Efficient prediction of relational structure and its application to natural language processing

Many tasks in Natural Language Processing (NLP) require us to predict a relational structure over entities. For example, in Semantic Role Labelling we try to predict the ’semantic role’ relation between a predicate verb and its argument constituents. Often NLP tasks not only involve related entities but also relations that are stochastically correlated. For instance, in Semantic Role Labelling the roles of different constituents are correlated: we cannot assign the agent role to one constituent if we have already assigned this role to another. Statistical Relational Learning (also known as First Order Probabilistic Logic) allows us to capture the aforementioned nature of NLP tasks because it is based on the notions of entities, relations and stochastic correlations between relationships. It is therefore often straightforward to formulate an NLP task using a First Order probabilistic language such as Markov Logic. However, the generality of this approach comes at a price: the process of finding the relational structure with highest probability, also known as maximum a posteriori (MAP) inference, is often inefficient, if not intractable. In this work we seek to improve the efficiency of MAP inference for Statistical Relational Learning. We propose a meta-algorithm, namely Cutting Plane Inference (CPI), that iteratively solves small subproblems of the original problem using any existing MAP technique and inspects parts of the problem that are not yet included in the current subproblem but could potentially lead to an improved solution. Our hypothesis is that this algorithm can dramatically improve the efficiency of existing methods while remaining at least as accurate. We frame the algorithm in Markov Logic, a language that combines First Order Logic and Markov Networks. Our hypothesis is evaluated using two tasks: Semantic Role Labelling and Entity Resolution. It is shown that the proposed algorithm improves the efficiency of two existing methods by two orders of magnitude and leads an approximate method to more probable solutions. We also give show that CPI, at convergence, is guaranteed to be at least as accurate as the method used within its inner loop. Another core contribution of this work is a theoretic and empirical analysis of the boundary conditions of Cutting Plane Inference. We describe cases when Cutting Plane Inference will definitely be difficult (because it instantiates large networks or needs many iterations) and when it will be easy (because it instantiates small networks and needs only few iterations)

Interpreting Embedding Models of Knowledge Bases: A Pedagogical Approach

Knowledge bases are employed in a variety of applications from natural language processing to semantic web search; alas, in practice their usefulness is hurt by their incompleteness. Embedding models attain state-of-the-art accuracy in knowledge base completion, but their predictions are notoriously hard to interpret. In this paper, we adapt "pedagogical approaches" (from the literature on neural networks) so as to interpret embedding models by extracting weighted Horn rules from them. We show how pedagogical approaches have to be adapted to take upon the large-scale relational aspects of knowledge bases and show experimentally their strengths and weaknesses.Comment: presented at 2018 ICML Workshop on Human Interpretability in Machine Learning (WHI 2018), Stockholm, Swede

kLog: A Language for Logical and Relational Learning with Kernels

We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials

End-to-End Differentiable Proving

We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules.Comment: NIPS 2017 camera-ready, NIPS 201