Amari, S. Natural Gradient Works E#ciently in Learning. Neural Computation 10, 1998 Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
First 50 documents
Blind Separation of Instantaneous Mixtures of Non Stationary.. - Pham, Cardoso (2001) (28 citations) (Correct)
....eqs. 21) and (32) Here, the underlying mechanism can be recognized as the classic Newton technique in which the gradient is left multiplied by the inverse of the Hessian for it to point in the best (in a certain sense) direction. Thus, it is likely that the natural gradient approach of Amari [20] would result in similar algorithms. We note that on line algorithm takes its particular simple form thanks to an approximation which is only valid when the model holds. When this is not the case, the algorithm is still well behaved because the gradient is rectified by a matrix which is always ....
Shun-Ichi Amari, "Natural gradient works e#ciently in learning", Neural Computation, vol. 10, pp. 251--276, 1998.
Blind Signal Separation: Statistical Principles - Cardoso (1998) (93 citations) (Correct)
....y = Bx; thus it actually characterizes the first order variation of the contrast function itself. It is of course possible to relate to a regular gradient with respect to B if y = Bx. Elementary calculus yields #B . 29) The notion of natural gradient was independently introduced by Amari [2]. It is distinct in general from the relative gradient: the latter is defined in any continuous group of transformation while the former is defined in any smooth statistical model. However, for the BSS model which, as a statistical transformation model combines both features, the two ideas yield ....
S.-I. Amari. Natural gradient works e#ciently in learning. Neural Computation, 10:251--276, 1998.
Optimisation Strategies for Nonconvex Functions and.. - Di Fiore, Fanelli.. (2001) (Correct)
....and network architecture guarantee local minima free error surfaces and the important contribution of [13] showing that the classical XOR problem has no real local minima. Furthermore, the fundamental and innovative approach founded on the natural gradient , introduced by Amari (see f.i. 1] [2], 17] was proved to be a powerful stochastic method to solve the critical problem of escaping from plateaus of the error surface, thereby ensuring an e ective steepest descent in any situation. Since algorithms based on the natural gradient have locally a QuasiNewtonian (QN) behaviour, ....
S.Amari, Natural gradient works eciently in lea rning, Neural Computation 10 (1998), 251-276.
Optimal Linear Representations of Images for Object.. - Liu, Srivastava, Gallivan (2003) (1 citation) (Correct)
....2 norm in d(I1 , I2 ; U) allows for this equality. Grassmann and similar manifolds have been used in the literature to derive e#ective algorithms but in di#erent contexts; see e.g. 18] for subspace tracking, 13] for motion and structure estimation, 15] for independent component analysis, and [1, 6] for neural network learning algorithms. gradient process has to account for its intrinsic geometry. Deterministic gradients such as NewtonRaphson method, on such manifolds with orthogonality constraints have been studied in [5] We will start by describing a deterministic gradient process (of F ....
....As shown in these examples and the ones in Figs. 2 and 3, the proposed algorithm converges quickly under di#erent kinds of conditions. We attribute this mainly to the fact that by taking into the geometry of the manifold into account, the gradient flow provides the most e#cient way for updating [1]. In fact, Amari [1] has shown that such a dynamical system is Fisher e#cient. Obviously, the e#ectiveness of the proposed algorithm depends on the choice of parameters; through experiments we have found that it works for a wide of parameter values. This can be attributed to the update rules in ....
[Article contains additional citation context not shown here]
S. Amari. Natural gradient works e#ciently in learning. Neural Computation, 10:251-276, 1998.
Scaling Reinforcement Learning Paradigms for Motor Control - Peters, Vijayakumar, Schaal (2003) (Correct)
No context found.
Amari, S. Natural Gradient Works E#ciently in Learning. Neural Computation 10, 1998
Reinforcement Learning for Humanoid Robotics - Peters, Vijayakumar, Schaal (2003) (Correct)
No context found.
Amari, S. Natural Gradient Works E#ciently in Learning. Neural Computation 10, 1998
Rprop Using the Natural Gradient - Igel, al. (2005) (Correct)
No context found.
S. Amari. Natural gradient works e#ciently in learning. Neural Computation, 10:251--276, 1998.
Uniqueness of linear independent component analysis and the .. - Fabian Theis Elmar (Correct)
No context found.
S. Amari. Natural gradient works e#ciently in learning. Neural Computation, 10(2):251--276, 1998.
The Evolution Of Genetic Representations And Modular Adaptation - Toussaint (2003) (4 citations) (Correct)
No context found.
Amari, S. (1998). Natural gradient works e#ciently in learning. Neural Computation 10, 251--276.
Division of Computer Science - University Of California (Correct)
No context found.
Amari, S. (1998). Natural gradient works e#ciently in learning. Neural Computation, 10(2):251--276.
Appearance-Based Classification And Recognition Using Spectral.. - Zhang (2005) (Correct)
No context found.
S. Amari, "Natural Gradient Works E#ciently in Learning," Neural Computation, vol. 10, pp. 251-276, 1998.
Improved Learning of Riemannian Metrics for Exploratory.. - Peltonen, Klami, Kaski (2004) (Correct)
No context found.
Amari, S., 1998. Natural gradient works e#ciently in learning. Neural Computation 10, 251--276.
Learning Metrics for Self-Organizing Maps - Kaski, Sinkkonen, Peltonen (2001) (Correct)
No context found.
S.-I. Amari, \Natural gradient works eciently in learning," Neural Computation, vol. 10, pp. 251-276, 1998.
Kernel Independent Component Analysis - Bach, Jordan (2002) (41 citations) (Correct)
No context found.
S. Amari. Natural gradient works eciently in learning. Neural Computation, 10(2):251{ 276, 1998.
Reinforcement Learning by Policy Search - Peshkin (2001) (7 citations) (Correct)
No context found.
Shun-ichi Amari, Natural gradient works e ciently in learning, Neural Computation 10 (1998), 251-276.
Compact Representations for Fast Nonrigid Registration of Medical .. - Timoner (2003) (Correct)
No context found.
S. Amari. Natural gradient works e#ciently in learning. Neural Computation, 10(2):251--276, 1998. amari98natural. html
Optimal Linear Representations of Images for Object Recognition - Xiuwen Liu Anuj (2003) (1 citation) (Correct)
No context found.
S. Amari. Natural gradient works e#ciently in learning. Neural Computation, 10:251-276, 1998.
Principle of Learning Metrics for Exploratory Data Analysis - Kaski, Sinkkonen (2003) (Correct)
No context found.
S.-I. Amari. "Natural gradient works e#ciently in learning," Neural Computation, vol. 10, 1998, pp. 251--276. 14
The Kernel Mutual Information - Gretton, Herbrich, Smola (2003) (Correct)
No context found.
S.-I. Amari. Natural gradient works e ciently in learning. Neural Computation, 10(2):251276, 1998.
Online Convex Programming and Generalized Infinitesimal Gradient .. - Zinkevich (2003) (6 citations) (Correct)
No context found.
S. Amari. Natural gradient works eciently in learning. Neural Computation, 10:251{ 276, 1998.
Application-Driven Dimension Reduction - Srivastava, Liu (2004) (Correct)
No context found.
S. Amari, Natural gradient works e#ciently in learning, Neural Computation 10 (1998) 251--276.
Iterative Scaled Trust-Region Learning in Krylov Subspaces.. - Mizutani, Demmel (2003) (Correct)
No context found.
Shun-ichi Amari. Natural gradient works e#ciently in learning. In Neural Computation, 10, pp. 251--276, 1998.
Gaussianization - Chen, Gopinath (2000) (1 citation) (Correct)
No context found.
S. Amari, \Natural Gradient Works Eciently in Learning", Neural Computation, Vol. 10, pp. 251-276, 1998.
Incremental Construction of Projection Generalizing Neural.. - Sugiyama, Ogawa (2002) (Correct)
No context found.
S. Amari, "Natural gradient works e#ciently in learning," Neural Computation, vol. 10, no. 2, pp. 251--276, 1998.
Unsupervised Neural Learning On Lie Group - Fiori (2002) (Correct)
No context found.
S.-I. Amari 1998, "Natural gradient works e#ciently in learning," Neural Computation 10, 251--276.
First 50 documents
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC