A novel approach to error function minimization for feedforward neural networks

Feedforward neural networks with error backpropagation (FFBP) are widely applied to pattern recognition. One general problem encountered with this type of neural networks is the uncertainty, whether the minimization procedure has converged to a global minimum of the cost function. To overcome this problem a novel approach to minimize the error function is presented. It allows to monitor the approach to the global minimum and as an outcome several ambiguities related to the choice of free parameters of the minimization procedure are removed.Comment: 11 pages, latex, 3 figures appended as uuencoded fil

MULTILAYER FEEDFORWARD NETWORKS WITH NON-POLYNOMIAL ACTIVATION FUNCTIONS CAN APPROXIMATE ANY FUNCTION

Several researchers characterized the activation functions under which multilayer feedforward networks can act as universal approximators. We show that all the characterizations that were reported thus far in the literature ark special cases of the following general result: a standard multilayer feedforward network can approximate any continuous function to any degree of accuracy if and only if the network's activation functions are not polynomial. We also emphasize the important role of the threshold, asserting that without it the last theorem doesn't hold.Information Systems Working Papers Serie

Infering Air Quality from Traffic Data using Transferable Neural Network Models

This work presents a neural network based model for inferring air quality from traffic measurements. It is important to obtain information on air quality in urban environments in order to meet legislative and policy requirements. Measurement equipment tends to be expensive to purchase and maintain. Therefore, a model based approach capable of accurate determination of pollution levels is highly beneficial. The objective of this study was to develop a neural network model to accurately infer pollution levels from existing data sources in Leicester, UK. Neural Networks are models made of several highly interconnected processing elements. These elements process information by their dynamic state response to inputs. Problems which were not solvable by traditional algorithmic approaches frequently can be solved using neural networks. This paper shows that using a simple neural network with traffic and meteorological data as inputs, the air quality can be estimated with a good level of generalisation and in near real-time. By applying these models to links rather than nodes, this methodology can directly be used to inform traffic engineers and direct traffic management decisions towards enhancing local air quality and traffic management simultaneously.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis

In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. We obtain consistency results which imply that the estimation of optimal parameters for functional MLP is statistically well defined. We finally show on simulated and real world data that the proposed model performs in a very satisfactory way.Comment: http://www.sciencedirect.com/science/journal/0893608

Genetic Classification of Populations using Supervised Learning

There are many instances in genetics in which we wish to determine whether two candidate populations are distinguishable on the basis of their genetic structure. Examples include populations which are geographically separated, case--control studies and quality control (when participants in a study have been genotyped at different laboratories). This latter application is of particular importance in the era of large scale genome wide association studies, when collections of individuals genotyped at different locations are being merged to provide increased power. The traditional method for detecting structure within a population is some form of exploratory technique such as principal components analysis. Such methods, which do not utilise our prior knowledge of the membership of the candidate populations. are termed \emph{unsupervised}. Supervised methods, on the other hand are able to utilise this prior knowledge when it is available. In this paper we demonstrate that in such cases modern supervised approaches are a more appropriate tool for detecting genetic differences between populations. We apply two such methods, (neural networks and support vector machines) to the classification of three populations (two from Scotland and one from Bulgaria). The sensitivity exhibited by both these methods is considerably higher than that attained by principal components analysis and in fact comfortably exceeds a recently conjectured theoretical limit on the sensitivity of unsupervised methods. In particular, our methods can distinguish between the two Scottish populations, where principal components analysis cannot. We suggest, on the basis of our results that a supervised learning approach should be the method of choice when classifying individuals into pre-defined populations, particularly in quality control for large scale genome wide association studies.Comment: Accepted PLOS On

{\sc CosmoNet}: fast cosmological parameter estimation in non-flat models using neural networks

We present a further development of a method for accelerating the calculation of CMB power spectra, matter power spectra and likelihood functions for use in cosmological Bayesian inference. The algorithm, called {\sc CosmoNet}, is based on training a multilayer perceptron neural network. We compute CMB power spectra (up to $\ell=2000$) and matter transfer functions over a hypercube in parameter space encompassing the $4\sigma$ confidence region of a selection of CMB (WMAP + high resolution experiments) and large scale structure surveys (2dF and SDSS). We work in the framework of a generic 7 parameter non-flat cosmology. Additionally we use {\sc CosmoNet} to compute the WMAP 3-year, 2dF and SDSS likelihoods over the same region. We find that the average error in the power spectra is typically well below cosmic variance for spectra, and experimental likelihoods calculated to within a fraction of a log unit. We demonstrate that marginalised posteriors generated with {\sc CosmoNet} spectra agree to within a few percent of those generated by {\sc CAMB} parallelised over 4 CPUs, but are obtained 2-3 times faster on just a \emph{single} processor. Furthermore posteriors generated directly via {\sc CosmoNet} likelihoods can be obtained in less than 30 minutes on a single processor, corresponding to a speed up of a factor of $\sim 32$. We also demonstrate the capabilities of {\sc CosmoNet} by extending the CMB power spectra and matter transfer function training to a more generic 10 parameter cosmological model, including tensor modes, a varying equation of state of dark energy and massive neutrinos. {\sc CosmoNet} and interfaces to both {\sc CosmoMC} and {\sc Bayesys} are publically available at {\tt www.mrao.cam.ac.uk/software/cosmonet}.Comment: 8 pages, submitted to MNRA

Bitcoin: An Impossibility Theorem for Proof-of-Work based Protocols

A key part of decentralized consensus protocols is a procedure for random selection, which is the source of the majority of miners cost and wasteful energy consumption in Bitcoin. We provide a simple economic model for random selection mechanism and show that any PoW protocol with natural desirable properties is outcome equivalent to the random selection mechanism used in Bitcoin

Bitcoin: An Impossibility Theorem for Proof-of-Work based Protocols

Bitcoin’s main innovation lies in allowing a decentralized system that relies on anonymous, profit driven miners who can freely join the system. We formalize these properties in three axioms: anonymity of miners, no incentives for miners to consolidate, and no incentive to assuming multiple fake identities. This novel axiomatic formalization allows us to characterize which other protocols are feasible: Every protocol with these properties must have the same reward scheme as Bitcoin. This implies an impossibility result for risk-averse miners: no protocol satisfies the aforementioned constraints simultaneously without giving miners a strict incentive to merge. Furthermore, any protocol either gives up on some degree of decentralization or its reward scheme is equivalent to Bitcoin’s

Gram-Negative Bacteremia upon Hospital Admission: When Should Pseudomonas aeruginosa Be Suspected?

Background. Pseudomonas aeruginosa is an uncommon cause of community-acquired bacteremia among patients without severe immunodeficiency. Because tension exists between the need to limit unnecessary use of anti-pseudomonal agents and the need to avoid a delay in appropriate therapy, clinicians require better guidance regarding when to cover empirically for P. aeruginosa. We sought to determine the occurrence of and construct a model to predict P. aeruginosa bacteremia upon hospital admission. Methods. A retrospective study was conducted in 4 tertiary care hospitals. Microbiology databases were searched to find all episodes of bacteremia caused by gram-negative rods (GNRs) ⩽48 h after hospital admission. Patient data were extracted from the medical records of 151 patients with P. aeruginosa bacteremia and of 152 randomly selected patients with bacteremia due to Enterobacteriaceae. Discriminative parameters were identified using logistic regression, and the probabilities of having P. aeruginosa bacteremia were calculated. Results. P. aeruginosa caused 6.8% of 4114 unique patient episodes of GNR bacteremia upon hospital admission (incidence ratio, 5 cases per 10,000 hospital admissions). Independent predictors of P. aeruginosa bacteremia were severe immunodeficiency, age >90 years, receipt of antimicrobial therapy within past 30 days, and presence of a central venous catheter or a urinary device. Among 250 patients without severe immunodeficiency, if no predictor variables existed, the likelihood of having P. aeruginosa bacteremia was 1:42. If ⩾2 predictors existed, the risk increased to nearly 1:3. Conclusions. P. aeruginosa bacteremia upon hospital admission in patients without severe immunodeficiency is rare. Among immunocompetent patients with suspected GNR bacteremia who have ⩾2 predictors, empirical anti-pseudomonal treatment is warrante