Outlier detection plays a significant role in various real world applications such as intrusion, malfunction, and fraud detection. Traditionally, outlier detection techniques are applied to find outliers in the context of the whole dataset. However, this practice neglects contextual outliers, that are not outliers in the whole dataset but in some specific neighborhoods. Contextual outliers are particularly important in data exploration and targeted anomaly explanation and diagnosis. In these scenarios, the data owner computes the following information: i) The attributes that contribute to the abnormality of an outlier (metric), ii) Contextual description of the outliers neighborhoods (context), and iii) The utility score of the context, e.g. its strength in showing the outliers significance, or in relation to a particular explanation for the outlier. However, revealing the outliers context leaks information about the other individuals in the population as well, violating their privacy. We address the issue of population privacy violations in this paper, and propose a solution for the two main challenges. In this setting, the data owner is required to release a valid context for the queried record, i.e. a context in which the record is an outlier. Hence, the first major challenge is that the privacy technique must preserve the validity of the context for each record. We propose techniques to protect the privacy of individuals through a relaxed notion of differential privacy to satisfy this requirement. The second major challenge is applying the proposed techniques efficiently, as they impose intensive computation to the base algorithm. To overcome this challenge, we propose a graph structure to map the contexts to, and introduce differentially private graph search algorithms as efficient solutions for the computation problem caused by differential privacy techniques.
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