Recognising daily activity patterns of people from low-level sensory data is an important problem. Traditional approaches typically rely on generative models such as the hidden Markov models and training on fully labelled data. While activity data can be readily acquired from pervasive sensors, e.g. in smart environments, providing manual labels to support fully supervised learning is often expensive. In this paper, we propose a new approach based on partially-supervised training of discriminative sequence models such as the conditional random field (CRF) and the maximum entropy Markov model (MEMM). We show that the approach can reduce labelling effort, and at the same time, provides us with the flexibility and accuracy of the discriminative framework. Our experimental results in the video surveillance domain illustrate that these models can perform better than their generative counterpart (i.e. the partially hidden Markov model), even when a substantial amount of labels are unavailable.