Projected bounds on ALPs from Athena

Error Bounds for Approximations from Projected Linear Equations

We consider linear fixed point equations and their approximations by projection on a low dimensional subspace. We derive new bounds on the approximation error of the solution, which are expressed in terms of low dimensional matrices and can be computed by simulation. When the fixed point mapping is a contraction, as is typically the case in Markov decision processes (MDP), one of our bounds is ...

Amazon Athena - Amazon Athena Documentation

Amazon Athena - Amazon Athena Documentation

Sharp Generalization Error Bounds for Randomly-projected Classifiers

We derive sharp bounds on the generalization error of a generic linear classifier trained by empirical risk minimization on randomlyprojected data. We make no restrictive assumptions (such as sparsity or separability) on the data: Instead we use the fact that, in a classification setting, the question of interest is really ‘what is the effect of random projection on the predicted class labels?’...

2D Polyhedral Bounds of a Clipped, Perspective-Projected 3D Sphere

We show how to efficiently compute 2D polyhedral bounds of the (elliptic) perspective projection of a 3D sphere that has been clipped to the near plane. For the special case of a 2D axis-aligned bounding box, the algorithm is especially efficient. This has applications for bounding the screen-space effect of an emitter under deferred shading, bounding the kernel in density estimation during ima...