We propose a general framework for computing expectations in edge-factored, non-projective spanning-tree models. Our algorithms exploit a fundamental connection between gradients and expectations, which allows us to derive efficient algorithms.  We motivate the development of our framework with several cautionary tales of previous research, which has developed numerous inefficient algorithms for computing expectations and their gradients. We demonstrate how our framework efficiently computes several quantities with known algorithms, including the Shannon entropy, the expected attachment score, and the generalized expectation criterion . As a bonus, we give algorithms for quantities that are missing in the literature, including the gradient of entropy, the KL divergence, and the gradient of the KL divergence . In all cases, our approach matches the efficiency of existing algorithms and, in several cases, reduces the runtime complexity by a factor of the sentence length. We validate  our framework through rigorous proofs of correctness and efficiency .
We give a general framework for inference in spanning tree models. We propose unified algorithms for the important cases of first-order expectations and second-order expectations in edge-factored, non-projective spanning-tree models. Our algorithms exploit a fundamental connection between gradients and expectations, which allows us to derive efficient algorithms. These algorithms are easy to implement with or without automatic differentiation software. We motivate the development of our framework with several cautionary tales of previous research, which has developed numerous inefficient algorithms for computing expectations and their gradients. We demonstrate how our framework efficiently computes several quantities with known algorithms, including the expected attachment score, entropy, and generalized expectation criteria . As a bonus, we give algorithms for quantities that are missing in the literature, including the KL divergence . In all cases, our approach matches the efficiency of existing algorithms and, in several cases, reduces the runtime complexity by a factor of the sentence length. We validate the implementation of our framework through runtime experiments. We find our algorithms are up to 15 and 9 times faster than previous algorithms for computing the Shannon entropy and the gradient of the generalized expectation objective, respectively .
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propose
give
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computing expectations
inference in spanning tree models. We propose unified algorithms for the important cases of first-order expectations and second-order expectations
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These algorithms are easy to implement with or without automatic differentiation software.
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Shannon entropy, the
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and the generalized expectation criterion
entropy, and generalized expectation criteria
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gradient of entropy, the KL divergence, and the gradient of the KL divergence
KL divergence
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the implementation of
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rigorous proofs of correctness and efficiency
runtime experiments. We find our algorithms are up to 15 and 9 times faster than previous algorithms for computing the Shannon entropy and the gradient of the generalized expectation objective, respectively