Abstract This paper introduces a novel wrapper-based outlier detection framework (WrapperOD) and its instance (HOUR) for identifying outliers in noisy data (i.e., data with noisy features) with strong couplings between outlying behaviors. Existing subspace or feature selection-based methods are significantly challenged by such data, as their search of feature subset(s) is independent of outlier scoring and thus can be misled by noisy features. In contrast, HOUR takes a wrapper approach to iteratively optimize the feature subset selection and outlier scoring using a top-k outlier ranking evaluation measure as its objective function. HOUR learns homophily couplings between outlying behaviors (i.e., abnormal behaviors are not independent - they bond together) in constructing a noise-resilient outlier scoring function to produce a reliable outlier ranking in each iteration. We show that HOUR (i) retains a 2-approximation outlier ranking to the optimal one; and (ii) significantly outperforms five stateof-the-art competitors on 15 real-world data sets with different noise levels in terms of AUC and/or P@n. The source code of HOUR is available at https://sites.google.com/site/gspangsite/sourcecode