Ulf Johansson

Evolving decision trees using oracle guides

Some data mining problems require predictive models to be not only accurate but also comprehensible. Comprehensibility enables human inspection and understanding of the model, making it possible to trace why individual predictions are made. Since most high-accuracy techniques produce opaque models, accuracy is, in practice, regularly sacrificed for comprehensibility. One frequently studied technique, often able to reduce this accuracy vs. comprehensibility tradeoff, is rule extraction, i.e., the activity where another, transparent, model is generated from the opaque. In this paper, it is argued that techniques producing transparent models, either directly from the dataset, or from an opaque model, could benefit from using an oracle guide. In the experiments, genetic programming is used to evolve decision trees, and a neural network ensemble is used as the oracle guide. More specifically, the datasets used by the genetic programming when evolving the decision trees, consist of several different combinations of the original training data and “oracle data”, i.e., training or test data instances, together with corresponding predictions from the oracle. In total, seven different ways of combining regular training data with oracle data were evaluated, and the results, obtained on 26 UCI datasets, clearly show that the use of an oracle guide improved the performance. As a matter of fact, trees evolved using training data only had the worst test set accuracy of all setups evaluated. Furthermore, statistical tests show that two setups, both using the oracle guide, produced significantly more accurate trees, compared to the setup using training data only.

Conformal Prediction Using Decision Trees

Conformal prediction is a relatively new framework in which the predictive models output sets of predictions with a bound on the error rate, i.e., in a classification context, the probability of excluding the correct class label is lower than a predefined significance level. An investigation of the use of decision trees within the conformal prediction framework is presented, with the overall purpose to determine the effect of different algorithmic choices, including split criterion, pruning scheme and way to calculate the probability estimates. Since the error rate is bounded by the framework, the most important property of conformal predictors is efficiency, which concerns minimizing the number of elements in the output prediction sets. Results from one of the largest empirical investigations to date within the conformal prediction framework are presented, showing that in order to optimize efficiency, the decision trees should be induced using no pruning and with smoothed probability estimates. The choice of split criterion to use for the actual induction of the trees did not turn out to have any major impact on the efficiency. Finally, the experimentation also showed that when using decision trees, standard inductive conformal prediction was as efficient as the recently suggested method cross-conformal prediction. This is an encouraging results since cross-conformal prediction uses several decision trees, thus sacrificing the interpretability of a single decision tree.

Regression conformal prediction with random forests

Regression conformal prediction produces prediction intervals that are valid, i.e., the probability of excluding the correct target value is bounded by a predefined confidence level. The most important criterion when comparing conformal regressors is efficiency; the prediction intervals should be as tight (informative) as possible. In this study, the use of random forests as the underlying model for regression conformal prediction is investigated and compared to existing state-of-the-art techniques, which are based on neural networks and k-nearest neighbors. In addition to their robust predictive performance, random forests allow for determining the size of the prediction intervals by using out-of-bag estimates instead of requiring a separate calibration set. An extensive empirical investigation, using 33 publicly available data sets, was undertaken to compare the use of random forests to existing state-of-the-art conformal predictors. The results show that the suggested approach, on almost all confidence levels and using both standard and normalized nonconformity functions, produced significantly more efficient conformal predictors than the existing alternatives.

Evolved decision trees as conformal predictors

In conformal prediction, predictive models output sets of predictions with a bound on the error rate. In classification, this translates to that the probability of excluding the correct class is lower than a predefined significance level, in the long run. Since the error rate is guaranteed, the most important criterion for conformal predictors is efficiency. Efficient conformal predictors minimize the number of elements in the output prediction sets, thus producing more informative predictions. This paper presents one of the first comprehensive studies where evolutionary algorithms are used to build conformal predictors. More specifically, decision trees evolved using genetic programming are evaluated as conformal predictors. In the experiments, the evolved trees are compared to decision trees induced using standard machine learning techniques on 33 publicly available benchmark data sets, with regard to predictive performance and efficiency. The results show that the evolved trees are generally more accurate, and the corresponding conformal predictors more efficient, than their induced counterparts. One important result is that the probability estimates of decision trees when used as conformal predictors should be smoothed, here using the Laplace correction. Finally, using the more discriminating Brier score instead of accuracy as the optimization criterion produced the most efficient conformal predictions.

Ensemble member selection using multi-objective optimization

Both theory and a wealth of empirical studies have established that ensembles are more accurate than single predictive models. Unfortunately, the problem of how to maximize ensemble accuracy is, especially for classification, far from solved. In essence, the key problem is to find a suitable criterion, typically based on training or selection set performance, highly correlated with ensemble accuracy on novel data. Several studies have, however, shown that it is difficult to come up with a single measure, such as ensemble or base classifier selection set accuracy, or some measure based on diversity, that is a good general predictor for ensemble test accuracy. This paper presents a novel technique that for each learning task searches for the most effective combination of given atomic measures, by means of a genetic algorithm. Ensembles built from either neural networks or random forests were empirically evaluated on 30 UCI datasets. The experimental results show that when using the generated combined optimization criteria to rank candidate ensembles, a higher test set accuracy for the top ranked ensemble was achieved, compared to using ensemble accuracy on selection data alone. Furthermore, when creating ensembles from a pool of neural networks, the use of the generated combined criteria was shown to generally outperform the use of estimated ensemble accuracy as the single optimization criterion.

The Importance of Diversity in Neural Network Ensembles - An Empirical Investigation

When designing ensembles, it is almost an axiom that the base classifiers must be diverse in order for the ensemble to generalize well. Unfortunately, there is no clear definition of the key term diversity, leading to several diversity measures and many, more or less ad hoc, methods for diversity creation in ensembles. In addition, no specific diversity measure has shown to have a high correlation with test set accuracy. The purpose of this paper is to empirically evaluate ten different diversity measures, using neural network ensembles and 11 publicly available data sets. The main result is that all diversity measures evaluated, in this study too, show low or very low correlation with test set accuracy. Having said that, two measures; double fault and difficulty show slightly higher correlations compared to the other measures. The study furthermore shows that the correlation between accuracy measured on training or validation data and test set accuracy also is rather low. These results challenge ensemble design techniques where diversity is explicitly maximized or where ensemble accuracy on a hold-out set is used for optimization.

Automatically balancing accuracy and comprehensibility in predictive modeling

One specific problem, when performing predictive modeling, is the tradeoff between accuracy and comprehensibility. When comprehensible models are required, this normally rules out high-accuracy techniques like neural networks and committee machines. Therefore, an automated choice of a standard technique, known to generally produce sufficiently accurate and comprehensible models, would be of great value. In this paper, it is argued that this requirement is met by an ensemble of classifiers, followed by rule extraction. The proposed technique is demonstrated, using an ensemble of common classifiers and our rule extraction algorithm G-REX, on 17 publicly available data sets. The results presented demonstrate that the suggested technique performs very well. More specifically, the ensemble clearly outperforms the individual classifiers regarding accuracy, while the extracted models have accuracy similar to the individual classifiers. The extracted models are, however, significantly more compact than corresponding models created directly from the data set using the standard tool CART; thus providing higher comprehensibility.

Trade-off between accuracy and interpretability for predictive in silico modeling

BACKGROUND Accuracy concerns the ability of a model to make correct predictions, while interpretability concerns to what degree the model allows for human understanding. Models exhibiting the former property are many times more complex and opaque, while interpretable models may lack the necessary accuracy. The trade-off between accuracy and interpretability for predictive in silico modeling is investigated. METHOD A number of state-of-the-art methods for generating accurate models are compared with state-of-the-art methods for generating transparent models. CONCLUSION Results on 16 biopharmaceutical classification tasks demonstrate that, although the opaque methods generally obtain higher accuracies than the transparent ones, one often only has to pay a quite limited penalty in terms of predictive performance when choosing an interpretable model.

Genetic programming - a tool for flexible rule extraction

Although data mining is performed to support decision making, many of the most powerful techniques, like neural networks and ensembles, produce opaque models. This lack of interpretability is an obvious disadvantage, since decision makers normally require some sort of explanation before taking action. To achieve comprehensibility, accuracy is often sacrificed by the use of simpler, transparent models, such as decision trees. Another alternative is rule extraction; i.e. to transform the opaque model into a comprehensible model, keeping acceptable accuracy. We have previously suggested a rule extraction algorithm named G-REX, which is based on genetic programming. One key property of G-REX, due to the use of genetic programming, is the possibility to use different representation languages. In this study we apply G-REX to estimation tasks. More specifically, three representation languages are evaluated using eight publicly available data sets. The quality of the extracted rules is compared to two standard techniques producing comprehensible models; multiple linear regression and the decision tree algorithm C&RT. The results show that G-REX outperforms the standard techniques, but that the choice of representation language is important.

Building Neural Network Ensembles using Genetic Programming

In this paper we present and evaluate a novel algorithm for ensemble creation. The main idea of the algorithm is to first independently train a fixed number of neural networks (here ten) and then use genetic programming to combine these networks into an ensemble. The use of genetic programming makes it possible to not only consider ensembles of different sizes, but also to use ensembles as intermediate building blocks. The final result is therefore more correctly described as an ensemble of neural network ensembles. The experiments show that the proposed method, when evaluated on 22 publicly available data sets, obtains very high accuracy, clearly outperforming the other methods evaluated. In this study several micro techniques are used, and we believe that they all contribute to the increased performance. One such micro technique, aimed at reducing overtraining, is the training method, called tombola training, used during genetic evolution. When using tombola training, training data is regularly resampled into new parts, called training groups. Each ensemble is then evaluated on every training group and the actual fitness is determined solely from the result on the hardest part.