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This is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Neurocomputing, VOL 160 (2015) DOI 10.1016/j.neucom.2014.12.086, Subsampling is used to generate bagging ensembles that are accurate and robust to class-label noise. The effect of using smaller bootstrap samples to train the base learners is to make the ensemble more diverse. As a result, the classification margins tend to decrease. In spite of having small margins, these ensembles can be robust to class-label noise. The validity of these observations is illustrated in a wide range of synthetic and real-world classification tasks. In the problems investigated, subsampling significantly outperforms standard bagging for different amounts of class-label noise. By contrast, the effectiveness of subsampling in random forest is problem dependent. In these types of ensembles the best overall accuracy is obtained when the random trees are built on bootstrap samples of the same size as the original training data. Nevertheless, subsampling becomes more effective as the amount of class-label noise increases., The authors acknowledge financial support from Spanish Plan Nacional I+D+i Grant TIN2013-42351-P and from Comunidad de Madrid Grant S2013/ICE-2845 CASI-CAM-CM.

This is the author’s version of a work that was accepted for publication in Pattern Recognition. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition 46.5 (2013): 1323 – 1336, DOI: 10.1016/j.patcog.2012.10.021, We propose to determine the size of a parallel ensemble by estimating the minimum number of classifiers that are required to obtain stable aggregate predictions. Assuming that majority voting is used, a statistical description of the convergence of the ensemble prediction to its asymptotic (infinite size) limit is given. The analysis of the voting process shows that for most test instances the ensemble prediction stabilizes after only a few classifiers are polled. By contrast, a small but non-negligible fraction of these instances require large numbers of classifier queries to reach stable predictions. Specifically, the fraction of instances whose stable predictions require more than T classifiers for T ≫ 1 has a universal form and is proportional to T−1/2. The ensemble size is determined as the minimum number of classifiers that are needed to estimate the infinite ensemble prediction at an average confidence level , close to one. This approach differs from previous proposals, which are based on determining the size for which the prediction error (not the predictions themselves) stabilizes. In particular, it does not require estimates of the generalization performance of the ensemble, which can be unreliable. It has general validity because it is based solely on the statistical description of the convergence of majority voting to its asymptotic limit. Extensive experiments using representative parallel ensembles (bagging and random forest) illustrate the application of the proposed framework in a wide range of classification problems. These experiments show that the optimal ensemble size is very sensitive to the particular classification problem considered., The authors acknowledge financial support from the Spanish Dirección General de Investigación, project TIN2010-21575-C02-02.

This is the author’s version of a work that was accepted for publication in Pattern Recognition. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition 44.7 (2011): 1426 – 1434, DOI: 10.1016/j.patcog.2010.12.021, In this paper we introduce a framework for making statistical inference on the asymptotic prediction of parallel classification ensembles. The validity of the analysis is fairly general. It only requires that the individual classifiers are generated in independent executions of some randomized learning algorithm, and that the final ensemble prediction is made via majority voting. Given an unlabeled test instance, the predictions of the classifiers in the ensemble are obtained sequentially. As the individual predictions become known, Bayes’ theorem is used to update an estimate of the probability that the class predicted by the current ensemble coincides with the classification of the corresponding ensemble of infinite size. Using this estimate, the voting process can be halted when the confidence on the asymptotic prediction is sufficiently high. An empirical investigation in several benchmark classification problems shows that most of the test instances require querying only a small number of classifiers to converge to the infinite ensemble prediction with a high degree of confidence. For these instances, the difference between the generalization error of the finite ensemble and the infinite ensemble limit is very small, often negligible., The authors acknowledge support from the Spanish Ministerio de Ciencia e Innovación, projects TIN2007-66862-C02-02 and TIN2010-21575-C02-02.

This is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Neurocomputing 74.12-13 (2011) DOI: 10.1016/j.neucom.2011.03.001, Identifying the optimal subset of regressors in a regression bagging ensemble is a difficult task that has exponential cost in the size of the ensemble. In this article we analyze two approximate techniques especially devised to address this problem. The first strategy constructs a relaxed version of the problem that can be solved using Semidefinite Programming. The second one is based on modifying the order of aggregation of the regressors. Ordered Aggregation is a simple forward selection algorithm that incorporates at each step the regressor that reduces the training error of the current subensemble the most. Both techniques can be used to identify subensembles that are close to the optimal ones, which can be obtained by exhaustive search at a larger computational cost. Experiments in a wide variety of synthetic and real-world regression problems show that pruned ensembles composed of only 20% of the initial regressors often have better generalization performance than the original bagging ensembles. These improvements are due to a reduction in the bias and the covariance components of the generalization error. Subensembles obtained using either SDP or Ordered Aggregation generally outperform subensembles obtained by other ensemble pruning methods and ensembles generated by the Adaboost.R2 algorithm, negative correlation learning or regularized linear stacked generalization. Ordered Aggregation has a slightly better overall performance than SDP in the problems investigated. However, the difference is not statistically significant. Ordered Aggregation has the further advantage that it produces a nested sequence of near-optimal subensembles of increasing size with no additional computational cost., The authors acknowledge support from the Spanish Ministerio de Ciencia e Innovación, Project TIN2010-21575-C02-02.

This is the author’s version of a work that was accepted for publication in Pattern Recognition Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition Letters 28.1 (2007): 156 – 165, DOI: 10.1016/j.patrec.2006.06.018, Boosting is used to determine the order in which classifiers are aggregated in a bagging ensemble. Early stopping in the aggregation of the classifiers in the ordered bagging ensemble allows the identification of subensembles that require less memory for storage, classify faster and can improve the generalization accuracy of the original bagging ensemble. In all the classification problems investigated pruned ensembles with 20 % of the original classifiers show statistically significant improvements over bagging. In problems where boosting is superior to bagging, these improvements are not sufficient to reach the accuracy of the corresponding boosting ensembles. However, ensemble pruning preserves the performance of bagging in noisy classification tasks, where boosting often has larger generalization errors. Therefore, pruned bagging should generally be preferred to complete bagging and, if no information about the level of noise is available, it is a robust alternative to AdaBoost., The authors acknowledge financial support from the Spanish Dirección General de Investigación, project TIN2004-07676-C02-02.

This is the author’s version of a work that was accepted for publication in Pattern Recognition. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition 38.10 (2005): 1483 – 1494, DOI: 10.1016/j.patcog.2005.02.020, Ensembles that combine the decisions of classi ers generated by using perturbed versions of the training set where the classes of the training examples are randomly switched can produce a signi cant error reduction, provided that large numbers of units and high class switching rates are used. The classi ers generated by this procedure have statistically uncorrelated errors in the training set. Hence, the ensembles they form exhibit a similar dependence of the training error on ensemble size, independently of the classi cation problem. In particular, for binary classi cation problems, the classi cation performance of the ensemble on the training data can be analysed in terms of a Bernoulli process. Experiments on several UCI datasets demonstrate the improvements in classi cation accuracy that can be obtained using these class-switching ensembles., This work has been supported by the Spanish "Dirección General de Investigación", project TIC2001-0572-C02-02.

The final publication is available at Springer via http://dx.doi.org/10.1007/s11042-011-0913-z, Spoken term detection (STD) is the task of searching for occurrences of spoken terms in audio archives. It relies on robust confidence estimation to make a hit/false alarm (FA) decision. In order to optimize the decision in terms of the STD evaluation metric, the confidence has to be discriminative. Multi-layer perceptrons (MLPs) and support vector machines (SVMs) exhibit good performance in producing discriminative confidence; however they are severely limited by the continuous objective functions, and are therefore less capable of dealing with complex decision tasks. This leads to a substantial performance reduction when measuring detection of out-of-vocabulary (OOV) terms, where the high diversity in term properties usually leads to a complicated decision boundary. In this paper we present a new discriminative confidence estimation approach based on evolutionary discriminant analysis (EDA). Unlike MLPs and SVMs, EDA uses the classification error as its objective function, resulting in a model optimized towards the evaluation metric. In addition, EDA combines heterogeneous projection functions and classification strategies in decision making, leading to a highly flexible classifier that is capable of dealing with complex decision tasks. Finally, the evolutionary strategy of EDA reduces the risk of local minima. We tested the EDA-based confidence with a state-of-the-art phoneme-based STD system on an English meeting domain corpus, which employs a phoneme speech recognition system to produce lattices within which the phoneme sequences corresponding to the enquiry terms are searched. The test corpora comprise 11 hours of speech data recorded with individual head-mounted microphones from 30 meetings carried out at several institutes including ICSI; NIST; ISL; LDC; the Virginia Polytechnic Institute and State University; and the University of Edinburgh. The experimental results demonstrate that EDA considerably outperforms MLPs and SVMs on both classification and confidence measurement in STD, and the advantage is found to be more significant on OOV terms than on in-vocabulary (INV) terms. In terms of classification performance, EDA achieved an equal error rate (EER) of 11% on OOV terms, compared to 34% and 31% with MLPs and SVMs respectively; for INV terms, an EER of 15% was obtained with EDA compared to 17% obtained with MLPs and SVMs. In terms of STD performance for OOV terms, EDA presented a significant relative improvement of 1.4% and 2.5% in terms of average term-weighted value (ATWV) over MLPs and SVMs respectively., This work was partially supported by the French Ministry of Industry (Innovative Web call) under contract 09.2.93.0966, ‘Collaborative Annotation for Video Accessibility’ (ACAV) and by ‘The Adaptable Ambient Living Assistant’ (ALIAS) project funded through the joint national Ambient Assisted Living (AAL) programme.

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-33266-1_70, Proceedings of 22nd International Conference on Artificial Neural Networks, Lausanne, Switzerland, September 11-14, 2012, In this work we will apply Diffusion Maps (DM), a recent technique for dimensionality reduction and clustering, to build local models for wind energy forecasting. We will compare ridge regression models for K–means clusters obtained over DM features, against the models obtained for clusters constructed over the original meteorological data or principal components, and also against a global model. We will see that a combination of the DM model for the low wind power region and the global model elsewhere outperforms other options., With partial support from grant TIN2010-21575-C02-01 of Spain’s Ministerio de Economía y Competitividad and the UAM–ADIC Chair for Machine Learning in Modelling and Prediction. The first author is also supported by an FPI-UAM grant and kindly thanks the Applied Mathematics Department of Yale University for receiving her during a visit. The second author is supported by the FPU-MEC grant AP2008-00167. We also thank Red Eléctrica de España, Spain’s TSO, for providing historic wind energy data

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-12127-2_11, Proceedings of 9th International Workshop, MCS 2010, Cairo, Egypt, April 7-9, 2010., This article introduces a double pruning algorithm that can be used to reduce the storage requirements, speed-up the classification process and improve the performance of parallel ensembles. A key element in the design of the algorithm is the estimation of the class label that the ensemble assigns to a given test instance by polling only a fraction of its classifiers. Instead of applying this form of dynamical (instance-based) pruning to the original ensemble, we propose to apply it to a subset of classifiers selected using standard ensemble pruning techniques. The pruned subensemble is built by first modifying the order in which classifiers are aggregated in the ensemble and then selecting the first classifiers in the ordered sequence. Experiments in benchmark problems illustrate the improvements that can be obtained with this technique. Specifically, using a bagging ensemble of 101 CART trees as a starting point, only the 21 trees of the pruned ordered ensemble need to be stored in memory. Depending on the classification task, on average, only 5 to 12 of these 21 classifiers are queried to compute the predictions. The generalization performance achieved by this double pruning algorithm is similar to pruned ordered bagging and significantly better than standard bagging.

Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. G. Martínez-Muñoz, D. Hernández-Lobato and A. Suárez, "An analysis of ensemble pruning techniques based on ordered aggregation", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 2, pp. 245-249, February 2009, Several pruning strategies that can be used to reduce the size and increase the accuracy of bagging ensembles are analyzed. These heuristics select subsets of complementary classifiers that, when combined, can perform better than the whole ensemble. The pruning methods investigated are based on modifying the order of aggregation of classifiers in the ensemble. In the original bagging algorithm, the order of aggregation is left unspecified. When this order is random, the generalization error typically decreases as the number of classifiers in the ensemble increases. If an appropriate ordering for the aggregation process is devised, the generalization error reaches a minimum at intermediate numbers of classifiers. This minimum lies below the asymptotic error of bagging. Pruned ensembles are obtained by retaining a fraction of the classifiers in the ordered ensemble. The performance of these pruned ensembles is evaluated in several benchmark classification tasks under different training conditions. The results of this empirical investigation show that ordered aggregation can be used for the efficient generation of pruned ensembles that are competitive, in terms of performance and robustness of classification, with computationally more costly methods that directly select optimal or near-optimal subensembles., The authors acknowledge support form the Spanish Ministerio de Educación y Ciencia under Project TIN2007-66862-C02-02

Proceedings of 17th International Conference ICANN, Porto, Portugal, September 9-13, 2007., The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-540-74690-4_33, This article presents a comprehensive study of different ensemble pruning techniques applied to a bagging ensemble composed of decision stumps. Six different ensemble pruning methods are tested. Four of these are greedy strategies based on first reordering the elements of the ensemble according to some rule that takes into account the complementarity of the predictors with respect to the classification task. Subensembles of increasing size are then constructed by incorporating the ordered classifiers one by one. A halting criterion stops the aggregation process before the complete original ensemble is recovered. The other two approaches are selection techniques that attempt to identify optimal subensembles using either genetic algorithms or semidefinite programming. Experiments performed on 24 benchmark classification tasks show that the selection of a small subset (≈ 10 − 15%) of the original pool of stumps generated with bagging can significantly increase the accuracy and reduce the complexity of the ensemble., This work has been supported by Consejería de Educación de la Comunidad Autónoma de Madrid, European Social Fund, and the Dirección General de Investigación, grant TIN2004-07676-C02-02

The final publication is available at Springer via http://dx.doi.org/10.1007/11840817_25, Proceedings of 16th International Conference on Artificial Neural Networks, Athens, Greece, September 10-14, 2006, Part I, Recently, bump formations in attractor neural networks with distance dependent connectivities has become of increasing interest for investigation in the field of biological and computational neuroscience. Although the distance dependent connectivity is common in biological networks, a common fault of these network is the sharp drop of the number of patterns p that can remembered, when the activity changes from global to bump-like, than effectively makes these networks low effective. In this paper we represent a bump-based recursive network specially designed in order to increase its capacity, which is comparable with that of randomly connected sparse network. To this aim, we have tested a selection of 700 natural images on a network with N = 64K neurons with connectivity per neuron C. We have shown that the capacity of the network is of order of C, that is in accordance with the capacity of highly diluted network. Preserving the number of connections per neuron, a non-trivial behavior with the radius of the connectivity has been observed. Our results show that the decrement of the capacity of the bumpy network can be avoided., The authors acknowledge the financial support from the Spanish Grants DGI.M. CyT. FIS2005-1729, Plan de Promoción de la Investigación UNED and TIN 2004–07676-G01-01.We also thank David Dominguez for the fruitful discussion of the manuscript.

This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ICML '06 Proceedings of the 23rd international conference on Machine learning, http://dx.doi.org/10.1145/1143844.1143921, We present a novel ensemble pruning method based on reordering the classifiers obtained from bagging and then selecting a subset for aggregation. Ordering the classifiers generated in bagging makes it possible to build subensembles of increasing size by including first those classifiers that are expected to perform best when aggregated. Ensemble pruning is achieved by halting the aggregation process before all the classifiers generated are included into the ensemble. Pruned subensembles containing between 15% and 30% of the initial pool of classifiers, besides being smaller, improve the generalization performance of the full bagging ensemble in the classification problems investigated., The authors acknowledge financial support from the Spanish Dirección General de Investigación, project TIN2004-07676-C02-02.

The final publication is available at Springer via http://dx.doi.org/10.1007/11840817_19, Proceedings of 16th International Conference, Athens, Greece, September 10-14, 2006, This article investigates the properties of ensembles of neural networks, in which each network in the ensemble is constructed using a perturbed version of the training data. The perturbation consists in switching the class labels of a subset of training examples selected at random. Experiments on several UCI and synthetic datasets show that these class-switching ensembles can obtain improvements in classification performance over both individual networks and bagging ensembles., The authors acknowledge financial support from the Spanish Dirección General de Investigación, project TIN2004-07676-C02-02.

Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. D. Hernandez-Lobato, G. Martínez-Munoz, and A. Suarez, "Pruning in Ordered Regression Bagging Ensembles", in International Joint Conference on Neural Networks, 2006. IJCNN '06, Vancouver, BC, pp. 1266 - 1273, An efficient procedure for pruning regression ensembles is introduced. Starting from a bagging ensemble, pruning proceeds by ordering the regressors in the original ensemble and then selecting a subset for aggregation. Ensembles of increasing size are built by including first the regressors that perform best when aggregated. This strategy gives an approximate solution to the problem of extracting from the original ensemble the minimum error subensemble, which we prove to be NP-hard. Experiments show that pruned ensembles with only 20% of the initial regressors achieve better generalization accuracies than the complete bagging ensembles. The performance of pruned ensembles is analyzed by means of the bias-variance decomposition of the error., This research has been supported by the Spanish Direccion General de Investigación , project TIN2004-07676-C02-02.

The final publication is available at Springer via http://dx.doi.org/10.1007/11494669_26, Proceedings of 8th International Work-Conference on Artificial Neural Networks, IWANN 2005, Vilanova i la Geltrú, Barcelona, Spain, June 8-10, 2005., Boosting constructs a weighted classifier out of possibly weak learners by successively concentrating on those patterns harder to classify. While giving excellent results in many problems, its performance can deteriorate in the presence of patterns with incorrect labels. In this work we shall use parallel perceptrons (PP), a novel approach to the classical committee machines, to detect whether a pattern’s label may not be correct and also whether it is redundant in the sense of being well represented in the training sample by many other similar patterns. Among other things, PP allow to naturally define margins for hidden unit activations, that we shall use to define the above pattern types. This pattern type classification allows a more nuanced approach to boosting. In particular, the procedure we shall propose, balanced boosting, uses it to modify boosting distribution updates. As we shall illustrate numerically, balanced boosting gives very good results on relatively hard classification problems, particularly in some that present a marked imbalance between class sizes., With partial support of Spain’s CICyT, TIC 01–572.

The final publication is available at Springer via http://dx.doi.org/10.1007/11499305_60, Proceedings of First International Work-Conference on the Interplay Between Natural and Artificial Computation, IWINAC 2005, Las Palmas, Canary Islands, Spain, June 15-18, 2005, Boosting combines an ensemble of weak learners to construct a new weighted classifier that is often more accurate than any of its components. The construction of such learners, whose training sets depend on the performance of the previous members of the ensemble, is carried out by successively focusing on those patterns harder to classify. This fact deteriorates boosting’s results when dealing with malicious noise as, for instance, mislabeled training examples. In order to detect and avoid those noisy examples during the learning process, we propose the use of Parallel Perceptrons. Among other things, these novel machines allow to naturally define margins for hidden unit activations. We shall use these margins to detect which patterns may have an incorrect label and also which are safe, in the sense of being well represented in the training sample by many other similar patterns. As candidates for being noisy examples we shall reduce the weights of the former ones, and as a support for the overall detection procedure we shall augment the weights of the latter ones., With partial support of Spain’s CICyT, TIC 01–572, TIN 2004–07676

Proceedings of 22nd International Conference on Artificial Neural Networks, Lausanne, Switzerland, September 11-14, 2012, The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-33266-1_70, In this work we will apply Diffusion Maps (DM), a recent technique for dimensionality reduction and clustering, to build local models for wind energy forecasting. We will compare ridge regression models for K–means clusters obtained over DM features, against the models obtained for clusters constructed over the original meteorological data or principal components, and also against a global model. We will see that a combination of the DM model for the low wind power region and the global model elsewhere outperforms other options., With partial support of Spain’s CICyT, projects TIC 01–572, TIN2004–07676.

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-540-30212-4_15, Revised and Selected Papers of ECCV 2004 Workshop SMVP 2004, Prague, Czech Republic, May 16, 2004, The lack of sufficient machine readable images makes impossible the direct computation of natural image 4 × 4 block statistics and one has to resort to indirect approximated methods to reduce their domain space. A natural approach to this is to collect statistics over compressed images; if the reconstruction quality is good enough, these statistics will be sufficiently representative. However, a requirement for easier statistics collection is that the method used provides a uniform representation of the compression information across all patches, something for which codebook techniques are well suited. We shall follow this approach here, using a fractal compression–inspired quantization scheme to approximate a given patch B by a triplet (D B , μ B , σ B ) with σ B the patch’s contrast, μ B its brightness and D B a codebook approximation to the mean–variance normalization (B – μ B )/σ B of B. The resulting reduction of the domain space makes feasible the computation of entropy and mutual information estimates that, in turn, suggest a factorization of the approximation of p(B) ≃ p(D B , μ B , σ B ) as p(D B , μ B , σ B ) ≃ p(D B )p(μ)p(σ)Φ(|| ∇ ||), with Φ being a high contrast correction., With partial support of Spain’s CICyT, TIC 01–572

This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in CompSysTech '03 Proceedings of the 4th international conference conference on Computer systems and technologies: e-Learning, http://dx.doi.org/10.1145/973620.973661., Natural images form very small subset of all images. In spite of the fact, the direct computation of their block densities is not possible. On the other hand, the existence of various successful image compression methods, in particularly, the fractal compression, indicates that the compression somehow is able to capture and use at least part of the natural image statistics. In this work we show how hash based fractal image compression can be used to derive quite precise the entropies of 4 × 4 patches of the natural images. We state that the probability density in first order factorize to the probability densities of the contrast, the brightness and the index of the codebook blocks.

Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. A. Barbero, M. O. Franz, W. Van Drongelen, J. R. Dorronsoro, B. Schölkopf,and M. Grosse-Wentrup, "Implicit Wiener series analysis of epileptic seizure recordings", in Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2009. EMBC 2009, Minneapolis, MN, 2009, pp. 5304 - 5307, Implicit Wiener series are a powerful tool to build Volterra representations of time series with any degree of non-linearity. A natural question is then whether higher order representations yield more useful models. In this work we shall study this question for ECoG data channel relationships in epileptic seizure recordings, considering whether quadratic representations yield more accurate classifiers than linear ones. To do so we first show how to derive statistical information on the Volterra coefficient distribution and how to construct seizure classification patterns over that information. As our results illustrate, a quadratic model seems to provide no advantages over a linear one. Nevertheless, we shall also show that the interpretability of the implicit Wiener series provides insights into the inter-channel relationships of the recordings., Universidad Autónoma de Madrid - Instituto de Ingeniería del Conocimiento . Authors have been partially supported by Spain’s TIN 2007– 66862 and Cátedra UAM–IIC en Modelado y Predicción. The first author is kindly supported by the FPU–MEC grant reference AP2006–02285.