Learning When Training Data are Costly: The Effect of Class Distribution on Tree Induction

For large, real-world inductive learning problems, the number of training examples often must be limited due to the costs associated with procuring, preparing, and storing the training examples and/or the computational costs associated with learning from them. In such circumstances, one question of practical importance is: if only n training examples can be selected, in what proportion should the classes be represented? In this article we help to answer this question by analyzing, for a fixed training-set size, the relationship between the class distribution of the training data and the performance of classification trees induced from these data. We study twenty-six data sets and, for each, determine the best class distribution for learning. The naturally occurring class distribution is shown to generally perform well when classifier performance is evaluated using undifferentiated error rate (0/1 loss). However, when the area under the ROC curve is used to evaluate classifier performance, a balanced distribution is shown to perform well. Since neither of these choices for class distribution always generates the best-performing classifier, we introduce a budget-sensitive progressive sampling algorithm for selecting training examples based on the class associated with each example. An empirical analysis of this algorithm shows that the class distribution of the resulting training set yields classifiers with good (nearly-optimal) classification performance

Asteroseismology and calibration of alpha Cen binary system

Using the oscillation frequencies of alpha Cen A recently discovered by Bouchy & Carrier, the available astrometric, photometric and spectroscopic data, we tried to improve the calibration of the visual binary system alpha Cen. With the revisited masses of Pourbaix et al. (2002) we do not succeed to obtain a solution satisfying all the seismic observational constraints. Relaxing the constraints on the masses, we have found an age t_alpha Cen=4850+-500 Myr, an initial helium mass fraction Y_i = 0.300+-0.008, and an initial metallicity (Z/X)_i=0.0459+-0.0019, with M_A=1.100+-0.006M_o and M_B=0.907+-0.006M_o for alpha Cen A&B.Comment: accepted for publication as a letter in A&