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Factorization machines are a generic supervised method for a wide range of tasks in the field of artificial intelligence, such as prediction, inference, etc., which can effectively model feature interactions. However, handling combinations of features is expensive due to the exponential growth of feature interactions with the order. In nature, not all feature interactions are equally useful for prediction. Recently, a large number of methods that perform feature interaction selection have attracted great attention because of their effectiveness at filtering out useless feature interactions. Current feature interaction selection methods suffered from the following limitations: (1) they assume that all users share the same feature interactions; and (2) they select pairwise feature interactions only. In this paper, we propose novel Bayesian variable selection methods, targeting feature interaction selection for factorization machines, which effectively reduce the number of interactions. We study personalized feature interaction selection to account for individual preferences, and further extend the model to investigate higher-order feature interaction selection on higher-order factorization machines. We provide empirical evidence for the advantages of the proposed Bayesian feature interaction selection methods using different prediction tasks. [ABSTRACT FROM AUTHOR]