Understanding the facial expressions of our interlocutor is important to enrich the communication and to give it a depth that goes beyond the explicitly expressed. In fact, studying one's facial expression gives insight into their hidden emotion state. However, even as humans, and despite our empathy and familiarity with the human emotional experience, we are only able to guess what the other might be feeling. In the fields of artificial intelligence and computer vision, Facial Emotion Recognition (FER) is a topic that is still in full growth mostly with the advancement of deep learning approaches and the improvement of data collection. The main purpose of this paper is to compare the performance of three state-of-the-art networks, each having their own approach to improve on FER tasks, on three FER datasets. The first and second sections respectively describe the three datasets and the three studied network architectures designed for an FER task. The experimental protocol, the results and their interpretation are outlined in the remaining sections.

Domain adaptation arises as an important problem in statistical learning theory when the data-generating processes differ between training and test samples, respectively called source and target domains. Recent theoretical advances show that the success of domain adaptation algorithms heavily relies on their ability to minimize the divergence between the probability distributions of the source and target domains. However, minimizing this divergence cannot be done independently of the minimization of other key ingredients such as the source risk or the combined error of the ideal joint hypothesis. The trade-off between these terms is often ensured by algorithmic solutions that remain implicit and not directly reflected by the theoretical guarantees. To get to the bottom of this issue, we propose in this paper a new theoretical framework for domain adaptation through hierarchical optimal transport. This framework provides more explicit generalization bounds and allows us to consider the natural hierarchical organization of samples in both domains into classes or clusters. Additionally, we provide a new divergence measure between the source and target domains called Hierarchical Wasserstein distance that indicates under mild assumptions, which structures have to be aligned to lead to a successful adaptation.