Stochastic Optimization of Neural Networks and Implications for Biological Learning PDF Download

Author: Russell Wayne Anderson
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 220

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Author: Bruno Apolloni
Publisher: Springer Science & Business Media
ISBN: 1402034326
Category : Computers
Languages : en
Pages : 389

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The book reports the proceedings of the 15th Italian workshop on neural networks issued by the Italian Society on Neural Networks SIREN. The longevity recipe of this conference stands in three main points that normally renders the reading of these proceedings so interesting as appealing. 1. The topics of the neural networks is considered an attraction pole for a set of researches centered on the inherent paradigm of the neural networks, rather than on a specific tool exclusively. Thus, the subsymbolic management of the data information content constitutes the key feature of papers in various fields such as Pattern Recognition, Stochastic Optimization, Learning, Granular Computing, and so on, with a special bias toward bioinformatics operational applications. An excerpt of all these matters may be found in the book. 2. Though managed at domestic level, the conference attracts contributions from foreign researchers as well, so that in the book the reader may capture the flavor of the state of the art in the international community. 3. The conference is a meeting of friends as well. Thus the papers generally reflect a relaxed atmosphere where researchers meet to generously exchange their thought and explain their actual results in view of a common cultural growing of the community.

Author: Omid Omidvar
Publisher: Academic Press
ISBN: 9780125264204
Category : Business & Economics
Languages : en
Pages : 380

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Pulse-coupled neural networks; A neural network model for optical flow computation; Temporal pattern matching using an artificial neural network; Patterns of dynamic activity and timing in neural network processing; A macroscopic model of oscillation in ensembles of inhibitory and excitatory neurons; Finite state machines and recurrent neural networks: automata and dynamical systems approaches; biased random-waldk learning; a neurobiological correlate to trial-and-error; Using SONNET 1 to segment continuous sequences of items; On the use of high-level petri nets in the modeling of biological neural networks; Locally recurrent networks: the gmma operator, properties, and extensions.

Author:
Publisher:
ISBN:
Category : Artificial intelligence
Languages : en
Pages : 184

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Author: Jun Lu
Publisher: Eliva Press
ISBN: 9789994981557
Category :
Languages : en
Pages : 0

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The goal of this book is to debunk and dispel the magic behind the black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving from simple intuitions, the mathematics behind the strategies. This book doesn't shy away from addressing both the formal and informal aspects of gradient descent and stochastic optimization methods. By doing so, it hopes to provide readers with a deeper understanding of these techniques as well as the when, the how and the why of applying these algorithms. Gradient descent is one of the most popular algorithms to perform optimization and by far the most common way to optimize machine learning tasks. Its stochastic version receives attention in recent years, and this is particularly true for optimizing deep neural networks. In deep neural networks, the gradient followed by a single sample or a batch of samples is employed to save computational resources and escape from saddle points. In 1951, Robbins and Monro published A stochastic approximation method, one of the first modern treatments on stochastic optimization that estimates local gradients with a new batch of samples. And now, stochastic optimization has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this article is to give a self-contained introduction to concepts and mathematical tools in gradient descent and stochastic optimization.

Author: Wenjun Zhang
Publisher: World Scientific
ISBN: 9814282634
Category : Computers
Languages : en
Pages : 310

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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

Author: Riccardo Zoppoli
Publisher: Springer Nature
ISBN: 3030296938
Category : Technology & Engineering
Languages : en
Pages : 532

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Neural Approximations for Optimal Control and Decision provides a comprehensive methodology for the approximate solution of functional optimization problems using neural networks and other nonlinear approximators where the use of traditional optimal control tools is prohibited by complicating factors like non-Gaussian noise, strong nonlinearities, large dimension of state and control vectors, etc. Features of the text include: • a general functional optimization framework; • thorough illustration of recent theoretical insights into the approximate solutions of complex functional optimization problems; • comparison of classical and neural-network based methods of approximate solution; • bounds to the errors of approximate solutions; • solution algorithms for optimal control and decision in deterministic or stochastic environments with perfect or imperfect state measurements over a finite or infinite time horizon and with one decision maker or several; • applications of current interest: routing in communications networks, traffic control, water resource management, etc.; and • numerous, numerically detailed examples. The authors’ diverse backgrounds in systems and control theory, approximation theory, machine learning, and operations research lend the book a range of expertise and subject matter appealing to academics and graduate students in any of those disciplines together with computer science and other areas of engineering.

Author: Olivier Picard Jean Catoni
Publisher:
ISBN: 9783662203248
Category :
Languages : en
Pages : 292

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Author: Jing An
Publisher:
ISBN:
Category :
Languages : en
Pages :

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This dissertation consists of two independent parts: nonlinear analysis of biological models (Part I), and stochastic analysis of machine learning methods (Part II). In the first part, we investigate two nonlinear partial differential equations arising in biology. The first model we consider is the Euler alignment system, which is a hydrodynamics limit of the Cucker-Smale model describing the collective dynamics of a flock of $N$ individuals (birds, fish, etc.) that tend to align their velocities locally. We prove that, as long as the weakly singular interaction kernel is not integrable, the solutions of the Euler alignment system stay globally regular. This result extends the previous regularity results to the critical case. The second model we consider is the Burgers-FKPP equation, which is a reaction-diffusion equation equipped with an advection term of the Burgers type. The Burgers-FKPP equation appears in many applications from chemical physics to population genetics, but the large time behavior of its solutions is rarely studied. An interesting feature of Burgers-FKPP is that when the coefficient of the Burgers nonlinearity increases, the propagating solutions have a phase transition from pulled fronts to pushed fronts. In this work, we show the convergence of a solution to a single traveling wave in the Burgers-FKPP equation, as well as some side discoveries including front asymptotics in higher orders. In the second part, we study the several machine learning models from the stochastic analysis viewpoint. Taking the continuous-time limit and using approximate stochastic differential equations (SDE) to analyze stochastic gradients algorithms has become popular in recent years, since it provides many new insights and compact proofs using developed toolkits. We exhibit the power of stochastic analysis in machine learning from two independent projects. In the first project, we consider the asynchronous stochastic gradient descent (ASGD) algorithm that updates iterates with a delay read, which plays an important role in large scale parallel computing. We derive corresponding SDEs to characterize the dynamics of the ASGD algorithm. Based on that, we can further explore algorithmic properties by considering the temperature factors in Langevin type equations, as well as identifying optimal hyper-parameters by using optimal control theory. In the second project, we consider data, model, and stochastic optimization algorithms as an integrated system. On the one side, we focus on comparing resampling and reweighting for correcting sampling biases. On the other side, we propose a combined resampling and reweighting strategy to handle the data feature disparities. Both problems arise as the models are non-convex, and by SDE approaches we explain how stochastic gradient algorithms select the minimum in different regions.

Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 994

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