information geometry

Information geometry tackles problems by using the concepts of differential geometry (like curvature) with tensor calculus. In his pioneer work, Rao considered.

www.ams.org·28.7 MB

A test's power depends on k(x;x0); P; and Q (and n). With characteristic kernel, MMD test has power ! 1 as n ! 1 for any (fixed) problem.

www.gatsby.ucl.ac.uk·16.7 MB

Latent space geometry has shown itself to provide a rich and rigorous framework for in- teracting with the latent variables of deep generative models.

proceedings.mlr.press·9.1 MB

We propose efficient numerical schemes for implementing the natural gradient descent (NGD) for a broad range of metric spaces with applications to PDE-based ...

yunany.github.io·3.6 MB

Introduction to Information Geometry. – based on the book “Methods of Information Geometry ”written by. Shun-Ichi Amari and Hiroshi Nagaoka.

faculty.coe.drexel.edu·3.4 MB

Information geometry is one such pow- erful framework, blending classical differential geometry with modern applications in probability and ...

arxiv.org·2.8 MB

Information geometry provides a differential-geometric structure on manifold M which useful for designing and studying statistical decision rules. One may ...

franknielsen.github.io·2.4 MB

Even though the integration by parts formula is commonly known as the Gauss-Green formula (or the divergence theorem, or Os- trogradsky's theorem), its ...

www.ams.org·2.2 MB

Natural gradient descent (NGD) requires computing the inverse of the Fisher information matrix (FIM), which is typically expensive at large-scale. Kronecker ...

www.cs.toronto.edu·2.0 MB

Abstract. A family of kernels for statistical learning is introduced that exploits the geometric struc- ture of statistical models.

www.cs.cmu.edu·1.4 MB

I declare that this thesis entitled Geometric Structures on a Statistical Manifold and. Geometry of Estimation submitted in partial fulfillment of the Degree of ...

events.iist.ac.in·1.4 MB

Natural gradients represent the steepest descent direction with respect to the underlying geometry of the parameter space. Iteratively following the natural ...

arxiv.org·1.3 MB

Natural gradient descent has proven effective at mitigating the effects of patho- logical curvature in neural network optimization, but little is known ...

proceedings.neurips.cc·1.3 MB

The geometric structure of statistical manifolds is remarkably rich. At its core lies the Fisher infor- mation metric, which Rao introduced as a ...

rjpn.org·1.1 MB

This paper uses a new formulation of the notion of duality that allows the unified treatment of a number of geometric problems. In particular, we are able to ...

www.cs.princeton.edu·1.0 MB

Natural gradient descent, which preconditions a gradient descent update with the. Fisher information matrix of the underlying statistical model, is a way to ...

proceedings.nips.cc·800.2 KB

This is why gradient descent has problems with badly scaled data. Natural gradient is a dimensionally correct optimization algorithm. In fact, the updates are ...

csc2541-f17.github.io·698.0 KB

In various geometric contexts, there are duality statements that are expressed in terms of appropriate categories of modules. We have in mind, for example, the.

www2.math.upenn.edu·650.6 KB

In this paper we propose a new class of natural gradient algorithms that provide more informed update directions by leveraging knowledge of both how the ...

proceedings.mlr.press·647.0 KB

Natural gradient descent is an optimization method traditionally motivated from the per- spective of information geometry, and works well for many ...

jmlr.org·643.5 KB