Variational inference is a fast and scalable alternative to Markov chain Monte Carlo and has been widely applied to posterior inference tasks in statistics and machine learning. A traditional approach for implementing mean-field variational inference (MFVI) is coordinate ascent variational inference (CAVI), which relies crucially on parametric assumptions on complete conditionals. In this paper, we introduce a novel particle-based algorithm for mean-field variational inference, which we term PArticle VI (PAVI). Notably, our algorithm does not rely on parametric assumptions on complete conditionals, and it applies to the nonparametric setting. We provide non-asymptotic finite-particle convergence guarantee for our algorithm. To our knowledge, this is the first end-to-end guarantee for particle-based MFVI.

In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces. Metric entropy characterizes the information complexity of function spaces and has implications for their approximability and learnability. Classical results show that embedding a function space into a reproducing kernel Hilbert space (RKHS) implies a bound on its metric entropy growth. Surprisingly, we prove a \textbf{converse}: a bound on the metric entropy growth of a function space allows its embedding to a $L_p-$type Reproducing Kernel Banach Space (RKBS). This shows that the ${L}_p-$type RKBS provides a broad modeling framework for learnable function classes with controlled metric entropies. Our results shed new light on the power and limitations of kernel methods for learning complex function spaces.

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.

In this paper, we propose a deep learning approach to tackle the automatic summarization tasks by incorporating topic information into the convolutional sequence-to-sequence (ConvS2S) model and using self-critical sequence training (SCST) for optimization. Through jointly attending to topics and word-level alignment, our approach can improve coherence, diversity, and informativeness of generated summaries via a biased probability generation mechanism. On the other hand, reinforcement training, like SCST, directly optimizes the proposed model with respect to the non-differentiable metric ROUGE, which also avoids the exposure bias during inference. We carry out the experimental evaluation with state-of-the-art methods over the Gigaword, DUC-2004, and LCSTS datasets. The empirical results demonstrate the superiority of our proposed method in the abstractive summarization.

Time series prediction has been studied in a variety of domains. However, it is still challenging to predict future series given historical observations and past exogenous data. Existing methods either fail to consider the interactions among different components of exogenous variables which may affect the prediction accuracy, or cannot model the correlations between exogenous data and target data. Besides, the inherent temporal dynamics of exogenous data are also related to the target series prediction, and thus should be considered as well. To address these issues, we propose an end-to-end deep learning model, i.e., Hierarchical attention-based Recurrent Highway Network (HRHN), which incorporates spatio-temporal feature extraction of exogenous variables and temporal dynamics modeling of target variables into a single framework. Moreover, by introducing the hierarchical attention mechanism, HRHN can adaptively select the relevant exogenous features in different semantic levels. We carry out comprehensive empirical evaluations with various methods over several datasets, and show that HRHN outperforms the state of the arts in time series prediction, especially in capturing sudden changes and sudden oscillations of time series.

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing the spectrum analysis on the weight matrices of the well-trained networks, and propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics and thus allows deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion processes and nonlocal Markov jump processes.