OxKBC: Outcome Explanation for Factorization Based Knowledge Base Completion

and YAGO ) are based on tensor factorization ( TF ) , e.g , DistMult , ComplEx . While they produce good results , they can not expose any rationale behind their predictions , potentially reducing the trust of a user in the outcome of the model . Previous works have explored creating an inherently explainable model , e.g . Neural Theorem Proving ( NTP ) , DeepPath , MINERVA , but explainability in them comes at the cost of performance . Others have tried to create an auxiliary explainable model having high fidelity with the underlying TF model , but unfortunately , they do not scale well to large KBs . In this work , we propose OXKBC – an Outcome eXplanation engine for KBC , which provides a post-hoc explanation for every triple inferred by a ( uninterpretable ) factorization based model . It first augments the underlying Knowledge Graph by introducing weighted edges between entities based on their similarity given by the underlying model . It then defines a notion of human-understandable explanation paths along with a language to generate them . Depending on the edges , the paths are aggregated into second–order templates for further selection . The best template with its grounding is then selected by a neural selection module that is trained with minimal supervision by a novel loss function . Experiments over Mechanical Turk demonstrate that users overwhelmingly find our explanations more trustworthy compared to rule mining . 1 . Introduction . Knowledge bases ( KBs ) store facts in the form of triples r ( s , o ) , which indicate that the head entity s is related to the tail entity o via the relation r , e.g. , capitalOf ( WashingtonDC , USA ) . These KBs are typically incomplete [ Bollacker et al. , 2008 ] and the task of KB Completion ( KBC ) aims to infer new facts from a given KB . Many state-of-the-art models for KBC on large-scale KBs use tensor factorization ( TF ) [ Sedghi and Sabharwal , 2018 , Lacroix et al. , 2018 , Jain et al. , 2018 , Xue et al. , 2018 ] . They learn embeddings for each entity and relation in a continuous vector space and define a scoring function to evaluate the validity of a given triple . At test time , given a query r ( s , ? ) they output a ranked list of entities o by sorting the model scores for r ( s , o ) for all possible tail entities . Though TF models achieve ∗ . Joint second author . excellent task performance , they are inherently opaque – it is very difficult to uncover a rationale for why the model scores an entity high for a query , because neither the dimensions nor the scoring function are human interpretable . Since users are often the final consumers of a KB ( e.g. , via a KB-based QA task , or an entity retrieval task [ Xiao et al. , 2016 ] ) , we believe providing a rationale behind a prediction to them is an important sub-task for building trust in these systems . Contributions : We present OXKBC : a post-hoc Outcome eXplanation engine , which is faithful to a given TF -based KBC model ( M ) . It works on the underlying Knowledge Graph , KG , corresponding to the facts given in the Knowledge Base , KB . It first augments the KG with weighted edges between entities based on their similarity as defined by the underlying model M . It then posits that an explanation for a prediction o for query r ( s , ? ) is a path between s and o in this augmented graph . A key contribution of our work is that similar paths are grouped into second-order templates and OXKBC trains a neural template selection module for explaining a given prediction . We define novel unsupervised and semi-supervised loss functions , so that this module can be trained with no or minimal training data . OXKBC outputs the highest scoring path within the selected template as an explanation to the user . We evaluate OXKBC explanations via a user study over Amazon Mechanical Turk . We find that workers overwhelmingly prefer OXKBC explanations compared to rule-mining techniques proposed earlier . 2 . Related Work . KBC : Other than TF based models , research has also explored path based approaches for KBC . They use random walk with restarts [ Lao and Cohen , 2010 ] and more recently , reinforcement learning [ Das et al. , 2018 , Xiong et al. , 2017 ] to construct multi-hop paths in the knowledge graph and use those to make predictions . The paths may offer natural interpretability [ Nickel et al. , 2016 ] , but the performance of these models is significantly lower than TF , especially on large KBs like FB15K [ Bordes et al. , 2013 ] , and YAGO [ Suchanek et al. , 2007 ] . See Appendix A.1 for a detailed comparison . [ Rocktäschel and Riedel , 2017 ] inductively learn first order rules to generate paths by using a differentiable version of backward chaining . Unfortunately , it does not scale beyond 10K facts in KB.1 In contamporaneous work , [ Minervini et al. , 2020 ] speed up neural theorem proving for this task . Unfortunately , we could not get their method to complete even after a week of continuous computation on FB15K , suggesting that their method still is not scalable to large KBs . Earlier , research had also considered symbolic Horn-clause style inference [ Lao and Cohen , 2010 , Schoenmackers et al. , 2010 ] , though these are no longer competitive with modern neural methods . TF methods , like DistMult [ Yang et al. , 2015 ] and ComplEx [ Trouillon et al. , 2016 ] , calculate the score SM ( s , r , o ) , of a triple r ( s , o ) via a latent tensor factorization over entity embeddings ( s , t ) and relation embeddings ( r ) . Key idea in these methods is to learn embeddings such that the score SM of the facts present in the KB is high . In this case , DistMult [ Yang et al. , 2015 ] aligns relation embeddings to the Hadamard product of the embeddings of head and tail entitites . It uses SM ( s , r , o ) = rT ( s • o ) , where • is the element-wise product , also known as Hadamard product . While in principle OXKBC may be adapted to explain any TF model ’ s predictions , in our experiments , we use TypedDistMult 2 [ Jain et al. , 2018 ] as our underlying model M . The key idea is to augment the scoring function used by DistMult to reduce type errors . Two new terms are introduced to account for head and tail entity type compatibility . The approach requires no explicit 1. https : //www.akbc.ws/2017/slides/sebastian-riedel-slides.pdf 2 . Code taken from https : //github.com/dair-iitd/KBI specification of type hierarchies or type supervision . The scoring function SM scores r ( s , o ) as SM ( s , r , o ) = σ ( rTw ( sw • ow ) ) σ ( rTtsst ) σ ( rTtoot ) , where σ is the sigmoid function . The subscript w denotes the world knowledge embedding , t denotes the type embedding of an entity and ts and to denote head and tail type embeddings of a relation , respectively . Explainability in KBC : There are broadly two approaches for explainable AI . One is to design a transparent model , which can inherently reveal its functioning ( e.g. , linear models , decision trees , Horn-clause inference for KBC ) . Unfortunately , transparent models often result in compromised performance in general [ Weld and Bansal , 2018 ] , as well as specifically for KBC ( as discussed earlier in this section ) . An alternative is to provide post-hoc explanations for the behaviour of a high-quality black box model [ Wachter et al. , 2017 ] . This approach is further divided into two categories : ‘ Model Explanation ’ ( MX ) and ‘ Outcome Explanation ’ ( OX ) [ Costabello et al. , 2019 ] . In MX , once the black–box model is learnt , a global explainable auxiliary model is built using the predictions of the black-box model such that the auxiliary model has high fidelity with the original black-box model . Rule mining [ Yang et al. , 2015 ] is an MX approach , which mines first order rules based on embeddings learnt by M . It identifies paths ( of length ≤ 3 ) using the notion of support and confidence borrowed from the frequent itemset mining literature [ Pei et al. , 2000 ] . Search space is pruned by considering only those relations which are close to each other in the embedding space . The extracted first order rules may be used to explain a prediction . We compare against this approach in our experiments . The other MX approach is known as the pedagogical approach – it trains a global auxiliary interpretable model ( weighted Horn clause rules ) from the output of the non-interpretable but accurate TF model [ Gusmão et al. , 2018 ] . Its experiments were on a toy dataset with only 13 relations , and unfortunately , we were unable to scale this to the size of our dataset ( see Appendix A.2 ) . OX , attempts to achieve a higher fidelity between explainable model and M by creating local model approximations around each prediction independently , e.g . [ Ribeiro et al. , 2016 ] . This approach often trains a new classifier for each prediction , which is slow if a large number of predictions need to be explained . In response , OXKBC takes a novel OX approach , which decomposes the explanation engine into two components : a global trained model that , for a given prediction , selects the most plausible second-order explanation template ( which quantifies over both relations and entities ) , and an explanation generator that outputs the best instantiation of the template for this prediction . This approach scales better , since the trained model is global and easy to train , and no retraining is required per prediction . Finally , a related task to OX is fact checking – verifying the truthfulness of a ( predicted ) triple r ( s , o ) based on existing facts in the KB . Many fact-checking approaches [ Shiralkar et al. , 2017 , Shi and Weninger , 2016 ] use path based techniques to check the veracity of a triple and generate paths as evidence . However , these methods do not use algorithms that use information from the underlying TF model . Thus , while these paths may be useful evidence , they should not be used as explanations , as they are not faithful to the TF model . In the future , it may be interesting to combine fact checking ideas with statistical information in TF models to develop a better outcome explanation engine . 3 . OXKBC : The Outcome Explanation Engine . We are given a knowledge base of facts , KB , with relations R and entities E , and a model M , trained on KB . M scores each triple r ( s , o ) using the score SM ( s , r , o ) . The goal of OXKBC is to show an end-user a reason why M predicts a tail entity o for the query r ( s , ? ) . It does so by finding an explanation path between s and o which entails the given relation r .

Summary: The paper proposes a novel approach to providing an explanation for the prediction made by off-the-shelf tensor factorization models by using its scores to create an augmented weighted knowledge graph and scoring higher order paths (aka templates) as explanations. The presentation is mostly clear and the results are convincing of the proposed idea. The paper however suffers from lack of sufficient novelty and adequate experimental comparison with other state-of-the-art approaches that offer explanations.