Many inference problems are naturally formulated using hard and soft constraints over relational domains: the desired solution must satisfy the hard constraints, while optimizing the objectives expressed by the soft constraints. Existing techniques for solving such constraints rely on efficiently grounding a sufficient subset of constraints that is tractable to solve. We present an eager-lazy grounding algorithm that eagerly exploits proofs and lazily refutes counterexamples. We show that our algorithm achieves significant speedup over existing approaches without sacrificing soundness for real-world applications from information retrieval and program analysis.

Massive Open Online Courses (MOOCs) have initiated a revolution in higher education by providing opportunities for interested students to learn from the comfort of their individual locations at their desired pace. However, an important and highly successful aspect of traditional classroom education/pedagogy, which is modulating content delivery based on understanding real-time student feedback, is conspicuously missing in such e-learning environments. We aim to bridge this gap by proposing a system for automatic recognition of students engagement levels during e-learning sessions, using a crowdsourced discriminative learning approach. The key contributions of this work include a custom dataset for engagement recognition that will be made publicly available with corresponding crowdsourced non-aggregated labels, as well as a novel instance-weighted Multiple Kernel Learning SVM method that can directly consider vote distributions from crowdsourcing platforms in the learning methodology. Our results showed a 14% improvement on the dataset against traditional methods, and a 46% improvement when the most ambiguous class from the dataset is ignored, corroborating the promise of the method.