Early Stop Criterion from the Bootstrap Ensemble

This paper addresses the problem of generalization error estimation in neural networks. A new early stop criterion based on a Bootstrap estimate of the generlization error is suggested. The estimate does not require the network to be trained to the minimum of the cost function, as required by other methods based on asymptotic theory. Moreover, in constrast to methods based on cross-validation which require data left out for testing, and thus biasing the estimate, the Bootstrap technique does not have this disadvantage. The potential of the suggested technique is demonstrated on various time-series problems. 1. INTRODUCTION The goal of neural network learning in signal processing is to identify robust functional dependencies between input and output data (for an introduction see e.g., [3]). Such learning usually proceeds from a finite random sample of training data; hence, the functions implemented by neural networks are stochastic depending on the particular available training set. T..

Training and evaluation of neural networks for multi-variate time series processing

We study training and generalization for multi-variate time series processing. It is suggested to used a quasi maximum likelihood approach rather than the standard sum of squared errors, thus taking dependencies among the errors of the individual time series into account. This may lead to improved generalization performance. Further, we extend the Optimal Brain Damage pruning technique to the multi-variate case. A key ingredient is an algebraic expression for the generalization ability of a multi-variate model. The variability of the suggested techniques are successfully demonstrated in a multi-variate scenario involving the prediction of the cylinder pressure in a marine engine. 1. Introduction Multi-variate nonlinear time series processing models are of interest in many neural network application areas. The application which motivates the present study is the supervision and fault diagnosis of marine engines. Time-series from sensors mounted on the engine are used as inputs to a si..

Measurements and Judgments of Sound in relation to Human Sound Perception:Part 1: Measurement positions for measurement of loudness

It is recognised that A-weighted measurements of sound pressure levels and sound power levels alone are insufficient for measurements in relation to product sound quality and noise annoyance potential. This has led to increasing interest in measures in c loser agreement with human sound perception as e.g. loudness, sharpness roughness. Equipment, which gives easy and reliable measurements of loudness and other psychoacoustic parameters, is now available, and therefore there is a need to supplement existi ng measurement methods with procedures for measurement of loudness etc. In the existing ISO-standards for measurements of A-weighted sound pressure levels and sound power levels, measurement positions are not defined with the purpose of giving meaningful measurements of e.g. loudness. Part 1 of this NORDTEST guideline gives instructions on how to supplement the A-weighted data with meaningful results of measurements of loudness