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.

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.

We study optimal conformity measures for various criteria of efficiency of setvalued classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic and argue for; 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.

Most existing examples of full conformal predictive systems, splitconformal 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.The version of this paper at http://alrw.net (Working Paper 23) is updated most often.

Health professional regulators aim to protect the health and well-being of patients and the public by setting standards for scrutinising and overseeing the training and conduct of health and care professionals. A major task of such regulators is the investigation of complaints against practitioners. However, processing a complaint often lasts several months and is particularly costly. Hence, we worked with international regulators from different countries (the UK, US and Australia), to develop the first decision support tool that aims to help such regulators process complaints more efficiently. Our system uses state-of-the-art machine learning and natural language processing techniques to process complaints and predict their risk level. Our tool also provides additional useful information including explanations, to help the regulatory staff interpret the prediction results, and similar past cases as well as non-compliance to regulations, to support the decision making.