There is increasing attention to evaluating the fairness of search system ranking decisions. These metrics often consider the membership of items to particular groups, often identified using protected attributes such as gender or ethnicity. To date, these metrics typically assume the availability and completeness of protected attribute labels of items. However, the protected attributes of individuals are rarely present, limiting the application of fair ranking metrics in large scale systems. In order to address this problem, we propose a sampling strategy and estimation technique for four fair ranking metrics. We formulate a robust and unbiased estimator which can operate even with very limited number of labeled items. We evaluate our approach using both simulated and real world data. Our experimental results demonstrate that our method can estimate this family of fair ranking metrics and provides a robust, reliable alternative to exhaustive or random data annotation.

Capturing the occurrence dynamics is crucial to predicting which type of events will happen next and when. A common method to do this is through Hawkes processes. To enhance their capacity, recurrent neural networks (RNNs) have been incorporated due to RNNs’ successes in processing sequential data such as languages. Recent evidence suggests that self-attention is more competent than RNNs in dealing with languages. However, we are unaware of the effectiveness of self-attention in the context of Hawkes processes. This study aims to fill the gap by designing a self-attentive Hawkes process (SAHP). SAHP employs self-attention to summarise the influence of history events and compute the probability of the next event. One deficit of the conventional self-attention when applied to event sequences is that its positional encoding only considers the order of a sequence ignoring the time intervals between events. To overcome this deficit, we modify its encoding by translating time intervals into phase shifts of sinusoidal functions. Experiments on goodness-of-fit and prediction tasks show the improved capability of SAHP. Furthermore, SAHP is more interpretable than RNN-based counterparts because the learnt attention weights reveal contributions of one event type to the happening of another type. To the best of our knowledge, this is the first work that studies the effectiveness of self-attention in Hawkes processes.