  In this work, a novel method based on the learning using privileged
information (LUPI) paradigm for recognizing complex human activities is
proposed that handles missing information during testing. We present a
supervised probabilistic approach that integrates LUPI into a hidden
conditional random field (HCRF) model. The proposed model is called HCRF+ and
may be trained using both maximum likelihood and maximum margin approaches. It
employs a self-training technique for automatic estimation of the
regularization parameters of the objective functions. Moreover, the method
provides robustness to outliers (such as noise or missing data) by modeling the
conditional distribution of the privileged information by a Student's
\textit{t}-density function, which is naturally integrated into the HCRF+
framework. Different forms of privileged information were investigated. The
proposed method was evaluated using four challenging publicly available
datasets and the experimental results demonstrate its effectiveness with
respect to the-state-of-the-art in the LUPI framework using both hand-crafted
features and features extracted from a convolutional neural network.
