scholarly journals A Universal Approximation Theorem for Mixture-of-Experts Models

2016 ◽  
Vol 28 (12) ◽  
pp. 2585-2593 ◽  
Author(s):  
Hien D. Nguyen ◽  
Luke R. Lloyd-Jones ◽  
Geoffrey J. McLachlan
Keyword(s):  
Network Architecture ◽  
Approximation Theorem ◽  
Target Function ◽  
Continuous Functions ◽  
Universal Approximation ◽  
Mixture Of Experts ◽  
Neural Network Architecture ◽  
Alternative Result ◽  
Unit Hypercube ◽  
Uniformly Convergent

The mixture-of-experts (MoE) model is a popular neural network architecture for nonlinear regression and classification. The class of MoE mean functions is known to be uniformly convergent to any unknown target function, assuming that the target function is from a Sobolev space that is sufficiently differentiable and that the domain of estimation is a compact unit hypercube. We provide an alternative result, which shows that the class of MoE mean functions is dense in the class of all continuous functions over arbitrary compact domains of estimation. Our result can be viewed as a universal approximation theorem for MoE models. The theorem we present allows MoE users to be confident in applying such models for estimation when data arise from nonlinear and nondifferentiable generative processes.

SCORING MODELING BASED ON NEURAL NETWORKS FOR DETERMINING A BANK BORROWER'S RATING

2020 ◽  
Vol 2020 (10) ◽  
pp. 54-62
Author(s):  
Oleksii VASYLIEV ◽  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Statistical Data ◽  
Activation Function ◽  
Decision Making Process ◽  
Neural Network Architecture ◽  
Acceptable Accuracy ◽  
The Neural Network ◽  
Sigmoid Activation Function

The problem of applying neural networks to calculate ratings used in banking in the decision-making process on granting or not granting loans to borrowers is considered. The task is to determine the rating function of the borrower based on a set of statistical data on the effectiveness of loans provided by the bank. When constructing a regression model to calculate the rating function, it is necessary to know its general form. If so, the task is to calculate the parameters that are included in the expression for the rating function. In contrast to this approach, in the case of using neural networks, there is no need to specify the general form for the rating function. Instead, certain neural network architecture is chosen and parameters are calculated for it on the basis of statistical data. Importantly, the same neural network architecture can be used to process different sets of statistical data. The disadvantages of using neural networks include the need to calculate a large number of parameters. There is also no universal algorithm that would determine the optimal neural network architecture. As an example of the use of neural networks to determine the borrower's rating, a model system is considered, in which the borrower's rating is determined by a known non-analytical rating function. A neural network with two inner layers, which contain, respectively, three and two neurons and have a sigmoid activation function, is used for modeling. It is shown that the use of the neural network allows restoring the borrower's rating function with quite acceptable accuracy.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

scholarly journals Fighting Together against the Pandemic: Learning Multiple Models on Tomography Images for COVID-19 Diagnosis

AI ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 261-273
Author(s):  
Mario Manzo ◽  
Simone Pellino
Keyword(s):  
Network Architecture ◽  
State Of The Art ◽  
Ensemble Classification ◽  
Effective Vaccine ◽  
Rt Pcr ◽  
Neural Network Architecture ◽  
Experimental Phase ◽  
Different Types ◽  
Polymerase Chain ◽  
Better Than

COVID-19 has been a great challenge for humanity since the year 2020. The whole world has made a huge effort to find an effective vaccine in order to save those not yet infected. The alternative solution is early diagnosis, carried out through real-time polymerase chain reaction (RT-PCR) tests or thorax Computer Tomography (CT) scan images. Deep learning algorithms, specifically convolutional neural networks, represent a methodology for image analysis. They optimize the classification design task, which is essential for an automatic approach with different types of images, including medical. In this paper, we adopt a pretrained deep convolutional neural network architecture in order to diagnose COVID-19 disease from CT images. Our idea is inspired by what the whole of humanity is achieving, as the set of multiple contributions is better than any single one for the fight against the pandemic. First, we adapt, and subsequently retrain for our assumption, some neural architectures that have been adopted in other application domains. Secondly, we combine the knowledge extracted from images by the neural architectures in an ensemble classification context. Our experimental phase is performed on a CT image dataset, and the results obtained show the effectiveness of the proposed approach with respect to the state-of-the-art competitors.

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