Learning to Reason with a Scalable Probabilistic Logic

Learning to reason and understand the world’s knowledge is a fundamental problem in Artificial Intelligence (AI). Traditional symbolic AI methods are popular in the 1980s, when first-order logic rules are mostly handwritten, and reasoning algorithms are built on top of them. In the 90s, more and more researchers are interested in statistical methods that deal with the uncertainty of the data, using probabilistic models. While it is always hypothesized that both the symbolic and statistical approaches are necessary for building intelligent systems, in practice, bridging the two in a combined framework might bring intractability— most probabilistic first-order logics are simply not efficient enough for real-world sized tasks. For example, Markov Logics [67] integrate first-order logics in the Markov random field theory, but when mapping the entities in a knowledge base (KB) to the propositional theory (i.e., grounding), the size of the network depends on the facts in the KB— i.e., O(nk) where k is the arity of the predicate, and n is the number of KB facts. In this thesis, we propose a new, scalable probabilistic logic called ProPPR [85] to combine the best of the symbolic and statistical worlds. ProPPR (Programming with Personalized PageRank) is a stochastic extension of the logic programming language Prolog —it has the rich semantic representation of Prolog, but we associate a feature vector φc to each clause c, such that each clause has a weight vector that can be learned from the training data. Another important contribution is the inference procedure of ProPPR: instead of searching over the entire graph for solutions, ProPPR uses a provably-correct approximate personalized PageRank to construct a subgraph for local grounding, and the inference time is theoretically bounded by o( 1 αε ), where α is the reset parameter to bias the solutions in shorter proofs, and ε is the worst-case approximation error. The discovery of ProPPR’s inference scheme leads to a surprising and important finding: the inference time is now independent of the size of the KB. Empirically, it is shown that ProPPR’s inference time and predictive accuracy outperform various bases in an entity disambiguation task, and a text classification task. Recently, it is also shown that ProPPR can be viewed as a recursive extension [89] to the popular path ranking algorithm (PRA) [43], and outperforms PRA in the inference task with one million facts from NELL [13], a large knowledge base with information extracted imperfectly from the Web. This thesis also provides a scalable solution to a core problem in statistical relational learning: structure learning to extract the inference rules from KBs. For example, we know that an athlete plays in a team, and a team plays in a league, we want to learn an inference rule that asserts that athletePlaysInLeague(A,L) :athletePlaysInTeam(A,T),teamInLeague(T,L). August 28, 2015 DRAFT To do this, we propose a second-order abductive theory [87], whose parameter corresponds to plausible first-order inference rules. To improve the performance, an iterative structural gradient approach is proposed to incrementally refine the set of learned rules. In experiments, we show that the proposed approach only needs a few minutes to learn the inference rules, and when using these learned rules, the predictive results improve traditional and statistical methods by a large margin. Furthermore, to learn a set of compact theory, we show that it is possible to apply a group Lasso based structured sparsity as soft predicate invention to this task [88], while obtaining state-of-the-art results. Finally, we demonstrate that ProPPR can be used as a generic framework to combine the knowledge and text based methods [83]: a partially-populated KB and a set of relation mentions in context are used as input, and we jointly learn (1) how to extract new KB facts from the relation mentions, and (2) a set of logical rules that allow one to infer new KB facts. It is shown that the proposed joint model for IE and relational learning outperforms universal schemas [69], a state-of-the-art joint method, and that incorporating latent context further improves the results. We also show that ProPPR can also be used as a programmable dependency parser [86] for theory engineering in structure prediction tasks on social media data, outperforming state-of-the-art parsers.