This improved performance may be sufficient to use CAD in the field of dermatology.

Breast cancer diagnosis using multiple activation deep neural network

2021 ◽  
pp. 1063293X2110251
Author(s):  
K Vijayakumar ◽  
Vinod J Kadam ◽  
Sudhir Kumar Sharma
Keyword(s):  
Breast Cancer ◽  
Neural Network ◽  
Deep Neural Network ◽  
Breast Cancer Diagnosis ◽  
Activation Function ◽  
Linear Functions ◽  
Cancer Data ◽  
Final Layer ◽  
Improved Performance ◽  
Hidden Layer

Deep Neural Network (DNN) stands for multilayered Neural Network (NN) that is capable of progressively learn the more abstract and composite representations of the raw features of the input data received, with no need for any feature engineering. They are advanced NNs having repetitious hidden layers between the initial input and the final layer. The working principle of such a standard deep classifier is based on a hierarchy formed by the composition of linear functions and a defined nonlinear Activation Function (AF). It remains uncertain (not clear) how the DNN classifier can function so well. But it is clear from many studies that within DNN, the AF choice has a notable impact on the kinetics of training and the success of tasks. In the past few years, different AFs have been formulated. The choice of AF is still an area of active study. Hence, in this study, a novel deep Feed forward NN model with four AFs has been proposed for breast cancer classification: hidden layer 1: Swish, hidden layer, 2:-LeakyReLU, hidden layer 3: ReLU, and final output layer: naturally Sigmoidal. The purpose of the study is twofold. Firstly, this study is a step toward a more profound understanding of DNN with layer-wise different AFs. Secondly, research is also aimed to explore better DNN-based systems to build predictive models for breast cancer data with improved accuracy. Therefore, the benchmark UCI dataset WDBC was used for the validation of the framework and evaluated using a ten-fold CV method and various performance indicators. Multiple simulations and outcomes of the experimentations have shown that the proposed solution performs in a better way than the Sigmoid, ReLU, and LeakyReLU and Swish activation DNN in terms of different parameters. This analysis contributes to producing an expert and precise clinical dataset classification method for breast cancer. Furthermore, the model also achieved improved performance compared to many established state-of-the-art algorithms/models.

scholarly journals A Method for Confidence Intervals of High Quantiles

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 70
Author(s):  
Mei Ling Huang ◽  
Xiang Raney-Yan
Keyword(s):  
Confidence Intervals ◽  
Computational Algorithm ◽  
Geometric Mean ◽  
Asymptotic Properties ◽  
Quantile Estimation ◽  
Heavy Tailed Distributions ◽  
High Quantiles ◽  
High Quantile ◽  
Heavy Tailed ◽  
Infinite Moments

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

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