A Bayesian Approach toward Active Learning for Collaborative Filtering

Collaborative filtering is a useful technique for exploiting the preference patterns of a group of users to predict the utility of items for the active user. In general, the performance of collaborative filtering depends on the number of rated examples given by the active user. The more the number of rated examples given by the active user, the more accurate the predicted ratings will be. Active learning provides an effective way to acquire the most informative rated examples from active users. Previous work on active learning for collaborative filtering only considers the expected loss function based on the estimated model, which can be misleading when the estimated model is inaccurate. This paper takes one step further by taking into account of the posterior distribution of the estimated model, which results in more robust active learning algorithm. Empirical studies with datasets of movie ratings show that when the number of ratings from the active user is restricted to be small, active learning methods only based on the estimated model don't perform well while the active learning method using the model distribution achieves substantially better performance.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004

Chronosymbolic Learning: Efficient CHC Solving with Symbolic Reasoning and Inductive Learning

Solving Constrained Horn Clauses (CHCs) is a fundamental challenge behind a wide range of verification and analysis tasks. Data-driven approaches show great promise in improving CHC solving without the painstaking manual effort of creating and tuning various heuristics. However, a large performance gap exists between data-driven CHC solvers and symbolic reasoning-based solvers. In this work, we develop a simple but effective framework, "Chronosymbolic Learning", which unifies symbolic information and numerical data points to solve a CHC system efficiently. We also present a simple instance of Chronosymbolic Learning with a data-driven learner and a BMC-styled reasoner. Despite its great simplicity, experimental results show the efficacy and robustness of our tool. It outperforms state-of-the-art CHC solvers on a dataset consisting of 288 benchmarks, including many instances with non-linear integer arithmetics