A Cyclic Contrastive Divergence Learning Algorithm for High-Order RBMs

2014 ◽  
Author(s):  
Dingsheng Luo ◽  
Yi Wang ◽  
Xiaoqiang Han ◽  
Xihong Wu
Keyword(s):  
Learning Algorithm ◽  
High Order ◽  
Contrastive Divergence

A NEW NEURAL OBSERVER FOR AN ANAEROBIC BIOREACTOR

2010 ◽  
Vol 20 (01) ◽  
pp. 75-86 ◽  
Author(s):  
R. BELMONTE-IZQUIERDO ◽  
S. CARLOS-HERNANDEZ ◽  
E. N. SANCHEZ
Keyword(s):  
Inorganic Carbon ◽  
Learning Algorithm ◽  
Real Data ◽  
Activation Function ◽  
High Order ◽  
Stirred Tank ◽  
Hyperbolic Tangent ◽  
Tank Reactor ◽  
Completely Stirred Tank Reactor ◽  
High Order Neural Network

In this paper, a recurrent high order neural observer (RHONO) for anaerobic processes is proposed. The main objective is to estimate variables of methanogenesis: biomass, substrate and inorganic carbon in a completely stirred tank reactor (CSTR). The recurrent high order neural network (RHONN) structure is based on the hyperbolic tangent as activation function. The learning algorithm is based on an extended Kalman filter (EKF). The applicability of the proposed scheme is illustrated via simulation. A validation using real data from a lab scale process is included. Thus, this observer can be successfully implemented for control purposes.

Contrastive Divergence in Gaussian Diffusions

2008 ◽  
Vol 20 (9) ◽  
pp. 2238-2252 ◽  
Author(s):  
Javier R. Movellan
Keyword(s):  
Neural Networks ◽  
Maximum Likelihood ◽  
Network Structure ◽  
Continuous Time ◽  
Learning Algorithm ◽  
Stochastic Neural Networks ◽  
Theoretical Understanding ◽  
Log Likelihood ◽  
Contrastive Divergence ◽  
Time Linear

This letter presents an analysis of the contrastive divergence (CD) learning algorithm when applied to continuous-time linear stochastic neural networks. For this case, powerful techniques exist that allow a detailed analysis of the behavior of CD. The analysis shows that CD converges to maximum likelihood solutions only when the network structure is such that it can match the first moments of the desired distribution. Otherwise, CD can converge to solutions arbitrarily different from the log-likelihood solutions, or they can even diverge. This result suggests the need to improve our theoretical understanding of the conditions under which CD is expected to be well behaved and the conditions under which it may fail. In, addition the results point to practical ideas on how to improve the performance of CD.

Quickly Generating Representative Samples from an RBM-Derived Process

2011 ◽  
Vol 23 (8) ◽  
pp. 2058-2073 ◽  
Author(s):  
Olivier Breuleux ◽  
Yoshua Bengio ◽  
Pascal Vincent
Keyword(s):  
Markov Chain ◽  
Lower Bound ◽  
Gibbs Sampling ◽  
Learning Algorithm ◽  
Training Data ◽  
Model Parameters ◽  
Sampling Process ◽  
Log Likelihood ◽  
Contrastive Divergence ◽  
Representative Samples

Two recently proposed learning algorithms, herding and fast persistent contrastive divergence (FPCD), share the following interesting characteristic: they exploit changes in the model parameters while sampling in order to escape modes and mix better during the sampling process that is part of the learning algorithm. We justify such approaches as ways to escape modes while keeping approximately the same asymptotic distribution of the Markov chain. In that spirit, we extend FPCD using an idea borrowed from Herding in order to obtain a pure sampling algorithm, which we call the rates-FPCD sampler. Interestingly, this sampler can improve the model as we collect more samples, since it optimizes a lower bound on the log likelihood of the training data. We provide empirical evidence that this new algorithm displays substantially better and more robust mixing than Gibbs sampling.

A BPTT-Like Optimal Control Algorithm With Vehicle Dynamics Control Application

2008 ◽  
Author(s):  
J. Kasac ◽  
J. Deur ◽  
B. Novakovic ◽  
I. Kolmanovsky
Keyword(s):  
Optimal Control ◽  
Vehicle Dynamics ◽  
Learning Algorithm ◽  
Tubular Reactor ◽  
Time Discretization ◽  
High Order ◽  
Dynamic Neural Networks ◽  
Backpropagation Through Time ◽  
Gradient Based ◽  
Vehicle Dynamics Control

The paper presents a gradient-based numerical algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm has a backward-in-time recurrent structure similar to the backpropagation-through-time (BPTT) algorithm, which is mostly used as a learning algorithm for dynamic neural networks. This paper presents an enhancement of the basic optimization algorithm. Our enhanced algorithm uses high-order Adams time-discretization schemes instead of the basic Euler discretization method, and a numerical calculation of Jacobians as an alternative to analytical Jacobians. Two examples are considered to illustrate the algorithm and its performance. The first example is that of a tubular reactor, for which an analytical solution is available, which can be readily used for validation of our approach. The second example is related to controlling vehicle dynamics based on a realistic high order model.

scholarly journals Convergence Analysis of Contrastive Divergence Algorithm Based on Gradient Method with Errors

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xuesi Ma ◽  
Xiaojie Wang
Keyword(s):  
Finite Number ◽  
Gibbs Sampling ◽  
Gradient Method ◽  
Convergence Theorem ◽  
Learning Algorithm ◽  
Restricted Boltzmann Machines ◽  
Convergence Conditions ◽  
Boltzmann Machines ◽  
Contrastive Divergence ◽  
Step Number

Contrastive Divergence has become a common way to train Restricted Boltzmann Machines; however, its convergence has not been made clear yet. This paper studies the convergence of Contrastive Divergence algorithm. We relate Contrastive Divergence algorithm to gradient method with errors and derive convergence conditions of Contrastive Divergence algorithm using the convergence theorem of gradient method with errors. We give specific convergence conditions of Contrastive Divergence learning algorithm for Restricted Boltzmann Machines in which both visible units and hidden units can only take a finite number of values. Two new convergence conditions are obtained by specifying the learning rate. Finally, we give specific conditions that the step number of Gibbs sampling must be satisfied in order to guarantee the Contrastive Divergence algorithm convergence.

Determination of the Burgers vector of a dislocation in a Fe-Mn alloy by weak-beam image in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 330-331
Author(s):  
Y. Ishida ◽  
H. Ishida ◽  
K. Kohra ◽  
H. Ichinose
Keyword(s):  
High Order ◽  
Simulation Technique ◽  
The Other ◽  
Image Simulation ◽  
Diffraction Vector ◽  
Burgers Vector ◽  
Weak Beam ◽  
Beam Image ◽  
Edge Component

IntroductionA simple and accurate technique to determine the Burgers vector of a dislocation has become feasible with the advent of HVEM. The conventional image vanishing technique(1) using Bragg conditions with the diffraction vector perpendicular to the Burgers vector suffers from various drawbacks; The dislocation image appears even when the g.b = 0 criterion is satisfied, if the edge component of the dislocation is large. On the other hand, the image disappears for certain high order diffractions even when g.b ≠ 0. Furthermore, the determination of the magnitude of the Burgers vector is not easy with the criterion. Recent image simulation technique is free from the ambiguities but require too many parameters for the computation. The weak-beam “fringe counting” technique investigated in the present study is immune from the problems. Even the magnitude of the Burgers vector is determined from the number of the terminating thickness fringes at the exit of the dislocation in wedge shaped foil surfaces.

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