Download or read book Training Hierarchical Networks for Function Approximation written by Brando Miranda (M. Eng.) and published by . This book was released on 2016 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work we investigate function approximation using Hierarchical Networks. We start of by investigating the theory proposed by Poggio et al [2] that Deep Learning Convolutional Neural Networks (DCN) can be equivalent to hierarchical kernel machines with the Radial Basis Functions (RBF).We investigate the difficulty of training RBF networks with stochastic gradient descent (SGD) and hierarchical RBF. We discovered that training singled layered RBF networks can be quite simple with a good initialization and good choice of standard deviation for the Gaussian. Training hierarchical RBFs remains as an open question, however, we clearly identified the issue surrounding training hierarchical RBFs and potential methods to resolve this. We also compare standard DCN networks to hierarchical Radial Basis Functions in tasks that has not been explored yet; the role of depth in learning compositional functions.

Download or read book Multivariate Statistical Machine Learning Methods for Genomic Prediction written by Osval Antonio Montesinos López and published by Springer Nature. This book was released on 2022-02-14 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.

Download or read book Function Approximation Guarantees for a Shallow Neural Network Trained by Gradient Flow written by Russell Gentile and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work features an original result linking approximation and optimization theory for deep learning. Several examples from recent literature show that, given the same number of learnable parameters, deep neural networks can approximate richer classes of functions, with better accuracy than classical methods. The bulk of approximation theory results though, are only concerned with the infimum error for all possible parameterizations of a given network size. Their proofs often rely on hand-crafted networks, where the weights and biases are carefully selected. Optimization theory indicates that such models would be difficult or impossible to realize with standard gradient-based training methods. The main result of this thesis proves that, for a single-layer neural network having m parameters, a conservative approximation rate, O(m−1/4), is achieved with gradient flow training on univariate functions. This is especially noteworthy since we make no assumption of overparameterization, as is typically done with neural tangent kernel (NTK) techniques. The proof relies on an assumption that the H1-norm of the residual error throughout the training process is uniformly bounded. This assumption is justified by numerical experiments which also show that rates beyond 1/4 are achieved in practice, indicating that a sharper theoretical result is most likely possible. Future work will focus on proving that the bounded H1 assumption is not needed and that variations of our main result can also be applied to multi-dimensional cases and deep networks.

Download or read book Function Approximation and Learning by Neural Networks written by Bhaskar DasGupta (Writer on neural networks) and published by . This book was released on 1994 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Hierarchical Algorithm for Neural Training and Control Revision written by and published by . This book was released on 1992 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lately, there has been an extensive interest in the possible uses of neural networks for nonlinear system identification and control. In this paper, we provide a framework for the simultaneous identification and control of a class of unknown, uncertain nonlinear systems. The identification portion relies on modeling the system by a neural network which is trained via a local variant of the Extended Kalman Filter. We will discuss this local algorithm for training a neural network to approximate a nonlinear feedback system. We also give a dynamic programming-based method of deriving near optimal control inputs for the real plant based on this approximation and a measure of its error (covariance). Finally, we combine these methods in a hierarchical algorithm for identification and control of a class of uncertain, unknown systems. The complexity of the whole algorithm is analyzed.

Download or read book Neural Networks for Localized Function Approximation written by and published by . This book was released on 1996 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: We studied the complexity problem for neural network used in function approximation; i.e., the problem of estimating the number of neurons needed to provide a given accuracy of approximation for any function, unknown except for a few a priori assumptions. We developed a unified theory, applicable to the traditional neural networks, radial basis function networks, and generalized regularization networks. While our main objective was to provide a solid theoretical foundation for the subject, we have also developed new training paradigms, where no optimization based technique such as back-propagation is required. Thus, the training of our networks is very simple and entirely free of all the traditional shortcomings, such as local minima. Our ideas were tested to develop neural networks for prediction of time series, and beamforming in phased array antennas. In both cases, we obtained spectacular improvements over previously known results. Our work has resulted in 14 publications. In addition, the grant has facilitated the completion of our book on weighted approximation as well as the fulfillment of our obligations as an invited guest editor for a special issue of Advances in Computational Mathematics on Mathematical Aspects of Neural Networks.

Download or read book Advances in Soft Computing written by Obdulia Pichardo-Lagunas and published by Springer. This book was released on 2017-08-01 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNAI 10061 and 10062 constitutes the proceedings of the 15th Mexican International Conference on Artificial Intelligence, MICAI 2016, held in Cancún, Mexico, in October 2016. The total of 86 papers presented in these two volumes was carefully reviewed and selected from 238 submissions. The contributions were organized in the following topical sections: Part I: natural language processing; social networks and opinion mining; fuzzy logic; time series analysis and forecasting; planning and scheduling; image processing and computer vision; robotics. Part II: general; reasoning and multi-agent systems; neural networks and deep learning; evolutionary algorithms; machine learning; classification and clustering; optimization; data mining; graph-based algorithms; and intelligent learning environments.

Download or read book Handbook of Learning and Approximate Dynamic Programming written by Jennie Si and published by John Wiley & Sons. This book was released on 2004-08-02 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete resource to Approximate Dynamic Programming (ADP), including on-line simulation code Provides a tutorial that readers can use to start implementing the learning algorithms provided in the book Includes ideas, directions, and recent results on current research issues and addresses applications where ADP has been successfully implemented The contributors are leading researchers in the field

Download or read book Computational Ecology written by Wenjun Zhang and published by World Scientific. This book was released on 2010 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ch. 1. Introduction. 1. Computational ecology. 2. Artificial neural networks and ecological applications -- pt. I. Artificial neural networks : principles, theories and algorithms. ch. 2. Feedforward neural networks. 1. Linear separability and perceptron. 2. Some analogies of multilayer feedforward networks. 3. Functionability of multilayer feedforward networks. ch. 3. Linear neural networks. 1. Linear neural networks. 2. LMS rule. ch. 4. Radial basis function neural networks. 1. Theory of RBF neural network. 2. Regularized RBF neural network. 3. RBF neural network learning. 4. Probabilistic neural network. 5. Generalized regression neural network. 6. Functional link neural network. 7. Wavelet neural network. ch. 5. BP neural network. 1. BP algorithm. 2. BP theorem. 3. BP training. 4. Limitations and improvements of BP algorithm. ch. 6. Self-organizing neural networks. 1. Self-organizing feature map neural network. 2. Self-organizing competitive learning neural network. 3. Hamming neural network. 4. WTA neural network. 5. LVQ neural network. 6. Adaptive resonance theory. ch. 7. Feedback neural networks. 1. Elman neural network. 2. Hopfield neural networks. 3. Simulated annealing. 4. Boltzmann machine. ch. 8. Design and customization of artificial neural networks. 1. Mixture of experts. 2. Hierarchical mixture of experts. 3. Neural network controller. 4. Customization of neural networks. ch. 9. Learning theory, architecture choice and interpretability of neural networks. 1. Learning theory. 2. Architecture choice. 3. Interpretability of neural networks. ch. 10. Mathematical foundations of artificial neural networks. 1. Bayesian methods. 2. Randomization, bootstrap and Monte Carlo techniques. 3. Stochastic process and stochastic differential equation. 4. Interpolation. 5. Function approximation. 6. Optimization methods. 7. Manifold and differential geometry. 8. Functional analysis. 9. Algebraic topology. 10. Motion stability. 11. Entropy of a system. 12. Distance or similarity measures. ch. 11. Matlab neural network toolkit. 1. Functions of perceptron. 2. Functions of linear neural networks. 3. Functions of BP neural network. 4. Functions of self-organizing neural networks. 5. Functions of radial basis neural networks. 6. Functions of probabilistic neural network. 7. Function of generalized regression neural network. 8. Functions of Hopfield neural network. 9. Function of Elman neural network -- pt. II. Applications of artificial neural networks in ecology. ch. 12. Dynamic modeling of survival process. 1. Model description. 2. Data description. 3. Results. 4. Discussion. ch. 13. Simulation of plant growth process. 1. Model description. 2. Data source. 3. Results. 4. Discussion. ch. 14. Simulation of food intake dynamics. 1. Model description. 2. Data description. 3. Results. 4. Discussion. ch. 15. Species richness estimation and sampling data documentation. 1. Estimation of plant species richness on grassland. 2. Documentation of sampling data of invertebrates. ch. 16. Modeling arthropod abundance from plant composition of grassland community. 1. Model description. 2. Data description. 3. Results. 4. Discussion. ch. 17. Pattern recognition and classification of ecosystems and functional groups. 1. Model description. 2. Data source. 3. Results. 4. Discussion. ch. 18. Modeling spatial distribution of arthropods. 1. Model description. 2. Data description. 3. Results. 4. Discussion. ch. 19. Risk assessment of species invasion and establishment. 1. Invasion risk assessment based on species assemblages. 2. Determination of abiotic factors influencing species invasion. ch. 20. Prediction of surface ozone. 1. BP prediction of daily total ozone. 2. MLP Prediction of hourly ozone levels. ch. 21. Modeling dispersion and distribution of oxide and nitrate pollutants. 1. Modeling nitrogen dioxide dispersion. 2. Simulation of nitrate distribution in ground water. ch. 22. Modeling terrestrial biomass. 1. Estimation of aboveground grassland biomass. 2. Estimation of trout biomass

Download or read book Hierarchical Neural Networks for Image Interpretation written by Sven Behnke and published by Springer. This book was released on 2003-11-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Human performance in visual perception by far exceeds the performance of contemporary computer vision systems. While humans are able to perceive their environment almost instantly and reliably under a wide range of conditions, computer vision systems work well only under controlled conditions in limited domains. This book sets out to reproduce the robustness and speed of human perception by proposing a hierarchical neural network architecture for iterative image interpretation. The proposed architecture can be trained using unsupervised and supervised learning techniques. Applications of the proposed architecture are illustrated using small networks. Furthermore, several larger networks were trained to perform various nontrivial computer vision tasks.

Download or read book Introduction to Deep Learning A Beginner s Edition written by Harshitha Raghavan Devarajan and published by INENCE PUBLICATIONS PVT LTD. This book was released on 2024-08-10 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Introduction to Deep Learning: A Beginner’s Edition" is a comprehensive guide designed specifically for newcomers to the field of deep learning. This book provides an accessible introduction to the fundamental concepts, making it an ideal starting point for those who are curious about artificial intelligence and its rapidly expanding applications. The book begins with a clear explanation of what deep learning is and how it differs from traditional machine learning, covering the basics of neural networks and how they are used to recognize patterns and make decisions. One of the key strengths of this book is its practical, hands-on approach. Readers are guided through the process of building, training, and deploying neural networks using popular frameworks like TensorFlow and PyTorch. The step-by-step instructions, along with code snippets, allow even those with little to no programming experience to engage actively with the material. Visual aids, such as diagrams and flowcharts, are used throughout the book to simplify complex topics, making it easier for readers to grasp the inner workings of neural networks. The book also explores real-world applications of deep learning, highlighting its impact across various industries, including healthcare, autonomous vehicles, and natural language processing. By providing context and practical examples, the book demonstrates how deep learning is being used to solve complex problems and transform industries. In addition to the core content, the book includes a glossary of key terms, quizzes, and exercises to reinforce learning. "Introduction to Deep Learning: A Beginner’s Edition" is more than just a textbook; it is a complete learning experience designed to equip beginners with the knowledge and skills needed to embark on a successful journey into the world of deep learning.

Download or read book Multi Scale Approaches to Continuum Approximations to Many Particle Systems and Loss Functions for Neural Networks written by Robert Creese and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems of interacting particles lead to interesting phenomena such as fish forming schools, flocks of birds, and ants marching in a line. In addition machine learning is a quickly growing field in which mathematics can be applied to the new concepts developed as well as used to create new branches. Both of these topics have seen the use of mathematics and modeling to explain the behavior of systems in both topics. In this dissertation we begin by studying a system of interacting particles with random initial conditions. We then consider continuum approximations of the system, based on truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy, including the Mean Field Approximation (MFA), the Kirkwood Superposition Approximation (KSA), and a recently developed truncation of the BBGKY hierarchy (the Truncation Approximation - TA). Comparing numerical approaches for approximating the solutions we show that TA is more computationally efficient and more stable than KSA, while still able to capture the effects of correlations. The next thrust of this work focus on the classification problem in machine learning. A novel two-scale loss function is proposed to train neural networks. The introduced method is compatible not only with any gradient descent method, but for a wide variety of algorithms including traditional feed-forward neural networks as well as recurrent neural networks and including support vector machines. This two-scale loss function focuses the training of the neural network onto objects which are not well classified. We demonstrate that this leads to an increase for several measures of performance when compared to a traditional single-scale cross-entropy loss on the MNIST, CIFAR10, and CIFAR100 data-sets.

Download or read book Modern Analysis of Customer Surveys written by Ron S. Kenett and published by John Wiley & Sons. This book was released on 2012-01-30 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Customer survey studies deals with customers, consumers and user satisfaction from a product or service. In practice, many of the customer surveys conducted by business and industry are analyzed in a very simple way, without using models or statistical methods. Typical reports include descriptive statistics and basic graphical displays. As demonstrated in this book, integrating such basic analysis with more advanced tools, provides insights on non-obvious patterns and important relationships between the survey variables. This knowledge can significantly affect the conclusions derived from a survey. Key features: Provides an integrated, case-studies based approach to analysing customer survey data. Presents a general introduction to customer surveys, within an organization’s business cycle. Contains classical techniques with modern and non standard tools. Focuses on probabilistic techniques from the area of statistics/data analysis and covers all major recent developments. Accompanied by a supporting website containing datasets and R scripts. Customer survey specialists, quality managers and market researchers will benefit from this book as well as specialists in marketing, data mining and business intelligence fields.

Download or read book Neural Networks and Statistical Learning written by Ke-Lin Du and published by Springer Nature. This book was released on 2019-09-12 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad yet detailed introduction to neural networks and machine learning in a statistical framework. A single, comprehensive resource for study and further research, it explores the major popular neural network models and statistical learning approaches with examples and exercises and allows readers to gain a practical working understanding of the content. This updated new edition presents recently published results and includes six new chapters that correspond to the recent advances in computational learning theory, sparse coding, deep learning, big data and cloud computing. Each chapter features state-of-the-art descriptions and significant research findings. The topics covered include: • multilayer perceptron; • the Hopfield network; • associative memory models;• clustering models and algorithms; • t he radial basis function network; • recurrent neural networks; • nonnegative matrix factorization; • independent component analysis; •probabilistic and Bayesian networks; and • fuzzy sets and logic. Focusing on the prominent accomplishments and their practical aspects, this book provides academic and technical staff, as well as graduate students and researchers with a solid foundation and comprehensive reference on the fields of neural networks, pattern recognition, signal processing, and machine learning.

Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

Download or read book Computational Methods for the Innovative Design of Electrical Devices written by Slawomir Wiak and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Methods for the Innovative Design of Electrical Devices is entirely focused on the optimal design of various classes of electrical devices. Emerging new methods, like e.g. those based on genetic algorithms, are presented and applied in the design optimization of different devices and systems. Accordingly, the solution to field analysis problems is based on the use of finite element method, and analytical methods as well. An original aspect of the book is the broad spectrum of applications in the area of electrical engineering, especially electrical machines. This way, traditional design criteria of conventional devices are revisited in a critical way, and some innovative solutions are suggested. In particular, the optimization procedures developed are oriented to three main aspects: shape design, material properties identification, machine optimal behaviour. Topics covered include: • New parallel finite-element solvers • Response surface method • Evolutionary computing • Multiobjective optimization • Swarm intelligence • MEMS applications • Identification of magnetic properties of anisotropic laminations • Neural networks for non-destructive testing • Brushless DC motors, transformers • Permanent magnet disc motors, magnetic separators • Magnetic levitation systems

Download or read book Hierarchical Control and Learning for Markov Decision Processes written by Ronald Edward Parr and published by . This book was released on 1998 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: