The most common transfer functions in neural networks are of the sigmoidal type. In this article other transfer functions are considered. Advantages of simple gaussians, giving hyperelliptical densities, and gaussian bar functions (sums of one-dimensional gaussians) are discussed. Bi-radial functions are formed from products of two sigmoids. Product of M bi-radial functions in N -dimensional pa...

This paper presents a receiver lter, based on V olterra functions, for a direct-sequence code-division-multiple-access (DS-CDMA) system. The envisaged application would be cellular tele-phony, where the receiver will be required to be adaptive due to changes to the channel characteristics. The results obtained from the V olterra lter are compared against the linear minimum-mean-square-error (MM...

Abstract. Radial basis functions (RBFs) are a powerful tool for interpolating/approximating multidimensional scattered data. Notwithstanding, RBFs pose computational challenges, such as the efficient evaluation of an n-center RBF expansion at m points. A direct summation requires O(nm) operations. We present a new multilevel method whose cost is only O((n + m) ln(1/δ)), where δ is the desired a...

Real communication channels with multipath propagation, interference and possible nonlinearities pose a difficult problem to the detecting receiver. This paper deals with neural approaches to solve those difficulties. Two types of neural networks, self-organizing map and radial basis functions have been studied. The results show that, while there are no actual benefits in using neural receivers...

Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are technically convenient because Gaussian integrals can be calculated analytically. Restricting to Gaussian processes, however, forbids for example the implementi...

We derive approximate numerical solutions for an ordinary differential equation common in engineering using two different types of basis functions, polynomial and Gaussian, and a maximum discrepancy error measure. We compare speed and accuracy of the two solutions. The basic finding for our example is that while Gaussian basis functions can be used, the computational effort is greater than that...

Random Feature Expansions for Deep Gaussian Processes Kurt Cutajar 1 Edwin V. Bonilla 2 Pietro Michiardi 1 Maurizio Filippone 1 A. Additional Experiments Using the experimental set-up described in Section 4, Figure 1 demonstrates how the competing models perform with regards to the RMSE (or error rate) and MNLL metric when two hidden layers are incorporated into the competing models. The result...

We start by noting that conditional independence X ⊥ Y |B⊤X does not necessarily imply the correlation between BX and Y is maximized. To see this, let X be a Gaussian random vairable with zero mean and diagonal covariance matrix. AssumeB is an identity matrix and Y = X = (BX) (elementwise square for a vectorial X). The conditional independence is obviously satisfied yet the correlation between ...

We examine advantages of using smooth basis functions in classifying fMRI (functional MR Imaging) data. fMRI data is a measurement of neural activity in the brain. It allows us to see how each part of the brain responses to stimuli. The task in which we are interested is to identify mental states from some given fMRI data. Specifically, we want to classify between two different states using lab...