Abstract
Venn Predictors (VPs) are machine learning algorithms that can provide well calibrated multiprobability outputs for their predictions. An important drawback of Venn Predictors is their computational inefficiency, especially in the case of large datasets. In this work, we investigate and propose Inductive Venn Predictors (IVPs), which can overcome the computational inefficiency problem of the original Transductive Venn Prediction framework. We develop an IVP algorithm and perform a detailed comparison of its time efficiency, accuracy, and quality of probabilistic outputs with those of the original Transductive Venn Predictor (TVP). The results demonstrate that our method provides well calibrated results while maintaining high accuracy. The IVP outperforms the original TVP method in terms of time efficiency, while also providing well-calibrated probabilistic estimates. Another observation is that the probability intervals of the IVP are tighter than those of the TVP.
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Bellotti, T., Luo, Z., Gammerman, A.: Reliable classification of childhood acute leukaemia from gene expression data using confidence machines. In: Proceedings of IEEE International Conference on Granular Computing (GRC ’06), pp. 148–153 (2006)
Bohanec, M., Rajkovic̆, V.: Knowledge acquisition and explanation for multi-attribute decision making. In: 8th International Workshop “Expert Systems and Their Applications” (1988)
Cortez, P., Cerdeira, A., Almeida, F., Matos, T., Reis, J.: Modeling wine preferences by data mining from physicochemical properties. Decis. Support. Syst. 47(4), 547–553 (2009)
Dashevskiy, M., Luo, Z.: Reliable probabilistic classification and its application to internet traffic. In: Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues, volume 5226 of LNCS, pp. 380–388. Springer (2008)
Dashevskiy, M., Luo, Z.: Predictions with confidence in applications. In: Perner, P. (ed.) Machine Learning and Data Mining in Pattern Recognition, volume 5632 of LNCS, pp. 775–786. Springer (2009)
Dmitry, D, Ilia, N: Prediction with confidence based on a random forest classifier. In: Papadopoulos, H., Andreou, A., Bramer, M. (eds.) Artificial Intelligence Applications and Innovations, vol. 339, pp. 37–44. Springer, Boston (2010)
Drish, J.: Obtaining calibrated probability estimates from Support Vector Machines (1998)
Frank, A., Asuncion, A.: UCI machine learning repository (2010)
Gammerman, A., Nouretdinov, I., Burford, B., Chervonenkis, A., Vovk, V., Luo, Z.: Clinical mass spectrometry proteomic diagnosis by conformal predictors. Stat. Appl. Genet. Mol. Biol. 7(2) (2008)
Gammerman, A., Vovk, V., Vapnik, V.: Learning by transduction. In: Uncertainty in Artificial Intelligence, pp. 148–155. Morgan Kaufmann (1998)
Lambrou, A., Papadopoulos, H., Gammerman, A.: Reliable confidence measures for medical diagnosis with evolutionary algorithms. IEEE Trans. Inf. Technol. Biomed. 15(1), 93–99 (2011)
Lambrou, A., Papadopoulos, H., Kyriacou, E., Pattichis, C.S., Pattichis, M.S., Gammerman, A., Nicolaides, A.: Evaluation of the risk of stroke with confidence predictions based on ultrasound carotid image analysis. Int. J. Artif. Intell. Tools 21(04), 1240016 (2012)
Lambrou, A., Papadopoulos, H., Nouretdinov, I., Gammerman, A.: Reliable probability estimates based on support vector machines for large multiclass datasets. In: Iliadis, L., Maglogiannis, I., Papadopoulos, H., Karatzas, K., Sioutas, S. (eds.) Artificial Intelligence Applications and Innovations, volume 382 of IFIP Advances in Information and Communication Technology, pp 182–191. Springer, Berlin Heidelberg (2012)
Papadopoulos, H.: Inductive conformal prediction: theory and application to neural networks. In: Fritzsche, P. (ed.) Tools in Artificial Intelligence, chapter 18, pp 315–330. InTech, Vienna (2008)
Papadopoulos, H.: Reliable probabilistic prediction for medical decision support. In: Proceedings of the 7th IFIP International Conference on Artificial Intelligence Appications and Innovations (AIAI 2011), volume 364 of IFIP AICT, pp. 265–274. Springer (2011)
Papadopoulos, H.: Reliable probabilistic classification with neural networks. Neurocomputing 107, 59–68 (2013)
Papadopoulos, H., Gammerman, A., Vovk, V.: Reliable diagnosis of acute abdominal pain with conformal prediction. Int. J. Eng. Intell. Syst. Electr. Eng. Commun. 17(2–3), 127–137 (2009)
Papadopoulos, H., Papatheocharous, E., Andreou, A.S.: Reliable confidence intervals for software effort estimation. In: Proceedings of the 2nd Workshop on Artificial Intelligence Techniques in Software Engineering (AISEW 2009), volume 475 of CEUR Workshop Proceedings, pp. 211–220. CEUR WS.org (2009)
Papadopoulos, H., Proedrou, K., Vovk, V., Gammerman, A.: Inductive confidence machines for regression. In: Proceedings of the 13th European Conference on Machine Learning (ECML’02), volume 2430 of LNCS, pp. 345–356. Springer (2002)
Papadopoulos, H., Vovk, V., Gammerman, A.: Regression conformal prediction with nearest neighbours. J. Artif. Intell. Res. 40, 815–840 (2011)
Papadopoulos, H., Vovk, V., Gammerman, A.: Qualified predictions for large data sets in the case of pattern recognition. In: Proceedings of the 2002 International Conference on Machine Learning and Applications (ICMLA’02), pp. 159–163. CSREA Press (2002)
Papadopoulos, H., Vovk, V., Gammerman, A.: Conformal prediction with neural networks. In: Proceedings of the 19th IEEE International Conference on Tools with Artificial Intelligence (ICTAI’07), vol. 2, pp. 388–395. IEEE Computer Society (2007)
Platt, J.C.: Fast training of support vector machines using sequential minimal optimization. In: Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.) Advances in kernel methods, pp 185–208. Cambridge (1999)
Platt, J.C.: Probabilistic outputs for Support Vector Machines and comparisons to regularized likelihood methods. In: Advances in large margin classifiers, pp. 61–74. MIT Press (1999)
Proedrou, K., Nouretdinov, I., Vovk, V., Gammerman, A.: Transductive confidence machines for pattern recognition. In: Proceedings of the 13th European Conference on Machine Learning (ECML’02), volume 2430 of Lecture Notes in Computer Science, pp. 381–390. Springer (2002)
Ross Quinlan, J.: C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers Inc., San Francisco (1993)
Saunders, C., Gammerman, A., Vovk, V.: Transduction with confidence and credibility. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence, vol. 2, pp. 722–726. Morgan Kaufmann, Los Altos (1999)
Vovk, V., Shafer, G., Nouretdinov, I.: Self-calibrating probability forecasting. In: Thrun, S., Saul, L.K., Schölkopf, B. (eds.) Advances in Neural Information Processing Systems 16, pp 1133–1140. MIT Press, Cambridge (2004)
Vovk, V., Gammerman, A., Saunders, C.: Machine-learning applications of algorithmic randomness. In: Proceedings of the Sixteenth International Conference on Machine Learning, pp. 444–453. Morgan Kaufmann (1999)
Vovk, V., Gammerman, A., Shafer, G.: Algorithmic Learning in a Random World. Springer, New York (2005)
Zadrozny, B., Elkan, C.: Transforming classifier scores into accurate multiclass probability estimates. In: Proceedings of the 8th ACM International Conference on Knowledge Discovery and Data Mining, pp. 694–699 (2002)
Zhou, C., Nouretdinov, I., Luo, Z., Adamskiy, D., Randell, L., Coldham, N., Gammerman, A.: A comparison of Venn Machine with Platt’s method in probabilistic outputs. In: Proceedings of the 7th IFIP International Conference on Artificial Intelligence Appications and Innovations (AIAI 2011), volume 364 of IFIP AICT, pp. 483–490. Springer (2011)
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Lambrou, A., Nouretdinov, I. & Papadopoulos, H. Inductive Venn Prediction. Ann Math Artif Intell 74, 181–201 (2015). https://doi.org/10.1007/s10472-014-9420-z
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DOI: https://doi.org/10.1007/s10472-014-9420-z