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

Solving Multiclass Learning Problems via Error-Correcting Output Codes

Multiclass learning problems involve finding a definition for an unknown function f(x) whose range is a discrete set containing k &gt 2 values (i.e., k ``classes''). The definition is acquired by studying collections of training examples of the form [x_i, f (x_i)]. Existing approaches to multiclass learning problems include direct application of multiclass algorithms such as the decision-tree algorithms C4.5 and CART, application of binary concept learning algorithms to learn individual binary functions for each of the k classes, and application of binary concept learning algorithms with distributed output representations. This paper compares these three approaches to a new technique in which error-correcting codes are employed as a distributed output representation. We show that these output representations improve the generalization performance of both C4.5 and backpropagation on a wide range of multiclass learning tasks. We also demonstrate that this approach is robust with respect to changes in the size of the training sample, the assignment of distributed representations to particular classes, and the application of overfitting avoidance techniques such as decision-tree pruning. Finally, we show that---like the other methods---the error-correcting code technique can provide reliable class probability estimates. Taken together, these results demonstrate that error-correcting output codes provide a general-purpose method for improving the performance of inductive learning programs on multiclass problems.Comment: See http://www.jair.org/ for any accompanying file

COMET: A Recipe for Learning and Using Large Ensembles on Massive Data

COMET is a single-pass MapReduce algorithm for learning on large-scale data. It builds multiple random forest ensembles on distributed blocks of data and merges them into a mega-ensemble. This approach is appropriate when learning from massive-scale data that is too large to fit on a single machine. To get the best accuracy, IVoting should be used instead of bagging to generate the training subset for each decision tree in the random forest. Experiments with two large datasets (5GB and 50GB compressed) show that COMET compares favorably (in both accuracy and training time) to learning on a subsample of data using a serial algorithm. Finally, we propose a new Gaussian approach for lazy ensemble evaluation which dynamically decides how many ensemble members to evaluate per data point; this can reduce evaluation cost by 100X or more

Parameter Tuning Using Gaussian Processes

Most machine learning algorithms require us to set up their parameter values before applying these algorithms to solve problems. Appropriate parameter settings will bring good performance while inappropriate parameter settings generally result in poor modelling. Hence, it is necessary to acquire the “best” parameter values for a particular algorithm before building the model. The “best” model not only reflects the “real” function and is well fitted to existing points, but also gives good performance when making predictions for new points with previously unseen values. A number of methods exist that have been proposed to optimize parameter values. The basic idea of all such methods is a trial-and-error process whereas the work presented in this thesis employs Gaussian process (GP) regression to optimize the parameter values of a given machine learning algorithm. In this thesis, we consider the optimization of only two-parameter learning algorithms. All the possible parameter values are specified in a 2-dimensional grid in this work. To avoid brute-force search, Gaussian Process Optimization (GPO) makes use of “expected improvement” to pick useful points rather than validating every point of the grid step by step. The point with the highest expected improvement is evaluated using cross-validation and the resulting data point is added to the training set for the Gaussian process model. This process is repeated until a stopping criterion is met. The final model is built using the learning algorithm based on the best parameter values identified in this process. In order to test the effectiveness of this optimization method on regression and classification problems, we use it to optimize parameters of some well-known machine learning algorithms, such as decision tree learning, support vector machines and boosting with trees. Through the analysis of experimental results obtained on datasets from the UCI repository, we find that the GPO algorithm yields competitive performance compared with a brute-force approach, while exhibiting a distinct advantage in terms of training time and number of cross-validation runs. Overall, the GPO method is a promising method for the optimization of parameter values in machine learning