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Robust optimization of spline models and complex regulatory networks : theory, methods and applications
This book introduces methods of robust optimization in multivariate adaptive regression splines (MARS) and Conic MARS in order to handle uncertainty and non-linearity. The proposed techniques are implemented and explained in two-model regulatory systems that can be found in the financial sector and in the contexts of banking, environmental protection, system biology and medicine. The book provides necessary background information on multi-model regulatory networks, optimization and regression. It presents the theory of and approaches to robust (conic) multivariate adaptive regression splines - R(C)MARS - and robust (conic) generalized partial linear models - R(C)GPLM - under polyhedral uncertainty. Further, it introduces spline regression models for multi-model regulatory networks and interprets (C)MARS results based on different datasets for the implementation. It explains robust optimization in these models in terms of both the theory and methodology. In this context it studies R(C)MARS results with different uncertainty scenarios for a numerical example. Lastly, the book demonstrates the implementation of the method in a number of applications from the financial, energy, and environmental sectors, and provides an outlook on future research.
Book
A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems
ranging from image classification/image recognition, speech recognition, time series analysis, game intelligence, and computational
advertising to numerical approximations of partial differential equations (PDEs). Such numerical simulations suggest that ANNs have the
capacity to very efficiently approximate high-dimensional functions and, especially, indicate that ANNs seem to admit the fundamental
power to overcome the curse of dimensionality when approximating the high-dimensional functions appearing in the above named
computational problems. There are a series of rigorous mathematical approximation results for ANNs in the scientific literature. Some of
them prove convergence without convergence rates and some of these mathematical results even rigorously establish convergence rates but
there are only a few special cases where mathematical results can rigorously explain the empirical success of ANNs when approximating
high-dimensional functions. The key contribution of this article is to disclose that ANNs can efficiently approximate high-dimensional
functions in the case of numerical approximations of Black-Scholes PDEs. More precisely, this work reveals that the number of required
parameters of an ANN to approximate the solution of the Black-Scholes PDE grows at most polynomially in both the reciprocal of the
prescribed approximation accuracy
eBook
A guide to convolutional neural networks for computer vision
Computer vision has become increasingly important and effective in recent years due to its wide-ranging applications in areas as diverse as smart surveillance and monitoring, health and medicine, sports and recreation, robotics, drones, and self-driving cars. Visual recognition tasks, such as image classification, localization, and detection, are the core building blocks of many of these applications, and recent developments in Convolutional Neural Networks (CNNs) have led to outstanding performance in these state-of-the-art visual recognition tasks and systems. As a result, CNNs now form the crux of deep learning algorithms in computer vision. This self-contained guide will benefit those who seek to both understand the theory behind CNNs and to gain hands-on experience on the application of CNNs in computer vision. It provides a comprehensive introduction to CNNs starting with the essential concepts behind neural networks: training, regularization, and optimization of CNNs. The book also discusses a wide range of loss functions, network layers, and popular CNN architectures, reviews the different techniques for the evaluation of CNNs, and presents some popular CNN tools and libraries that are commonly used in computer vision. Further, this text describes and discusses case studies that are related to the application of CNN in computer vision, including image classification, object detection, semantic segmentation, scene understanding, and image generation. This book is ideal for undergraduate and graduate students, as no prior background knowledge in the field is required to follow the material, as well as new researchers, developers, engineers, and practitioners who are interested in gaining a quick understanding of CNN models.
Book
A modified Adam algorithm for deep neural network optimization
Deep Neural Networks (DNNs) are widely regarded as the most effective learning tool for dealing with large datasets, and they have been successfully used in thousands of applications in a variety of fields. Based on these large datasets, they are trained to learn the relationships between various variables. The adaptive moment estimation (Adam) algorithm, a highly efficient adaptive optimization algorithm, is widely used as a learning algorithm in various fields for training DNN models. However, it needs to improve its generalization performance, especially when training with large-scale datasets. Therefore, in this paper, we propose HN Adam, a modified version of the Adam Algorithm, to improve its accuracy and convergence speed. The HN_Adam algorithm is modified by automatically adjusting the step size of the parameter updates over the training epochs. This automatic adjustment is based on the norm value of the parameter update formula according to the gradient values obtained during the training epochs. Furthermore, a hybrid mechanism was created by combining the standard Adam algorithm and the AMSGrad algorithm. As a result of these changes, the HN_Adam algorithm, like the stochastic gradient descent (SGD) algorithm, has good generalization performance and achieves fast convergence like other adaptive algorithms. To test the proposed HN_Adam algorithm performance, it is evaluated to train a deep convolutional neural network (CNN) model that classifies images using two different standard datasets: MNIST and CIFAR-10. The algorithm results are compared to the basic Adam algorithm and the SGD algorithm, in addition to other five recent SGD adaptive algorithms. In most comparisons, the HN Adam algorithm outperforms the compared algorithms in terms of accuracy and convergence speed. AdaBelief is the most competitive of the compared algorithms. In terms of testing accuracy and convergence speed (represented by the consumed training time), the HN-Adam algorithm outperforms the AdaBelief algorithm by an improvement of 1.0% and 0.29% for the MNIST dataset, and 0.93% and 1.68% for the CIFAR-10 dataset, respectively.
Journal Article
Artificial higher order neural networks for economics and business
\"This book is the first book to provide opportunities for millions working in economics, accounting, finance and other business areas education on HONNs, the ease of their usage, and directions on how to obtain more accurate application results. It provides significant, informative advancements in the subject and introduces the HONN group models and adaptive HONNs\"--Provided by publisher.
Book
Optimizing connection weights in neural networks using the whale optimization algorithm
The learning process of artificial neural networks is considered as one of the most difficult challenges in machine learning and has attracted many researchers recently. The main difficulty of training a neural network is the nonlinear nature and the unknown best set of main controlling parameters (weights and biases). The main disadvantages of the conventional training algorithms are local optima stagnation and slow convergence speed. This makes stochastic optimization algorithm reliable alternative to alleviate these drawbacks. This work proposes a new training algorithm based on the recently proposed whale optimization algorithm (WOA). It has been proved that this algorithm is able to solve a wide range of optimization problems and outperform the current algorithms. This motivated our attempts to benchmark its performance in training feedforward neural networks. For the first time in the literature, a set of 20 datasets with different levels of difficulty are chosen to test the proposed WOA-based trainer. The results are verified by comparisons with back-propagation algorithm and six evolutionary techniques. The qualitative and quantitative results prove that the proposed trainer is able to outperform the current algorithms on the majority of datasets in terms of both local optima avoidance and convergence speed.
Journal Article
Quantum machine learning for image classification
Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.
Journal Article
Analysis of Explainers of Black Box Deep Neural Networks for Computer Vision: A Survey
Deep Learning is a state-of-the-art technique to make inference on extensive or complex data. As a black box model due to their multilayer nonlinear structure, Deep Neural Networks are often criticized as being non-transparent and their predictions not traceable by humans. Furthermore, the models learn from artificially generated datasets, which often do not reflect reality. By basing decision-making algorithms on Deep Neural Networks, prejudice and unfairness may be promoted unknowingly due to a lack of transparency. Hence, several so-called explanators, or explainers, have been developed. Explainers try to give insight into the inner structure of machine learning black boxes by analyzing the connection between the input and output. In this survey, we present the mechanisms and properties of explaining systems for Deep Neural Networks for Computer Vision tasks. We give a comprehensive overview about the taxonomy of related studies and compare several survey papers that deal with explainability in general. We work out the drawbacks and gaps and summarize further research ideas.
Journal Article
A survey on Image Data Augmentation for Deep Learning
Deep convolutional neural networks have performed remarkably well on many Computer Vision tasks. However, these networks are heavily reliant on big data to avoid overfitting. Overfitting refers to the phenomenon when a network learns a function with very high variance such as to perfectly model the training data. Unfortunately, many application domains do not have access to big data, such as medical image analysis. This survey focuses on Data Augmentation, a data-space solution to the problem of limited data. Data Augmentation encompasses a suite of techniques that enhance the size and quality of training datasets such that better Deep Learning models can be built using them. The image augmentation algorithms discussed in this survey include geometric transformations, color space augmentations, kernel filters, mixing images, random erasing, feature space augmentation, adversarial training, generative adversarial networks, neural style transfer, and meta-learning. The application of augmentation methods based on GANs are heavily covered in this survey. In addition to augmentation techniques, this paper will briefly discuss other characteristics of Data Augmentation such as test-time augmentation, resolution impact, final dataset size, and curriculum learning. This survey will present existing methods for Data Augmentation, promising developments, and meta-level decisions for implementing Data Augmentation. Readers will understand how Data Augmentation can improve the performance of their models and expand limited datasets to take advantage of the capabilities of big data.
Journal Article
Temporal convolutional neural (TCN) network for an effective weather forecasting using time-series data from the local weather station
Non-predictive or inaccurate weather forecasting can severely impact the community of users such as farmers. Numerical weather prediction models run in major weather forecasting centers with several supercomputers to solve simultaneous complex nonlinear mathematical equations. Such models provide the medium-range weather forecasts, i.e., every 6 h up to 18 h with grid length of 10–20 km. However, farmers often depend on more detailed short-to medium-range forecasts with higher-resolution regional forecasting models. Therefore, this research aims to address this by developing and evaluating a lightweight and novel weather forecasting system, which consists of one or more local weather stations and state-of-the-art machine learning techniques for weather forecasting using time-series data from these weather stations. To this end, the system explores the state-of-the-art temporal convolutional network (TCN) and long short-term memory (LSTM) networks. Our experimental results show that the proposed model using TCN produces better forecasting compared to the LSTM and other classic machine learning approaches. The proposed model can be used as an efficient localized weather forecasting tool for the community of users, and it could be run on a stand-alone personal computer.
Journal Article