Tensor completion is a problem of lling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide a ention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data analytics characterized by diverse variety, large volume, and high velocity. We characterize these advances from four perspectives: general tensor completion algorithms, tensor completion with auxiliary information (variety), scalable tensor completion algorithms (volume), and dynamic tensor completion algorithms (velocity). Further, we identify several tensor completion applications on real-world data-driven problems and present some common experimental frameworks popularized in the literature. Our goal is to summarize these popular methods and introduce them to researchers and practitioners for promoting future research and applications. We conclude with a discussion of key challenges and promising research directions in this community for future exploration.

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In the slot-filling paradigm, where a user can refer back to slots in the context during a conversation, the goal of the contextual understanding system is to resolve the referring expressions to the appropriate slots in the context. In large-scale multi-domain systems, this presents two challenges -scaling to a very large and potentially unbounded set of slot values, and dealing with diverse schemas. We present a neural network architecture that addresses the slot value scalability challenge by reformulating the contextual interpretation as a decision to carryover a slot from a set of possible candidates. To deal with heterogenous schemas, we introduce a simple data-driven method for transforming the candidate slots. Our experiments show that our approach can scale to multiple domains and provides competitive results over a strong baseline.

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