this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

This paper presents convergence results for the Box Gaussian Mixture Filter (BGMF). BGMF is a Gaussian Mixture Filter (GMF) that is based on a bank of Extended Kalman Filters. The critical part of GMF is the approximation of probability density function (pdf) as pdf of Gaussian mixture such that its components have small enough covariance matrices. Because GMF approximates prior and posterior a...

Many techniques for calculating bit-error probabilities (BEPs) of direct-sequence spread-spectrum multiple-access systems (DS-SSMA) have been reported. Among them are the following three techniques: 1) the standard Gaussian approximation; 2) the improved Gaussian approximation; 3) and the simplified improved Gaussian approximation. We extend these techniques to derive the BEPs of multicode DS-S...

PESC computes a Gaussian approximation to the NFCPD (main text, Eq. (11)) using Expectation Propagation (EP) (Minka, 2001). EP is a method for approximating a product of factors (often a single prior factor and multiple likelihood factors) with a tractable distribution, for example a Gaussian. EP generates a Gaussian approximation by approximating each individual factor with a Gaussian. The pro...

It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no s...

The Gaussian process (GP) is a simple yet powerful probabilistic framework for various machine learning tasks. However, exact algorithms for learning and prediction are prohibitive to be applied to large datasets due to inherent computational complexity. To overcome this main limitation, various techniques have been proposed, and in particular, local GP algorithms that scales ”truly linearly” w...

The variational approximation of posterior distributions by multivariate gaussians has been much less popular in the machine learning community compared to the corresponding approximation by factorizing distributions. This is for a good reason: the gaussian approximation is in general plagued by an Omicron(N)(2) number of variational parameters to be optimized, N being the number of random vari...

With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the co...

The Gaussian integration of moments is systematically discussed. It is shown that the well-known diffusivityfactor approximation is equivalent to a one-node Gaussian quadrature. The limit as the moment power approaches infinity in a one-node Gaussian quadrature produces a diffusivity factor of e1/2 5 1.648 721 3, which is very close to the value of 1.66 suggested by Elsasser. The errors due to ...