A central goal in the cognitive sciences is the development of computational models of mental representations of object concepts. In this paper we introduce Variational Interpretable Concept Embeddings (VICE), an approximate Bayesian method for learning interpretable object concept embeddings from human behavior in an odd-one-out triplet task. We use variational inference to obtain a sparse, non-negative solution with uncertainty estimates about each embedding value. We exploit these estimates to automatically select the dimensions that explain the data. We introduce a PAC learning bound for VICE that can be used to estimate generalization performance or determine a sufficient sample size for different experimental designs. VICE rivals or outperforms its predecessor, SPoSE, at predicting human behavior in a triplet task. VICE object representations are substantially more reproducible and consistent across different random initializations.