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.

[Q]: We propose a framework to model the distribution of sequential data coming from
 a set of entities connected in a graph with a known topology. The method is
 based on a mixture of shared hidden Markov models (HMMs), which are trained
 in order to exploit the knowledge of the graph structure and in such a way that the
 obtained mixtures tend to be sparse. Experiments in different application domains
 demonstrate the effectiveness and versatility of the method.
[A]: A method to model the generative distribution of sequences coming from graph connected entities.


[Q]: Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the underlying factors driving their empirical success in min-max problems such as GANs remain unclear. In this paper, we aim at bridging  this gap from both theoretical and empirical perspectives. First, we analyze a variant of Optimistic Stochastic Gradient (OSG) proposed in~\citep{daskalakis2017training} for solving a class of non-convex non-concave min-max problem and establish $O(\epsilon^{-4})$ complexity for finding $\epsilon$-first-order stationary point, in which the algorithm only requires invoking one stochastic first-order oracle while enjoying state-of-the-art iteration complexity achieved by stochastic extragradient method by~\citep{iusem2017extragradient}. Then we propose an adaptive variant of OSG named Optimistic Adagrad (OAdagrad) and reveal an \emph{improved} adaptive complexity $\widetilde{O}\left(\epsilon^{-\frac{2}{1-\alpha}}\right)$~\footnote{Here $\widetilde{O}(\cdot)$ compresses a logarithmic factor of $\epsilon$. }, where $\alpha$ characterizes the growth rate of the cumulative stochastic gradient and $0\leq \alpha\leq 1/2$. To the best of our knowledge, this is the first work for establishing adaptive complexity in non-convex non-concave min-max optimization. Empirically, our experiments show that indeed adaptive gradient algorithms outperform their non-adaptive counterparts in GAN training. Moreover, this observation can be explained by the slow growth rate of the cumulative stochastic gradient, as observed empirically.
[A]: This paper provides novel analysis of adaptive gradient algorithms for solving non-convex non-concave min-max problems as GANs, and explains the reason why adaptive gradient methods outperform its non-adaptive counterparts by empirical studies.


[Q]: Topic modeling of text documents is one of the most important tasks in representation learning. In this work, we propose iTM-VAE, which is a Bayesian nonparametric (BNP) topic model with variational auto-encoders. On one hand, as a BNP topic model, iTM-VAE potentially has infinite topics and can adapt the topic number to data automatically. On the other hand, different with the other BNP topic models, the inference of iTM-VAE is modeled by neural networks, which has rich representation capacity and can be computed in a simple feed-forward manner. Two variants of iTM-VAE are also proposed in this paper, where iTM-VAE-Prod models the generative process in products-of-experts fashion for better performance and iTM-VAE-G places a prior over the concentration parameter such that the model can adapt a suitable concentration parameter to data automatically. Experimental results on 20News and Reuters RCV1-V2 datasets show that the proposed models outperform the state-of-the-arts in terms of perplexity, topic coherence and document retrieval tasks. Moreover, the ability of adjusting the concentration parameter to data is also confirmed by experiments.
[A]:
A Bayesian Nonparametric Topic Model with Variational Auto-Encoders which achieves the state-of-the-arts on public benchmarks in terms of perplexity, topic coherence and retrieval tasks.