Ivan Petej

Ivan Petej, Vladimir Vovk

Venn-Abers predictors are probabilistic predictors that enjoy appealing properties of validity, but their major limitation is that they are applicable only to the case of binary classification, with a recent extension to bounded regression. We generalize them to the case of unbounded regression, which requires adding an element of conformal prediction. In our simulation and empirical studies we investigate the predictive efficiency of point regressors derived from Venn-Abers regressors and argue that they somewhat improve the predictive efficiency of standard regressors for larger training sets.

Ivan Petej

This paper introduces a new Python package specifically designed to address calibration of probabilistic classifiers under dataset shift. The method is demonstrated in binary and multi-class settings and its effectiveness is measured against a number of existing post-hoc calibration methods. The empirical results are promising and suggest that our technique can be helpful in a variety of settings for batch and online learning classification problems where the underlying data distribution changes between the training and test sets.

Vladimir Vovk, Ivan Petej, Alex Gammerman

This paper proposes a way of protecting probabilistic prediction models against changes in the data distribution, concentrating on the case of classification and paying particular attention to binary classification. This is important in applications of machine learning, where the quality of a trained prediction algorithm may drop significantly in the process of its exploitation. Our techniques are based on recent work on conformal test martingales and older work on prediction with expert advice, namely tracking the best expert.

Vladimir Vovk, Ivan Petej, Ilia Nouretdinov et al.

We argue for supplementing the process of training a prediction algorithm by setting up a scheme for detecting the moment when the distribution of the data changes and the algorithm needs to be retrained. Our proposed schemes are based on exchangeability martingales, i.e., processes that are martingales under any exchangeable distribution for the data. Our method, based on conformal prediction, is general and can be applied on top of any modern prediction algorithm. Its validity is guaranteed, and in this paper we make first steps in exploring its efficiency.

Vladimir Vovk, Ivan Petej, Ilia Nouretdinov et al.

Conformal predictive systems are a recent modification of conformal predictors that output, in regression problems, probability distributions for labels of test observations rather than set predictions. The extra information provided by conformal predictive systems may be useful, e.g., in decision making problems. Conformal predictive systems inherit the relative computational inefficiency of conformal predictors. In this paper we discuss two computationally efficient versions of conformal predictive systems, which we call split conformal predictive systems and cross-conformal predictive systems. The main advantage of split conformal predictive systems is their guaranteed validity, whereas for cross-conformal predictive systems validity only holds empirically and in the absence of excessive randomization. The main advantage of cross-conformal predictive systems is their greater predictive efficiency.

Vladimir Vovk, Ivan Petej, Paolo Toccaceli et al.

Most existing examples of full conformal predictive systems, split-conformal predictive systems, and cross-conformal predictive systems impose severe restrictions on the adaptation of predictive distributions to the test object at hand. In this paper we develop split-conformal and cross-conformal predictive systems that are fully adaptive. Our method consists in calibrating existing predictive systems; the input predictive system is not supposed to satisfy any properties of validity, whereas the output predictive system is guaranteed to be calibrated in probability. It is interesting that the method may also work without the IID assumption, standard in conformal prediction.

Vladimir Vovk, Ilia Nouretdinov, Valentina Fedorova et al.

We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.

Vladimir Vovk, Ivan Petej, Valentina Fedorova

This paper studies theoretically and empirically a method of turning machine-learning algorithms into probabilistic predictors that automatically enjoys a property of validity (perfect calibration) and is computationally efficient. The price to pay for perfect calibration is that these probabilistic predictors produce imprecise (in practice, almost precise for large data sets) probabilities. When these imprecise probabilities are merged into precise probabilities, the resulting predictors, while losing the theoretical property of perfect calibration, are consistently more accurate than the existing methods in empirical studies.

Vladimir Vovk, Ivan Petej, Valentina Fedorova

This paper proposes a new method of probabilistic prediction, which is based on conformal prediction. The method is applied to the standard USPS data set and gives encouraging results.

Vladimir Vovk, Ivan Petej

This paper continues study, both theoretical and empirical, of the method of Venn prediction, concentrating on binary prediction problems. Venn predictors produce probability-type predictions for the labels of test objects which are guaranteed to be well calibrated under the standard assumption that the observations are generated independently from the same distribution. We give a simple formalization and proof of this property. We also introduce Venn-Abers predictors, a new class of Venn predictors based on the idea of isotonic regression, and report promising empirical results both for Venn-Abers predictors and for their more computationally efficient simplified version.