We would like to thank all three reviewers for acknowledging our contributions and providing valuable feedback. Thank you for the positive comments on the novelty of our idea and insightful questions for further improvement. We first characterize the solutions of DEAN. Other choices for the energy objective will be left to future works. Rejection rates for d = 1 (left) and d = 3 .

Pattern discovery is a machine learning technique that aims to find sets of items, subsequences, or substructures that are present in a dataset with a higher frequency value than a manually set threshold. This process helps to identify recurring patterns or relationships within the data, allowing for valuable insights and knowledge extraction. In this work, we propose Information Gained Subgroup Discovery (IGSD), a new SD algorithm for pattern discovery that combines Information Gain (IG) and Odds Ratio (OR) as a multi-criteria for pattern selection. The algorithm tries to tackle some limitations of state-of-the-art SD algorithms like the need for fine-tuning of key parameters for each dataset, usage of a single pattern search criteria set by hand, usage of non-overlapping data structures for subgroup space exploration, and the impossibility to search for patterns by fixing some relevant dataset variables. Thus, we compare the performance of IGSD with two state-of-the-art SD algorithms: FSSD and SSD++. Eleven datasets are assessed using these algorithms. For the performance evaluation, we also propose to complement standard SD measures with IG, OR, and p-value. Obtained results show that FSSD and SSD++ algorithms provide less reliable patterns and reduced sets of patterns than IGSD algorithm for all datasets considered. Additionally, IGSD provides better OR values than FSSD and SSD++, stating a higher dependence between patterns and targets. Moreover, patterns obtained for one of the datasets used, have been validated by a group of domain experts. Thus, patterns provided by IGSD show better agreement with experts than patterns obtained by FSSD and SSD++ algorithms. These results demonstrate the suitability of the IGSD as a method for pattern discovery and suggest that the inclusion of non-standard SD metrics allows to better evaluate discovered patterns.

Out-of-Distribution (OoD) detection is important for building safe artificial intelligence systems. However, current OoD detection methods still cannot meet the performance requirements for practical deployment. In this paper, we propose a simple yet effective algorithm based on a novel observation: in a trained neural network, OoD samples with bounded norms well concentrate in the feature space. We call the center of OoD features the Feature Space Singularity (FSS), and denote the distance of a sample feature to FSS as FSSD. Then, OoD samples can be identified by taking a threshold on the FSSD. Our analysis of the phenomenon reveals why our algorithm works. We demonstrate that our algorithm achieves state-of-the-art performance on various OoD detection benchmarks. Besides, FSSD also enjoys robustness to slight corruption in test data and can be further enhanced by ensembling. These make FSSD a promising algorithm to be employed in real world. We release our code at \url{https://github.com/megvii-research/FSSD_OoD_Detection}.