The Experts below are selected from a list of 4338 Experts worldwide ranked by ideXlab platform

Roderick Edwards - One of the best experts on this subject based on the ideXlab platform.

  • Universal approximation results for the temporal restricted Boltzmann machine and the recurrent temporal restricted Boltzmann machine
    Journal of Machine Learning Research, 2016
    Co-Authors: Simon Odense, Roderick Edwards
    Abstract:

    The Restricted Boltzmann Machine (RBM) has proved to be a powerful tool in machine learning, both on its own and as the building block for Deep Belief Networks (multi-layer generative graphical models). The RBM and Deep Belief Network have been shown to be universal Approximators for probability distributions on binary vectors. In this paper we prove several similar universal approximation results for two variations of the Restricted Boltzmann Machine with time dependence, the Temporal Restricted Boltzmann Machine (TRBM) and the Recurrent Temporal Restricted Boltzmann Machine (RTRBM). We show that the TRBM is a universal approximator for Markov chains and generalize the theorem to sequences with longer time dependence. We then prove that the RTRBM is a universal approximator for stochastic processes with _nite time dependence. We conclude with a discussion on efficiency and how the constructions developed could explain some previous experimental results.

Corrado Possieri - One of the best experts on this subject based on the ideXlab platform.

  • A Universal Approximation Result for Difference of Log-Sum-Exp Neural Networks
    IEEE Transactions on Neural Networks and Learning Systems, 2026
    Co-Authors: Giuseppe C. Calafiore, Stephane Gaubert, Corrado Possieri
    Abstract:

    We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation function in the output node, referred to as log-sum-exp (LSE) network, is a smooth universal approximator of continuous functions over convex, compact sets. By using a logarithmic transform, this class of network maps to a family of subtraction-free ratios of generalized posynomials (GPOS), which we also show to be universal Approximators of positive functions over log-convex, compact subsets of the positive orthant. The main advantage of difference-LSE networks with respect to classical feedforward neural networks is that, after a standard training phase, they provide surrogate models for a design that possesses a specific difference-of-convex-functions form, which makes them optimizable via relatively efficient numerical methods. In particular, by adapting an existing difference-of-convex algorithm to these models, we obtain an algorithm for performing an effective optimization-based design. We illustrate the proposed approach by applying it to the data-driven design of a diet for a patient with type-2 diabetes and to a nonconvex optimization problem.

Li-xin Wang - One of the best experts on this subject based on the ideXlab platform.

Tao Zhao - One of the best experts on this subject based on the ideXlab platform.

  • observer based dynamic surface control for flexible joint manipulator system with input saturation and unknown disturbance using type 2 fuzzy neural network
    Neurocomputing, 2021
    Co-Authors: Songyi Dian, Rui Guo, Tao Zhao
    Abstract:

    Abstract In this paper, the nonlinear disturbance observer (NDO) based dynamic surface control (DSC) with interval type-2 fuzzy neural network (IT2FNN) approximator is proposed for flexible-joint manipulator with the input saturation and unknown nonlinear disturbance. The DSC technique has tremendous advantages in eliminating the ’explosion of complexity’ problem. The IT2FNN approximator is used to deal with parameter uncertainties. The NDO is applied to estimate the unknown external disturbance and compensate the saturation constrain. From Lyapunov stability analysis, it is proved that with the proposed control scheme, all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Simulation results are carried out to demonstrate the effectiveness of the proposed scheme. Compared with the adaptive DSC with neural network (NN) approximator and type-1 fuzzy (T1F) approximator, the tracking error of the proposed control scheme converges to a sufficiently small value.

John N Tsitsiklis - One of the best experts on this subject based on the ideXlab platform.

  • an analysis of temporal difference learning with function approximation
    IEEE Transactions on Automatic Control, 1997
    Co-Authors: John N Tsitsiklis
    Abstract:

    We discuss the temporal-difference learning algorithm, as applied to approximating the cost-to-go function of an infinite-horizon discounted Markov chain. The algorithm we analyze updates parameters of a linear function approximator online during a single endless trajectory of an irreducible aperiodic Markov chain with a finite or infinite state space. We present a proof of convergence (with probability one), a characterization of the limit of convergence, and a bound on the resulting approximation error. Furthermore, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. In addition to proving new and stronger positive results than those previously available, we identify the significance of online updating and potential hazards associated with the use of nonlinear function Approximators. First, we prove that divergence may occur when updates are not based on trajectories of the Markov chain. This fact reconciles positive and negative results that have been discussed in the literature, regarding the soundness of temporal-difference learning. Second, we present an example illustrating the possibility of divergence when temporal difference learning is used in the presence of a nonlinear function approximator.