Probabilistic reframing for cost-sensitive regression

© ACM, 2014. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Knowledge Discovery from Data (TKDD), VOL. 8, ISS. 4, (October 2014) http://doi.acm.org/10.1145/2641758Common-day applications of predictive models usually involve the full use of the available contextual information. When the operating context changes, one may fine-tune the by-default (incontextual) prediction or may even abstain from predicting a value (a reject). Global reframing solutions, where the same function is applied to adapt the estimated outputs to a new cost context, are possible solutions here. An alternative approach, which has not been studied in a comprehensive way for regression in the knowledge discovery and data mining literature, is the use of a local (e.g., probabilistic) reframing approach, where decisions are made according to the estimated output and a reliability, confidence, or probability estimation. In this article, we advocate for a simple two-parameter (mean and variance) approach, working with a normal conditional probability density. Given the conditional mean produced by any regression technique, we develop lightweight “enrichment” methods that produce good estimates of the conditional variance, which are used by the probabilistic (local) reframing methods. We apply these methods to some very common families of costsensitive problems, such as optimal predictions in (auction) bids, asymmetric loss scenarios, and rejection rules.This work was supported by the MEC/MINECO projects CONSOLIDER-INGENIO CSD2007-00022 and TIN 2010-21062-C02-02, and TIN 2013-45732-C4-1-P and GVA projects PROMETEO/2008/051 and PROMETEO2011/052. Finally, part of this work was motivated by the REFRAME project (http://www.reframe-d2k.org) granted by the European Coordinated Research on Long-term Challenges in Information and Communication Sciences & Technologies ERA-Net (CHIST-ERA) and funded by Ministerio de Economia y Competitividad in Spain (PCIN-2013-037).Hernández Orallo, J. (2014). Probabilistic reframing for cost-sensitive regression. ACM Transactions on Knowledge Discovery from Data. 8(4):1-55. https://doi.org/10.1145/2641758S15584G. Bansal, A. Sinha, and H. Zhao. 2008. Tuning data mining methods for cost-sensitive regression: A study in loan charge-off forecasting. Journal of Management Information System 25, 3 (Dec. 2008), 315--336.A. P. Basu and N. Ebrahimi. 1992. Bayesian approach to life testing and reliability estimation using asymmetric loss function. Journal of Statistical Planning and Inference 29, 1--2 (1992), 21--31.A. Bella, C. Ferri, J. Hernández-Orallo, and M. J. Ramírez-Quintana. 2010. Quantification via probability estimators. In Proceedings of the 2010 IEEE International Conference on Data Mining. IEEE, 737--742.A. Bella, C. Ferri, J. Hernández-Orallo, and M. J. Ramírez-Quintana. 2013. Aggregative quantification for regression. Data Mining and Knowledge Discovery (2013), 1--44.A. Bella, C. Ferri, J. Hernández-Orallo, and M. J. Ramírez-Quintana. 2009. Calibration of machine learning models. In Handbook of Research on Machine Learning Applications. IGI Global, 128--146.A. Bella, C. Ferri, J. Hernández-Orallo, and M. J. Ramírez-Quintana. 2011. Using negotiable features for prescription problems. Computing 91, 2 (2011), 135--168.J. Bi and K. P. Bennett. 2003. Regression error characteristic curves. In Proceedings of the 20th International Conference on Machine Learning (ICML’03).Z. Bosnić and I. Kononenko. 2008. Comparison of approaches for estimating reliability of individual regression predictions. Data & Knowledge Engineering 67, 3 (2008), 504--516.Z. Bosnić and I. Kononenko. 2009. An overview of advances in reliability estimation of individual predictions in machine learning. Intelligent Data Analysis 13, 2 (2009), 385--401.L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone. 1984. Classification and Regression Trees. Wadsworth.P. F. Christoffersen and F. X. Diebold. 1996. Further results on forecasting and model selection under asymmetric loss. Journal of Applied Econometrics 11, 5 (1996), 561--571.P. F. Christoffersen and F. X. Diebold. 1997. Optimal prediction under asymmetric loss. Econometric Theory 13 (1997), 808--817.I. Cohen and M. Goldszmidt. 2004. Properties and benefits of calibrated classifiers. Knowledge Discovery in Databases: PKDD 2004 (2004), 125--136.S. Crone. 2002. Training artificial neural networks for time series prediction using asymmetric cost functions. In Proceedings of the 9th International Conference on Neural Information Processing.J. Demšar. 2006. Statistical comparisons of classifiers over multiple data sets. The Journal of Machine Learning Research 7 (2006), 1--30.M. Dumas, L. Aldred, G. Governatori, and A. H. M. Ter Hofstede. 2005. Probabilistic automated bidding in multiple auctions. Electronic Commerce Research 5, 1 (2005), 25--49.C. Elkan. 2001. The foundations of cost-sensitive learning. In Proceedings of the 17th International Conference on Artificial Intelligence (’01), Bernhard Nebel (Ed.). San Francisco, CA, 973--978.G. Elliott and A. Timmermann. 2004. Optimal forecast combinations under general loss functions and forecast error distributions. Journal of Econometrics 122, 1 (2004), 47--79.T. Fawcett. 2006a. An introduction to ROC analysis. Pattern Recognition Letters 27, 8 (2006), 861--874.T. Fawcett. 2006b. ROC graphs with instance-varying costs. Pattern Recognition Letters 27, 8 (2006), 882--891.C. Ferri, P. Flach, and J. Hernández-Orallo. 2002. Learning decision trees using the area under the ROC curve. In Proceedings of the International Conference on Machine Learning. 139--146.C. Ferri, P. Flach, and J. Hernández-Orallo. 2003. Improving the AUC of probabilistic estimation trees. In Proceedings of the 14th European Conference on Machine Learning (ECML’03). Springer, 121--132.C. Ferri and J. Hernández-Orallo. 2004. Cautious classifiers. In ROC Analysis in Artificial Intelligence, 1st International Workshop, ROCAI-2004, Valencia, Spain, August 22, 2004, J. Hernández-Orallo, C. Ferri, N. Lachiche, and P. A. Flach (Eds.). 27--36.P. Flach. 2012. Machine Learning: The Art and Science of Algorithms that Make Sense of Data. Cambridge University Press.G. Forman. 2008. Quantifying counts and costs via classification. Data Mining and Knowledge Discovery 17, 2 (2008), 164--206.S. García and F. Herrera. 2008. An extension on statistical comparisons of classifiers over multiple data sets for all pairwise comparisons. The Journal of Machine Learning Research 9, 2677--2694 (2008), 66.R. Ghani. 2005. Price prediction and insurance for online auctions. In Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining (KDD’05). ACM, New York, NY, 411--418.C. W. J. Granger. 1969. Prediction with a generalized cost of error function. Operational Research (1969), 199--207.C. W. J. Granger. 1999. Outline of forecast theory using generalized cost functions. Spanish Economic Review 1, 2 (1999), 161--173.P. Hall, J. Racine, and Q. Li. 2004. Cross-validation and the estimation of conditional probability densities. Journal of the American Statistical Association 99, 468 (2004), 1015--1026.P. Hall, R. C. L. Wolff, and Q. Yao. 1999. Methods for estimating a conditional distribution function. Journal of the American Statistical Association (1999), 154--163.T. J. Hastie, R. J. Tibshirani, and J. H. Friedman. 2009. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer.J. Hernández-Orallo. 2013. ROC curves for regression. Pattern Recognition 46, 12 (2013), 3395--3411.J. Hernández-Orallo, P. Flach, and C. Ferri. 2012. A unified view of performance metrics: Translating threshold choice into expected classification loss. Journal of Machine Learning Research 13 (2012), 2813--2869.J. Hernández-Orallo, P. Flach, and C. Ferri. 2013. ROC curves in cost space. Machine Learning 93, 1 (2013), 71--91.J. N. Hwang, S. R. Lay, and A. Lippman. 1994. Nonparametric multivariate density estimation: A comparative study. IEEE Transactions on Signal Processing 42, 10 (1994), 2795--2810.R. J. Hyndman, D. M. Bashtannyk, and G. K. Grunwald. 1996. Estimating and visualizing conditional densities. Journal of Computational and Graphical Statistics (1996), 315--336.N. Japkowicz and M. Shah. 2011. Evaluating Learning Algorithms: A Classification Perspective. Cambridge University Press.M. Jino, B. T. de Abreu, and others. 2010. Machine learning methods and asymmetric cost function to estimate execution effort of software testing. In Proceedings of the 2010 3rd International Conference on Software Testing, Verification and Validation (ICST’10). IEEE, 275--284.B. Kitts and B. Leblanc. 2004. Optimal bidding on keyword auctions. Electronic Markets 14, 3 (2004), 186--201.N. Lachiche and P. Flach. 2003. Improving accuracy and cost of two-class and multi-class probabilistic classifiers using ROC curves. In Proceedings of the International Conference on Machine Learning, Vol. 20-1. 416.H. Papadopoulos. 2008. Inductive conformal prediction: Theory and application to neural networks. Tools in Artificial Intelligence 18 (2008), 315--330.H. Papadopoulos, K. Proedrou, V. Vovk, and A. Gammerman. 2002. Inductive confidence machines for regression. In Machine Learning: ECML 2002, Tapio Elomaa, Heikki Mannila, and Hannu Toivonen (Eds.). Lecture Notes in Computer Science, Vol. 2430. Springer, Berlin, 185--194.H. Papadopoulos, V. Vovk, and A. Gammerman. 2011. Regression conformal prediction with nearest neighbours. Journal of Artificial Intelligence Research 40, 1 (2011), 815--840.T. Pietraszek. 2007. On the use of ROC analysis for the optimization of abstaining classifiers. Machine Learning 68, 2 (2007), 137--169.J. C. Platt. 1999. Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In Advances in Large Margin Classifiers. MIT Press, Boston, 61--74.F. Provost and P. Domingos. 2003. Tree induction for probability-based ranking. Machine Learning 52, 3 (2003), 199--215.R Team and others. 2012. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.R. Ribeiro. 2011. Utility-based Regression. PhD thesis, Department of Computer Science, Faculty of Sciences, University of Porto.M. Rosenblatt. 1969. Conditional probability density and regression estimators. Multivariate Analysis II 25 (1969), 31.S. Rosset, C. Perlich, and B. Zadrozny. 2007. Ranking-based evaluation of regression models. Knowledge and Information Systems 12, 3 (2007), 331--353.R. E. Schapire, P. Stone, D. McAllester, M. L. Littman, and J. A. Csirik. 2002. Modeling auction price uncertainty using boosting-based conditional density estimation. In Proceedings of the International Conference on Machine Learning. 546--553.G. Shafer and V. Vovk. 2008. A tutorial on conformal prediction. Journal of Machine Learning Research 9 (2008), 371--421.J. A. Swets, R. M. Dawes, and J. Monahan. 2000. Better decisions through science. Scientific American 283, 4 (Oct. 2000), 82--87.R. D. Thompson and A. P. Basu. 1996. Asymmetric loss functions for estimating system reliability. In Bayesian Analysis in Statistics and Econometrics. John Wiley & Sons, 471--482.L. Torgo. 2005. Regression error characteristic surfaces. In Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining. ACM, 697--702.L. Torgo. 2010. Data Mining with R. Chapman and Hall/CRC Press.L. Torgo and R. Ribeiro. 2007. Utility-based regression. Knowledge Discovery in Databases: PKDD 2007. 597--604.L. Torgo and R. Ribeiro. 2009. Precision and recall for regression. In Discovery Science. Springer, 332--346.P. Turney. 2000. Types of cost in inductive concept learning. Canada National Research Council Publications Archive.L. Wasserman. 2006. All of Nonparametric Statistics. Springer-Verlag, New York.M. P. Wellman, D. M. Reeves, K. M. Lochner, and Y. Vorobeychik. 2004. Price prediction in a trading agent competition. Journal of Artificial Intelligence Research 21 (2004), 19--36.K. Yu and M. C. Jones. 2004. Likelihood-based local linear estimation of the conditional variance function. Journal of the American Statistical Association 99, 465 (2004), 139--144.B. Zadrozny and C. Elkan. 2002. Transforming classifier scores into accurate multiclass probability estimates. In Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 694--699.A. Zellner. 1986. Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association (1986), 446--451.H. Zhao, A. P. Sinha, and G. Bansal. 2011. An extended tuning method for cost-sensitive regression and forecasting. Decision Support Systems

Reframing in context: A systematic approach for model reuse in machine learning

We describe a systematic approach called reframing, defined as the process of preparing a machine learning model (e.g., a classifier) to perform well over a range of operating contexts. One way to achieve this is by constructing a versatile model, which is not fitted to a particular context, and thus enables model reuse. We formally characterise reframing in terms of a taxonomy of context changes that may be encountered and distinguish it from model retraining and revision. We then identify three main kinds of reframing: input reframing, output reframing and structural reframing. We proceed by reviewing areas and problems where some notion of reframing has already been developed and shown useful, if under different names: re-optimising, adapting, tuning, thresholding, etc. This exploration of the landscape of reframing allows us to identify opportunities where reframing might be possible and useful. Finally, we describe related approaches in terms of the problems they address or the kind of solutions they obtain. The paper closes with a re-interpretation of the model development and deployment process with the use of reframing.We thank the anonymous reviewers for their comments, which have helped to improve this paper significantly. This work was supported by the REFRAME project, granted by the European Coordinated Research on Long-term Challenges in Information and Communication Sciences Technologies ERA-Net (CHIST-ERA), funded by their respective national funding agencies in the UK (EPSRC, EP/K018728), France and Spain (MINECO, PCIN-2013-037). It has also been partially supported by the EU (FEDER) and Spanish MINECO grant TIN2015-69175-C4-1-R and by Generalitat Valenciana PROMETEOII/2015/013.Hernández Orallo, J.; Martínez Usó, A.; Prudencio, RBC.; Kull, M.; Flach, P.; Ahmed, CF.; Lachiche, N. (2016). Reframing in context: A systematic approach for model reuse in machine learning. AI Communications. 29(5):551-566. https://doi.org/10.3233/AIC-160705S55156629

Proceedings from the Synthetic LBD International Seminar

On May 9, 2017, we hosted a seminar to discuss the conditions necessary to im- plement the SynLBD approach with interested parties, with the goal of providing a straightforward toolkit to implement the same procedure on other data. The proceed- ings summarize the discussions during the workshop

Multidimensional Prediction Models When the Resolution Context Changes

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-23525-7_31Multidimensional data is systematically analysed at multiple granularities by applying aggregate and disaggregate operators (e.g., by the use of OLAP tools). For instance, in a supermarket we may want to predict sales of tomatoes for next week, but we may also be interested in predicting sales for all vegetables (higher up in the product hierarchy) for next Friday (lower down in the time dimension). While the domain and data are the same, the operating context is different. We explore several approaches for multidimensional data when predictions have to be made at different levels (or contexts) of aggregation. One method relies on the same resolution, another approach aggregates predictions bottom-up, a third approach disaggregates predictions top-down and a final technique corrects predictions using the relation between levels. We show how these strategies behave when the resolution context changes, using several machine learning techniques in four application domains.This work was supported by the Spanish MINECO under grants TIN 2010-21062-C02-02 and TIN 2013-45732-C4-1-P, and the REFRAME project, granted by the European Coordinated Research on Longterm Challenges in Information and Communication Sciences Technologies ERA-Net (CHIST-ERA), and funded by MINECO in Spain (PCIN-2013-037) and by Generalitat Valenciana PROMETEOII2015/013.Martínez Usó, A.; Hernández Orallo, J. (2015). Multidimensional Prediction Models When the Resolution Context Changes. En Machine Learning and Knowledge Discovery in Databases. Springer. 509-524. https://doi.org/10.1007/978-3-319-23525-7_31S509524Agrawal, R., Gupta, A., Sarawagi, S.: Modeling multidimensional databases. In: Proceedings of the Thirteenth International Conference on Data Engineering, ICDE 1997, pp. 232–243. IEEE Computer Society (1997)Bella, A., Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.: Quantification via probability estimators. In: IEEE ICDM, pp. 737–742 (2010)Bella, A., Ferri, C., Hernández-Orallo, J., Ramírez-Quintana, M.J.: Aggregative quantification for regression. DMKD 28(2), 475–518 (2014)Bickel, R.: Multilevel analysis for applied research: It’s just regression! Guilford Press (2012)Cabibbo, L., Torlone, R.: A logical approach to multidimensional databases. In: Schek, H.-J., Saltor, F., Ramos, I., Alonso, G. (eds.) EDBT 1998. LNCS, vol. 1377, p. 183. Springer, Heidelberg (1998)Chaudhuri, S., Dayal, U.: An overview of data warehousing and OLAP technology. ACM Sigmod Record 26(1), 65–74 (1997)Chen, B.C.: Cube-Space Data Mining. ProQuest (2008)Chen, B.C., Chen, L., Lin, Y., Ramakrishnan, R.: Prediction cubes. In: Proc. of the 31st Intl. Conf. on Very Large Data Bases, pp. 982–993 (2005)Datahub: Car fuel consumptions and emissions 2000–2013 (2013). http://datahub.io/dataset/car-fuel-consumptions-and-emissionsDhurandhar, A.: Using coarse information for real valued prediction. Data Mining and Knowledge Discovery 27(2), 167–192 (2013)Forman, G.: Quantifying counts and costs via classification. Data Min. Knowl. Discov. 17(2), 164–206 (2008)Goldstein, H.: Multilevel Statistical Models, vol. 922. John Wiley & Sons (2011)Golfarelli, M., Maio, D., Rizzi, S.: The dimensional fact model: a conceptual model for data warehouses. Intl. J. of Coop. Information Systems 7, 215–247 (1998)Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H.: The WEKA data mining software: An update. SIGKDD Explor. 11(1), 10–18 (2009)Hernández-Orallo, J.: Probabilistic reframing for cost-sensitive regression. ACM Transactions on Knowledge Discovery from Data 8(3) (2014)IBM Corporation: Introduction to Aroma and SQL (2006). http://www.ibm.com/developerworks/data/tutorials/dm0607cao/dm0607cao.htmlKamber, M., Jenny, J.H., Chiang, Y., Han, J., Chiang, J.Y.: Metarule-guided mining of multi-dimensional association rules using data cubes. In: KDD, pp. 207–210 (1997)Lin, T., Yao, Y., Zadeh, L.: Data Mining, Rough Sets and Granular Computing. Studies in Fuzziness and Soft Computing. Physica-Verlag HD (2002)Páircéir, R., McClean, S., Scotney, B.: Discovery of multi-level rules and exceptions from a distributed database. In: Proc. of the 6th ACM SIGKDD Intl. Conf. on Knowledge discovery and data mining, pp. 523–532. ACM (2000)Pastor, O., Casamayor, J.C., Celma, M., Mota, L., Pastor, M.A., Levin, A.M.: Conceptual Modeling of Human Genome: Integration Challenges. In: Düsterhöft, A., Klettke, M., Schewe, K.-D. (eds.) Conceptual Modelling and Its Theoretical Foundations. LNCS, vol. 7260, pp. 231–250. Springer, Heidelberg (2012)Perlich, C., Provost, F.: Distribution-based aggregation for relational learning with identifier attributes. Machine Learning 62(1–2), 65–105 (2006)Team, R., et al.: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2012)Ramakrishnan, R., Chen, B.C.: Exploratory mining in cube space. Data Mining and Knowledge Discovery 15(1), 29–54 (2007)Raudenbush, S.W., Bryk, A.S.: Hierarchical linear models: applications and data analysis methods, vol. 1. Sage (2002)UCI Repository: UJIIndoorLoc data set (2014). http://archive.ics.uci.edu/ml/datasets/UJIIndoorLocVassiliadis, P.: Modeling multidimensional databases, cubes and cube operations. In: Proc. of the 10th SSDBM Conference, pp. 53–62 (1998