Proper feature selection for unsupervised outlier detection can improve detection performance but is very challenging due to complex feature interactions, the mixture of relevant features with noisy/redundant features in imbalanced data, and the unavailability of class labels. Little work has been done on this challenge. This paper proposes a novel Coupled Unsupervised Feature Selection framework (CUFS for short) to filter out noisy or redundant features for subsequent outlier detection in categorical data. CUFS quantifies the outlierness (or relevance) of features by learning and integrating both the feature value couplings and feature couplings. Such value-To-feature couplings capture intrinsic data characteristics and distinguish relevant features from those noisy/redundant features. CUFS is further instantiated into a parameter-free Dense Subgraph-based Feature Selection method, called DSFS. We prove that DSFS retains a 2-Approximation feature subset to the optimal subset. Extensive evaluation results on 15 real-world data sets show that DSFS obtains an average 48% feature reduction rate, and enables three different types of pattern-based outlier detection methods to achieve substantially better AUC improvements and/or perform orders of magnitude faster than on the original feature set. Compared to its feature selection contender, on average, all three DSFS-based detectors achieve more than 20% AUC improvement.