Nonconformity Measures and Ensemble Strategies : An Analysis of Conformal Predictor Efficiency and Validity

Abstract: 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.