Conformal predictors are a family of predictive models that associate with each of their predictions a measure of confidence, enabling them to provide quantitative information about their own trustworthiness. In risk-laden machine learning applications, where bad predictions may lead to economic loss, personal injury, or worse, such inherent quality control appears highly beneficial, if not required. While the foundations of conformal prediction were initially published some twenty years ago, their use, and further development, is still (at the time of writing this thesis) not widespread in the machine learning community, and several open questions remain regarding the proper design and use of conformal prediction systems. In this thesis, we attempt to tackle some of these questions, focusing our attention on three specific characteristics of conformal predictors. First, conformal predictors rely on so-called nonconformity functions, which are mappings from the object space onto the real line, typically based on traditional classification or regression models; here, we investigate properties of the underlying learning algorithm and characteristics of the resulting conformal predictor. Second, conformal predictors output predictions on a form that is distinct from traditional prediction methods, by supplying multi-valued prediction regions with a statistically valid coverage probability; we propose two procedures for post-processing the output from conformal classification models that provide interpretations more closely related to traditional predictive models, while still retaining meaningful confidence information. Finally, we provide contributions relating to the construction of conformal predictor ensembles, illustrating potential issues with existing ensemble procedures, as well as proposing and evaluating an alternative ensemble method.

Avhandlingen behandlar områdetconformal prediction, som beskriver en fa-milj prediktiva modeller vars prediktioner associeras med ett konfidensmått,som låter modellerna själva uttrycka sig om sin egen tillförlitlighet. I hög-riskapplikationer, där dåliga prediktioner kan få allvarliga ekonomiska konse-kvenser, eller leda till personskada, tycks en sådan inbyggd säkerhetskontrollhögst värdefull, om inte nödvändig. Medan den teoretiska grunden till confor-mal prediction lades för cirka 20 år sedan, är forskningsområdet fortfaranderelativt ungt, och många öppna frågor kvarstår gällande design och använd-ning av conformal prediction-system. I avhandlingen behandlas några av des-sa öppna frågor, och fokus läggs på tre specifika karakteristika hos conformal-prediktorer. Först behandlas de så kallade icke-konformitetsfunktionerna (non-conformity functions) som ligger till grund för conformal prediction, och sam-bandet utforskas mellan egenskaper hos icke-konformitetsfunktionerna och deresulterande prediktorerna. även egenskaper hos de prediktioner som produ-ceras i en conformal predictor undersöks, och två post-processeringsmetoderpresenteras i ett försök att bistå med en mer intuitivt begriplig tolkning av des-sa prediktioner. Slutligen utforskas strategier för konstruktion av ensemblerav conformal prediction-modeller, där svagheter illustreras i vedertagna stra-tegier, följt av en presentation av en ny ensemblestrategi som ämnar adresseradessa svagheter.

In this paper, we study a generalization of a recently developed strategy for generating conformal predictor ensembles: out-of-bag calibration. The ensemble strategy is evaluated, both theoretically and empirically, against a commonly used alternative ensemble strategy, bootstrap conformal prediction, as well as common non-ensemble strategies. A thorough analysis is provided of out-of-bag calibration, with respect to theoretical validity, empirical validity (error rate), efficiency (prediction region size) and p-value stability (the degree of variance observed over multiple predictions for the same object). Empirical results show that out-of-bag calibration displays favorable characteristics with regard to these criteria, and we propose that out-of-bag calibration be adopted as a standard method for constructing conformal predictor ensembles.

In this paper, we propose a practically useful means of interpreting the predictions produced by a conformal classifier. The proposed interpretation leads to a classifier with a reject option, that allows the user to limit the number of erroneous predictions made on the test set, without any need to reveal the true labels of the test objects. The method described in this paper works by estimating the cumulative error count on a set of predictions provided by a conformal classifier, ordered by their confidence. Given a test set and a user-specified parameter k, the proposed classification procedure outputs the largest possible amount of predictions containing on average at most k errors, while refusing to make predictions for test objects where it is too uncertain. We conduct an empirical evaluation using benchmark datasets, and show that we are able to provide accurate estimates for the error rate on the test set.

This paper suggests a modification of the Conformal Prediction framework for regression that will strengthen the associated guarantee of validity. We motivate the need for this modification and argue that our conformal regressors are more closely tied to the actual error distribution of the underlying model, thus allowing for more natural interpretations of the prediction intervals. In the experimentation, we provide an empirical comparison of our conformal regressors to traditional conformal regressors and show that the proposed modification results in more robust two-tailed predictions, and more efficient one-tailed predictions.