Minimum Rates of Approximate Sufficient Statistics

Given a sufficient statistic for a parametric family of distributions, one can estimate the parameter without access to the data. However, the memory or code size for storing the sufficient statistic may nonetheless still be prohibitive. Indeed, for $n$ independent samples drawn from a $k$-nomial distribution with $d=k-1$ degrees of freedom, the length of the code scales as $d\log n+O(1)$. In many applications, we may not have a useful notion of sufficient statistics (e.g., when the parametric family is not an exponential family) and we also may not need to reconstruct the generating distribution exactly. By adopting a Shannon-theoretic approach in which we allow a small error in estimating the generating distribution, we construct various {\em approximate sufficient statistics} and show that the code length can be reduced to $\frac{d}{2}\log n+O(1)$. We consider errors measured according to the relative entropy and variational distance criteria. For the code constructions, we leverage Rissanen's minimum description length principle, which yields a non-vanishing error measured according to the relative entropy. For the converse parts, we use Clarke and Barron's formula for the relative entropy of a parametrized distribution and the corresponding mixture distribution. However, this method only yields a weak converse for the variational distance. We develop new techniques to achieve vanishing errors and we also prove strong converses. The latter means that even if the code is allowed to have a non-vanishing error, its length must still be at least $\frac{d}{2}\log n$.Comment: To appear in the IEEE Transactions on Information Theor

Deconvolutional Latent-Variable Model for Text Sequence Matching

A latent-variable model is introduced for text matching, inferring sentence representations by jointly optimizing generative and discriminative objectives. To alleviate typical optimization challenges in latent-variable models for text, we employ deconvolutional networks as the sequence decoder (generator), providing learned latent codes with more semantic information and better generalization. Our model, trained in an unsupervised manner, yields stronger empirical predictive performance than a decoder based on Long Short-Term Memory (LSTM), with less parameters and considerably faster training. Further, we apply it to text sequence-matching problems. The proposed model significantly outperforms several strong sentence-encoding baselines, especially in the semi-supervised setting.Comment: Accepted by AAAI-201

Deep Recurrent Generative Decoder for Abstractive Text Summarization

We propose a new framework for abstractive text summarization based on a sequence-to-sequence oriented encoder-decoder model equipped with a deep recurrent generative decoder (DRGN). Latent structure information implied in the target summaries is learned based on a recurrent latent random model for improving the summarization quality. Neural variational inference is employed to address the intractable posterior inference for the recurrent latent variables. Abstractive summaries are generated based on both the generative latent variables and the discriminative deterministic states. Extensive experiments on some benchmark datasets in different languages show that DRGN achieves improvements over the state-of-the-art methods.Comment: 10 pages, EMNLP 201