Recommender systems often represent products with learnable embeddings.Yet, we seldom examine the structure of the embedding space, and what implications it has for the recommendation task at hand.In contrast, embeddings in natural language processing are well-understood and offer intuitive properties through word analogies (e.g."queen -king = woman -man").In this work, we present a corresponding approach that reveals latent knowledge in the structure of product embeddings.We prove their relevance in evaluating several embeddings learned from different data modalities in a home-furnishing context.Our findings evince distinct embedding strengths: visual embeddings capture explicit attributes like colour and shape; textual embeddings encode abstract concepts like style and functionality; while behavioural embeddings offer versatile representations driven by user interactions.We also highlight trade-offs, and link our evaluations to practical considerations in embedding development within the e-commerce domain.

The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth signals. Moreover, inference in the GPCM currently requires (1) a mean-field assumption, resulting in poorly calibrated uncertainties, and (2) a tedious variational optimisation of large covariance matrices. We redesign the GPCM model to induce a richer distribution over the spectrum with relaxed assumptions about smoothness: the Causal Gaussian Process Convolution Model (CGPCM) introduces a causality assumption into the GPCM, and the Rough Gaussian Process Convolution Model (RGPCM) can be interpreted as a Bayesian nonparametric generalisation of the fractional Ornstein-Uhlenbeck process. We also propose a more effective variational inference scheme, going beyond the mean-field assumption: we design a Gibbs sampler which directly samples from the optimal variational solution, circumventing any variational optimisation entirely. The proposed variations of the GPCM are validated in experiments on synthetic and real-world data, showing promising results.