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Yayın Calculating the VC-dimension of decision trees(IEEE, 2009) Aslan, Özlem; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemWe propose an exhaustive search algorithm that calculates the VC-dimension of univariate decision trees with binary features. The VC-dimension of the univariate decision tree with binary features depends on (i) the VC-dimension values of the left and right subtrees, (ii) the number of inputs, and (iii) the number of nodes in the tree. From a training set of example trees whose VC-dimensions are calculated by exhaustive search, we fit a general regressor to estimate the VC-dimension of any binary tree. These VC-dimension estimates are then used to get VC-generalization bounds for complexity control using SRM in decision trees, i.e., pruning. Our simulation results shows that SRM-pruning using the estimated VC-dimensions finds trees that are as accurate as those pruned using cross-validation.Yayın Incremental construction of classifier and discriminant ensembles(Elsevier Science Inc, 2009-04-15) Ulaş, Aydın; Semerci, Murat; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemWe discuss approaches to incrementally construct an ensemble. The first constructs an ensemble of classifiers choosing a subset from a larger set, and the second constructs an ensemble of discriminants, where a classifier is used for some classes only. We investigate criteria including accuracy, significant improvement, diversity, correlation, and the role of search direction. For discriminant ensembles, we test subset selection and trees. Fusion is by voting or by a linear model. Using 14 classifiers on 38 data sets. incremental search finds small, accurate ensembles in polynomial time. The discriminant ensemble uses a subset of discriminants and is simpler, interpretable, and accurate. We see that an incremental ensemble has higher accuracy than bagging and random subspace method; and it has a comparable accuracy to AdaBoost. but fewer classifiers.Yayın Cost-conscious comparison of supervised learning algorithms over multiple data sets(Elsevier Sci Ltd, 2012-04) Ulaş, Aydın; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemIn the literature, there exist statistical tests to compare supervised learning algorithms on multiple data sets in terms of accuracy but they do not always generate an ordering. We propose Multi(2)Test, a generalization of our previous work, for ordering multiple learning algorithms on multiple data sets from "best" to "worst" where our goodness measure is composed of a prior cost term additional to generalization error. Our simulations show that Multi2Test generates orderings using pairwise tests on error and different types of cost using time and space complexity of the learning algorithms.Yayın Eigenclassifiers for combining correlated classifiers(Elsevier Science Inc, 2012-03-15) Ulaş, Aydın; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemIn practice, classifiers in an ensemble are not independent. This paper is the continuation of our previous work on ensemble subset selection [A. Ulas, M. Semerci, O.T. Yildiz, E. Alpaydin, Incremental construction of classifier and discriminant ensembles, Information Sciences, 179 (9) (2009) 1298-1318] and has two parts: first, we investigate the effect of four factors on correlation: (i) algorithms used for training, (ii) hyperparameters of the algorithms, (iii) resampled training sets, (iv) input feature subsets. Simulations using 14 classifiers on 38 data sets indicate that hyperparameters and overlapping training sets have higher effect on positive correlation than features and algorithms. Second, we propose postprocessing before fusing using principal component analysis (PCA) to form uncorrelated eigenclassifiers from a set of correlated experts. Combining the information from all classifiers may be better than subset selection where some base classifiers are pruned before combination, because using all allows redundancy.
