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  • 1.
    Jansson, Karl
    et al.
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Sundell, Håkan
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Boström, Henrik
    Stockholms Universitet.
    gpuRF and gpuERT: Efficient and Scalable GPU Algorithms for Decision Tree Ensembles2014Inngår i: Parallel & Distributed Processing Symposium Workshops (IPDPSW), 2014 IEEE International, 2014, s. 1612-1621Konferansepaper (Fagfellevurdert)
  • 2.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Löfström, Tuve
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Conformal Prediction Using Decision Trees2013Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.

  • 3.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Löfström, Tuve
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Linusson, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Regression conformal prediction with random forests2014Inngår i: Machine Learning, ISSN 0885-6125, E-ISSN 1573-0565, Vol. 97, nr 1-2, s. 155-176Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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 stateof- 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.

  • 4.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    König, Rikard
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Linusson, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Löfström, Tuve
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Rule Extraction with Guaranteed Fidelity2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper extends the conformal prediction framework to rule extraction, making it possible to extract interpretable models from opaque models in a setting where either the infidelity or the error rate is bounded by a predefined significance level. Experimental results on 27 publicly available data sets show that all three setups evaluated produced valid and rather efficient conformal predictors. The implication is that augmenting rule extraction with conformal prediction allows extraction of models where test set errors or test sets infidelities are guaranteed to be lower than a chosen acceptable level. Clearly this is beneficial for both typical rule extraction scenarios, i.e., either when the purpose is to explain an existing opaque model, or when it is to build a predictive model that must be interpretable.

  • 5.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    König, Rikard
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Löfström, Tuwe
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Evolved Decision Trees as Conformal Predictors2013Konferansepaper (Fagfellevurdert)
    Abstract [en]

    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.

  • 6.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Löfström, Tuve
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Overproduce-and-Select: The Grim Reality2013Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Overproduce-and-select (OPAS) is a frequently used paradigm for building ensembles. In static OPAS, a large number of base classifiers are trained, before a subset of the available models is selected to be combined into the final ensemble. In general, the selected classifiers are supposed to be accurate and diverse for the OPAS strategy to result in highly accurate ensembles, but exactly how this is enforced in the selection process is not obvious. Most often, either individual models or ensembles are evaluated, using some performance metric, on available and labeled data. Naturally, the underlying assumption is that an observed advantage for the models (or the resulting ensemble) will carry over to test data. In the experimental study, a typical static OPAS scenario, using a pool of artificial neural networks and a number of very natural and frequently used performance measures, is evaluated on 22 publicly available data sets. The discouraging result is that although a fairly large proportion of the ensembles obtained higher test set accuracies, compared to using the entire pool as the ensemble, none of the selection criteria could be used to identify these highly accurate ensembles. Despite only investigating a specific scenario, we argue that the settings used are typical for static OPAS, thus making the results general enough to question the entire paradigm.

  • 7.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Löfström, Tuve
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Random Brains2013Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, we introduce and evaluate a novel method, called random brains, for producing neural network ensembles. The suggested method, which is heavily inspired by the random forest technique, produces diversity implicitly by using bootstrap training and randomized architectures. More specifically, for each base classifier multilayer perceptron, a number of randomly selected links between the input layer and the hidden layer are removed prior to training, thus resulting in potentially weaker but more diverse base classifiers. The experimental results on 20 UCI data sets show that random brains obtained significantly higher accuracy and AUC, compared to standard bagging of similar neural networks not utilizing randomized architectures. The analysis shows that the main reason for the increased ensemble performance is the ability to produce effective diversity, as indicated by the increase in the difficulty diversity measure.

  • 8.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Löfström, Tuve
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Sundell, Håkan
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Linnusson, Henrik
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Gidenstam, Anders
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Boström, Henrik
    School of Information and Communication Technology, Royal Institute of Technology, Sweden.
    Venn predictors for well-calibrated probability estimation trees2018Inngår i: 7th Symposium on Conformal and Probabilistic Prediction and Applications: COPA 2018, 11-13 June 2018, Maastricht, The Netherlands / [ed] Alex J. Gammerman and Vladimir Vovk and Zhiyuan Luo and Evgueni N. Smirnov and Ralf L. M. Peeter, 2018, s. 3-14Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Successful use of probabilistic classification requires well-calibrated probability estimates, i.e., the predicted class probabilities must correspond to the true probabilities. The standard solution is to employ an additional step, transforming the outputs from a classifier into probability estimates. In this paper, Venn predictors are compared to Platt scaling and isotonic regression, for the purpose of producing well-calibrated probabilistic predictions from decision trees. The empirical investigation, using 22 publicly available datasets, showed that the probability estimates from the Venn predictor were extremely well-calibrated. In fact, in a direct comparison using the accepted reliability metric, the Venn predictor estimates were the most exact on every data set.

  • 9.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Sönströd, Cecilia
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Linusson, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Regression Trees for Streaming Data with Local Performance Guarantees2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Online predictive modeling of streaming data is a key task for big data analytics. In this paper, a novel approach for efficient online learning of regression trees is proposed, which continuously updates, rather than retrains, the tree as more labeled data become available. A conformal predictor outputs prediction sets instead of point predictions; which for regression translates into prediction intervals. The key property of a conformal predictor is that it is always valid, i.e., the error rate, on novel data, is bounded by a preset significance level. Here, we suggest applying Mondrian conformal prediction on top of the resulting models, in order to obtain regression trees where not only the tree, but also each and every rule, corresponding to a path from the root node to a leaf, is valid. Using Mondrian conformal prediction, it becomes possible to analyze and explore the different rules separately, knowing that their accuracy, in the long run, will not be below the preset significance level. An empirical investigation, using 17 publicly available data sets, confirms that the resulting rules are independently valid, but also shows that the prediction intervals are smaller, on average, than when only the global model is required to be valid. All-in-all, the suggested method provides a data miner or a decision maker with highly informative predictive models of streaming data.

  • 10.
    Linusson, Henrik
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Johansson, Ulf
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Löfström, Tuve
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Efficiency Comparison of Unstable Transductive and Inductive Conformal Classifiers2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In the conformal prediction literature, it appears axiomatic that transductive conformal classifiers possess a higher predictive efficiency than inductive conformal classifiers, however, this depends on whether or not the nonconformity function tends to overfit misclassified test examples. With the conformal prediction framework’s increasing popularity, it thus becomes necessary to clarify the settings in which this claim holds true. In this paper, the efficiency of transductive conformal classifiers based on decision tree, random forest and support vector machine classification models is compared to the efficiency of corresponding inductive conformal classifiers. The results show that the efficiency of conformal classifiers based on standard decision trees or random forests is substantially improved when used in the inductive mode, while conformal classifiers based on support vector machines are more efficient in the transductive mode. In addition, an analysis is presented that discusses the effects of calibration set size on inductive conformal classifier efficiency.

  • 11.
    Linusson, Henrik
    et al.
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Norinder, Ulf
    Swetox, Karolinska Institutet.
    Boström, Henrik
    Dept. of Computer Science and Informatics, Stockholm University.
    Johansson, Ulf
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    Löfström, Tuve
    Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT.
    On the Calibration of Aggregated Conformal Predictors2017Inngår i: Proceedings of Machine Learning Research, 2017Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Conformal prediction is a learning framework that produces models that associate witheach of their predictions a measure of statistically valid confidence. These models are typi-cally constructed on top of traditional machine learning algorithms. An important result ofconformal prediction theory is that the models produced are provably valid under relativelyweak assumptions—in particular, their validity is independent of the specific underlyinglearning algorithm on which they are based. Since validity is automatic, much research onconformal predictors has been focused on improving their informational and computationalefficiency. As part of the efforts in constructing efficient conformal predictors, aggregatedconformal predictors were developed, drawing inspiration from the field of classification andregression ensembles. Unlike early definitions of conformal prediction procedures, the va-lidity of aggregated conformal predictors is not fully understood—while it has been shownthat they might attain empirical exact validity under certain circumstances, their theo-retical validity is conditional on additional assumptions that require further clarification.In this paper, we show why validity is not automatic for aggregated conformal predictors,and provide a revised definition of aggregated conformal predictors that gains approximatevalidity conditional on properties of the underlying learning algorithm.

  • 12.
    Löfström, Tuve
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Johansson, Ulf
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Effective Utilization of Data in Inductive Conformal Prediction2013Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Conformal prediction is a new framework producing region predictions with a guaranteed error rate. Inductive conformal prediction (ICP) was designed to significantly reduce the computational cost associated with the original transductive online approach. The drawback of inductive conformal prediction is that it is not possible to use all data for training, since it sets aside some data as a separate calibration set. Recently, cross-conformal prediction (CCP) and bootstrap conformal prediction (BCP) were proposed to overcome that drawback of inductive conformal prediction. Unfortunately, CCP and BCP both need to build several models for the calibration, making them less attractive. In this study, focusing on bagged neural network ensembles as conformal predictors, ICP, CCP and BCP are compared to the very straightforward and cost-effective method of using the out-of-bag estimates for the necessary calibration. Experiments on 34 publicly available data sets conclusively show that the use of out-of-bag estimates produced the most efficient conformal predictors, making it the obvious preferred choice for ensembles in the conformal prediction framework.

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