We develop an automated variational inference method for Bayesian structured prediction problems with Gaussian process (GP) priors and linear-chain likelihoods. Our approach does not need to know the details of the structured likelihood model and can scale up to a large number of observations. Furthermore, we show that the required expected likelihood term and its gradients in the variational objective (ELBO) can be estimated efficiently by using expectations over very low-dimensional Gaussian distributions. Optimization of the ELBO is fully parallelizable over sequences and amenable to stochastic optimization, which we use along with control variate techniques and state-of-the-art incremental optimization to make our framework useful in practice. Results on a set of natural language processing tasks show that our method can be as good as (and sometimes better than) hard-coded approaches including SVM-struct and CRFs, and overcomes the scalability limitations of previous inference algorithms based on sampling. Overall, this is a fundamental step to developing automated inference methods for Bayesian structured prediction.
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