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How does predicate invention affect human comprehensibility?
During the 1980s Michie defined Machine Learning in terms of two orthogonal axes of performance: predictive accuracy and comprehensibility of generated hypotheses. Since predictive accuracy was readily measurable and comprehensibility not so, later definitions in the 1990s, such as that of Mitchell, tended to use a one-dimensional approach to Machine Learning based solely on predictive accuracy, ultimately favouring statistical over symbolic Machine Learning approaches. In this paper we provide a definition of comprehensibility of hypotheses which can be estimated using human participant trials. We present the results of experiments testing human comprehensibility of logic programs learned with and without predicate invention. Results indicate that comprehensibility is affected not only by the complexity of the presented program but also by the existence of anonymous predicate symbols
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
Models of Co-occurrence
A model of co-occurrence in bitext is a boolean predicate that indicates
whether a given pair of word tokens co-occur in corresponding regions of the
bitext space. Co-occurrence is a precondition for the possibility that two
tokens might be mutual translations. Models of co-occurrence are the glue that
binds methods for mapping bitext correspondence with methods for estimating
translation models into an integrated system for exploiting parallel texts.
Different models of co-occurrence are possible, depending on the kind of bitext
map that is available, the language-specific information that is available, and
the assumptions made about the nature of translational equivalence. Although
most statistical translation models are based on models of co-occurrence,
modeling co-occurrence correctly is more difficult than it may at first appear
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