A clustering may be considered as fair on pre-specified sensitive attributes if the proportions of sensitive attribute groups in each cluster reflect that in the dataset. In this paper, we consider the task of fair clustering for scenarios involving multiple multi-valued or numeric sensitive attributes. We propose a fair clustering method, FairKM (Fair K-Means), that is inspired by the popular K-Means clustering formulation. We outline a computational notion of fairness which is used along with a cluster coherence objective, to yield the FairKM clustering method. We empirically evaluate our approach, wherein we quantify both the quality and fairness of clusters, over real-world datasets. Our experimental evaluation illustrates that the clusters generated by FairKM fare significantly better on both clustering quality and fair representation of sensitive attribute groups compared to the clusters from a state-of-the-art baseline fair clustering method.

From the latter half of the last decade, there has been a growing interest in developing algorithms for automatically solving mathematical word problems (MWP). It is a challenging and unique task that demands blending surface level text pattern recognition with mathematical reasoning. In spite of extensive research, we are still miles away from building robust representations of elementary math word problems and effective solutions for the general task. In this paper, we critically examine the various models that have been developed for solving word problems, their pros and cons and the challenges ahead. In the last two years, a lot of deep learning models have recorded competing results on benchmark datasets, making a critical and conceptual analysis of literature highly useful at this juncture. We take a step back and analyse why, in spite of this abundance in scholarly interest, the predominantly used experiment and dataset designs continue to be a stumbling block. From the vantage point of having analyzed the literature closely, we also endeavour to provide a road-map for future math word problem research.

Solving kinematics word problems is a specialized task which is best addressed through bespoke logical reasoners. Reasoners, however, require structured input in the form of kinematics parameter values, and translating textual word problems to such structured inputs is a key step in enabling end-to-end automated word problem solving. Span detection for a kinematics parameter is the process of identifying the smallest span of text from a kinematics word problem that has the information to estimate the value of that parameter. A key aspect differentiating kinematics span detection from other span detection tasks is the presence of multiple inter-related parameters for which separate spans need to be identified. State-of-the-art span detection methods are not capable of leveraging the existence of a plurality of inter-dependent span identification tasks. We propose a novel neural architecture that is designed to exploit the inter-relatedness between the separate span detection tasks using a single joint model. This allows us to train the same network for span detection over multiple kinematics parameters, implicitly and automatically transferring knowledge across the kinematics parameters. We show that such a joint training delivers an improvement of accuracies over real-world datasets against state-of-the-art methods for span detection.