Context-aware recommendation (CAR) can lead to significant improvements in the relevance of the recommended items by modeling the nuanced ways in which context influences preferences. The dominant approach in context-aware recommendation has been the multidimensional latent factors approach in which users, items, and context variables are represented as latent features in a low-dimensional space. An interaction between a user, item, and a context variable is typically modeled as some linear combination of their latent features. However, given the many possible types of interactions between user, items and contextual variables, it may seem unrealistic to restrict the interactions among them to linearity. To address this limitation, we develop a novel and powerful non-linear probabilistic algorithm for context-aware recommendation using Gaussian processes. The method which we call Gaussian Process Factorization Machines (GPFM) is applicable to both the explicit feedback setting (e.g. numerical ratings as in the Netflix dataset) and the implicit feedback setting (i.e. purchases, clicks). We derive stochastic gradient descent optimization to allow scalability of the model. We test GPFM on five different benchmark contextual datasets. Experimental results demonstrate that GPFM outperforms state-of-the-art context-aware recommendation methods.

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Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer discrepancy or Earth Mover's distance, but those metrics are either ineffective in measuring the differences between point clouds or computationally expensive. In this paper, we conduct a systematic study with extensive experiments on distance metrics for 3D point clouds. From this study, we propose to use a variant of the Wasserstein distance, named the sliced Wasserstein distance, for learning representations of 3D point clouds. Experiments show that the sliced Wasserstein distance allows the neural network to learn a more efficient representation compared to the Chamfer discrepancy. We demonstrate the efficiency of the sliced Wasserstein metric on several tasks in 3D computer vision including training a point cloud autoencoder, generative modeling, transfer learning, and point cloud registration.