In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

[EX Q]: In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One way to address this question is to find an upper bound on the probability (equivalently a lower bound on the negative log likelihood) that the model can assign to some data as one varies the prior and/or the likelihood function in a latent variable model. The core of our contribution is to formally show that the problem of optimizing priors in latent variable models is exactly an instance of the variational optimization problem that information theorists solve when computing rate-distortion functions, and then to use this to derive a lower bound on negative log likelihood. Moreover, we will show that if changing the prior can improve the log likelihood, then there is a way to change the likelihood function instead and attain the same log likelihood, and thus rate-distortion theory is of relevance to both optimizing priors as well as optimizing likelihood functions. We will experimentally argue for the usefulness of quantities derived from rate-distortion theory in latent variable modeling by applying them to a problem in image modeling.
[EX A]: Use rate-distortion theory to bound how much a latent variable model can be improved

[EX Q]: This paper proposes variational domain adaptation, a unified, scalable, simple framework for learning multiple distributions through variational inference. Unlike the existing methods on domain transfer through deep generative models, such as StarGAN (Choi et al., 2017) and UFDN (Liu et al., 2018), the variational domain adaptation has three advantages. Firstly, the  samples from the target are not required. Instead, the framework requires one known source as a prior $p(x)$ and binary discriminators, $p(\mathcal{D}_i|x)$, discriminating the target domain $\mathcal{D}_i$ from others. Consequently, the framework regards a target as a posterior that can be explicitly formulated through the Bayesian inference, $p(x|\mathcal{D}_i) \propto p(\mathcal{D}_i|x)p(x)$, as exhibited by a further proposed model of dual variational autoencoder (DualVAE). Secondly, the framework is scablable to large-scale domains. As well as VAE encodes a sample $x$ as a mode on a latent space: $\mu(x) \in \mathcal{Z}$, DualVAE encodes a domain $\mathcal{D}_i$ as a mode on the dual latent space $\mu^*(\mathcal{D}_i) \in \mathcal{Z}^*$, named domain embedding. It reformulates the posterior with a natural paring $\langle, \rangle: \mathcal{Z} \times \mathcal{Z}^* \rightarrow \Real$, which can be expanded to uncountable infinite domains such as continuous domains as well as interpolation. Thirdly, DualVAE fastly converges without sophisticated automatic/manual hyperparameter search in comparison to GANs as it requires only one additional parameter to VAE. Through the numerical experiment, we demonstrate the three benefits with multi-domain image generation task on CelebA with up to 60 domains, and exhibits that DualVAE records the state-of-the-art performance outperforming StarGAN and UFDN.
[EX A]: This paper proposes variational domain adaptation, a uniﬁed, scalable, simple framework for learning multiple distributions through variational inference

[EX Q]: We propose a unified framework for building unsupervised representations of individual objects or entities (and their compositions), by associating with each object both a distributional as well as a point estimate (vector embedding). This is made possible by the use of optimal transport, which allows us to build these associated estimates while harnessing the underlying geometry of the ground space. Our method gives a novel perspective for building rich and powerful feature representations that simultaneously capture uncertainty (via a distributional estimate) and interpretability (with the optimal transport map). As a guiding example, we formulate unsupervised representations for text, in particular for sentence representation and entailment detection. Empirical results show strong advantages gained through the proposed framework. This approach can be used for any unsupervised or supervised problem (on text or other modalities) with a co-occurrence structure, such as any sequence data. The key tools underlying the framework are Wasserstein distances and Wasserstein barycenters (and, hence the title!).
[EX A]:
Represent each entity based on its histogram of contexts and then Wasserstein is all you need!