16,324 research outputs found
Popular Ensemble Methods: An Empirical Study
An ensemble consists of a set of individually trained classifiers (such as
neural networks or decision trees) whose predictions are combined when
classifying novel instances. Previous research has shown that an ensemble is
often more accurate than any of the single classifiers in the ensemble. Bagging
(Breiman, 1996c) and Boosting (Freund and Shapire, 1996; Shapire, 1990) are two
relatively new but popular methods for producing ensembles. In this paper we
evaluate these methods on 23 data sets using both neural networks and decision
trees as our classification algorithm. Our results clearly indicate a number of
conclusions. First, while Bagging is almost always more accurate than a single
classifier, it is sometimes much less accurate than Boosting. On the other
hand, Boosting can create ensembles that are less accurate than a single
classifier -- especially when using neural networks. Analysis indicates that
the performance of the Boosting methods is dependent on the characteristics of
the data set being examined. In fact, further results show that Boosting
ensembles may overfit noisy data sets, thus decreasing its performance.
Finally, consistent with previous studies, our work suggests that most of the
gain in an ensemble's performance comes in the first few classifiers combined;
however, relatively large gains can be seen up to 25 classifiers when Boosting
decision trees
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
Modular Autoencoders for Ensemble Feature Extraction
We introduce the concept of a Modular Autoencoder (MAE), capable of learning
a set of diverse but complementary representations from unlabelled data, that
can later be used for supervised tasks. The learning of the representations is
controlled by a trade off parameter, and we show on six benchmark datasets the
optimum lies between two extremes: a set of smaller, independent autoencoders
each with low capacity, versus a single monolithic encoding, outperforming an
appropriate baseline. In the present paper we explore the special case of
linear MAE, and derive an SVD-based algorithm which converges several orders of
magnitude faster than gradient descent.Comment: 18 pages, 8 figures, to appear in a special issue of The Journal Of
Machine Learning Research (vol.44, Dec 2015
A novel two stage scheme utilizing the test set for model selection in text classification
Text classification is a natural application domain for semi-supervised learning, as labeling documents is expensive, but on the other hand usually an abundance of unlabeled documents is available. We describe a novel simple two stage scheme based on dagging which allows for utilizing the test set in model selection. The dagging ensemble can also be used by itself instead of the original classifier. We evaluate the performance of a meta classifier choosing between various base learners and their respective dagging ensembles. The selection process seems to perform robustly especially for small percentages of available labels for training
Bagging ensemble selection for regression
Bagging ensemble selection (BES) is a relatively new ensemble learning strategy. The strategy can be seen as an ensemble of the ensemble selection from libraries of models (ES) strategy. Previous experimental results on binary classiļ¬cation problems have shown that using random trees as base classiļ¬ers, BES-OOB (the most successful variant of BES) is competitive with (and in many cases, superior to) other ensemble learning strategies, for instance, the original ES algorithm, stacking with linear regression, random forests or boosting. Motivated by the promising results in classiļ¬cation, this paper examines the predictive performance of the BES-OOB strategy for regression problems. Our results show that the BES-OOB strategy outperforms Stochastic Gradient Boosting and Bagging when using regression trees as the base learners. Our results also suggest that the advantage of using a diverse model library becomes clear when the model library size is relatively large. We also present encouraging results indicating that the non negative least squares algorithm is a viable approach for pruning an ensemble of ensembles
Building Combined Classifiers
This chapter covers different approaches that may be taken when building an
ensemble method, through studying specific examples of each approach from research
conducted by the authors. A method called Negative Correlation Learning illustrates a
decision level combination approach with individual classifiers trained co-operatively. The
Model level combination paradigm is illustrated via a tree combination method. Finally,
another variant of the decision level paradigm, with individuals trained independently
instead of co-operatively, is discussed as applied to churn prediction in the
telecommunications industry
Analysis of the Correlation Between Majority Voting Error and the Diversity Measures in Multiple Classifier Systems
Combining classifiers by majority voting (MV) has
recently emerged as an effective way of improving
performance of individual classifiers. However, the
usefulness of applying MV is not always observed and
is subject to distribution of classification outputs in a
multiple classifier system (MCS). Evaluation of MV
errors (MVE) for all combinations of classifiers in MCS
is a complex process of exponential complexity.
Reduction of this complexity can be achieved provided
the explicit relationship between MVE and any other
less complex function operating on classifier outputs is
found. Diversity measures operating on binary
classification outputs (correct/incorrect) are studied in
this paper as potential candidates for such functions.
Their correlation with MVE, interpreted as the quality
of a measure, is thoroughly investigated using artificial
and real-world datasets. Moreover, we propose new
diversity measure efficiently exploiting information
coming from the whole MCS, rather than its part, for
which it is applied
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