The paper addresses face presentation attack detection in the challenging conditions of an unseen attack scenario where the system is exposed to novel presentation attacks that were not present in the training step. For this purpose, a pure one-class face presentation attack detection approach based on kernel regression is developed which only utilises bona fide (genuine) samples for training. In the context of the proposed approach, a number of innovations, including multiple kernel fusion, client-specific modelling, sparse regularisation and probabilistic modelling of score distributions are introduced to improve the efficacy of the method. The results of experimental evaluations conducted on the OULU-NPU, Replay-Mobile, Replay-Attack and MSU-MFSD datasets illustrate that the proposed method compares very favourably with other methods operating in an unseen attack detection scenario while achieving very competitive performance to multi-class methods (benefiting from presentation attack data for training) despite using only bona fide samples for training.