Pavel Sountsov
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NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
Josh Dillon
arXiv preprint (2019)
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Hamiltonian Monte Carlo is a powerful algorithm for sampling from difficult-to-normalize posterior distributions. However, when the geometry of the posterior is unfavorable, it may take many expensive evaluations of the target distribution and its gradient to converge and mix. We propose neural transport (NeuTra) HMC, a technique for learning to correct this sort of unfavorable geometry using inverse autoregressive flows (IAF), a powerful neural variational inference technique. The IAF is trained to minimize the KL divergence from an isotropic Gaussian to the warped posterior, and then HMC sampling is performed in the warped space. We evaluate NeuTra HMC on a variety of synthetic and real problems, and find that it significantly outperforms vanilla HMC both in time to reach the stationary distribution and asymptotic effective-sample-size rates.
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Preview abstract
Encoder-decoder networks are popular for modeling sequences probabilistically in many applications. These models use the power of the Long Short-Term Memory (LSTM) architecture to capture the full dependence among variables, unlike earlier models like CRFs that typically assumed conditional independence among non-adjacent variables. However in practice encoder-decoder models exhibit a bias towards short sequences that surprisingly gets worse with increasing beam size.
In this paper we show that such phenomenon is due to a discrepancy between the full sequence margin and the per-element margin enforced by the locally conditioned training objective of a encoder-decoder model. The discrepancy more adversely impacts long sequences, explaining the bias towards predicting short sequences.
For the case where the predicted sequences come from a closed set, we show that a globally conditioned model alleviates the above problems of encoder-decoder models. From a practical point of view, our proposed model also eliminates the need for a beam-search during inference, which reduces to an efficient dot-product based search in a vector-space.
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