64,756 research outputs found
Advances in forecasting with neural networks? Empirical evidence from the NN3 competition on time series prediction
This paper reports the results of the NN3 competition, which is a replication of the M3 competition with an extension of the competition towards neural network (NN) and computational intelligence (CI) methods, in order to assess what progress has been made in the 10 years since the M3 competition. Two masked subsets of the M3 monthly industry data, containing 111 and 11 empirical time series respectively, were chosen, controlling for multiple data conditions of time series length (short/long), data patterns (seasonal/non-seasonal) and forecasting horizons (short/medium/long). The relative forecasting accuracy was assessed using the metrics from the M3, together with later extensions of scaled measures, and non-parametric statistical tests. The NN3 competition attracted 59 submissions from NN, CI and statistics, making it the largest CI competition on time series data. Its main findings include: (a) only one NN outperformed the damped trend using the sMAPE, but more contenders outperformed the AutomatANN of the M3; (b) ensembles of CI approaches performed very well, better than combinations of statistical methods; (c) a novel, complex statistical method outperformed all statistical and Cl benchmarks; and (d) for the most difficult subset of short and seasonal series, a methodology employing echo state neural networks outperformed all others. The NN3 results highlight the ability of NN to handle complex data, including short and seasonal time series, beyond prior expectations, and thus identify multiple avenues for future research. (C) 2011 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved
Linear and Order Statistics Combiners for Pattern Classification
Several researchers have experimentally shown that substantial improvements
can be obtained in difficult pattern recognition problems by combining or
integrating the outputs of multiple classifiers. This chapter provides an
analytical framework to quantify the improvements in classification results due
to combining. The results apply to both linear combiners and order statistics
combiners. We first show that to a first order approximation, the error rate
obtained over and above the Bayes error rate, is directly proportional to the
variance of the actual decision boundaries around the Bayes optimum boundary.
Combining classifiers in output space reduces this variance, and hence reduces
the "added" error. If N unbiased classifiers are combined by simple averaging,
the added error rate can be reduced by a factor of N if the individual errors
in approximating the decision boundaries are uncorrelated. Expressions are then
derived for linear combiners which are biased or correlated, and the effect of
output correlations on ensemble performance is quantified. For order statistics
based non-linear combiners, we derive expressions that indicate how much the
median, the maximum and in general the ith order statistic can improve
classifier performance. The analysis presented here facilitates the
understanding of the relationships among error rates, classifier boundary
distributions, and combining in output space. Experimental results on several
public domain data sets are provided to illustrate the benefits of combining
and to support the analytical results.Comment: 31 page
Noise-robust preparation contextuality shared between any number of observers via unsharp measurements
Multiple observers who independently harvest nonclassical correlations from a
single physical system share the system's ability to enable quantum
correlations. We show that any number of independent observers can share the
preparation contextual outcome statistics enabled by state ensembles in quantum
theory. Furthermore, we show that even in the presence of any amount of white
noise, there exists quantum ensembles that enable such shared preparation
contextuality. The findings are experimentally realised by applying sequential
unsharp measurements to an optical qubit ensemble which reveals three shared
demonstrations of preparation contextuality.Comment: H. A. and N. W. contributed equally to this wor
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