Abstract--The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their advantages inanalyzing large-scale networks. However, most existing NRL methods are designed to preserve the local topology of a network, they fail to capture the global topology. To tackle this issue, we propose a new NRL framework, named HSRL, to help existing NRL methods capture both the local and global topological information of a network. Then, an existing NRL method is used to learn node embeddings for each compressed network. Finally, the node embeddings of the input network are obtained by concatenating the node embeddings from all compressed networks. Empirical studies for link prediction on five real-world datasets demonstrate the advantages of HSRL over state-of-the-art methods. I. INTRODUCTION The science of networks has been widely used to understand thebehaviours of complex systems.

We consider learning two layer neural networks using stochastic gradient descent. The mean-field description of this learning dynamics approximates the evolution of the network weights by an evolution in the space of probability distributions in $R^D$ (where $D$ is the number of parameters associated to each neuron). This evolution can be defined through a partial differential equation or, equivalently, as the gradient flow in the Wasserstein space of probability distributions. Earlier work shows that (under some regularity assumptions), the mean field description is accurate as soon as the number of hidden units is much larger than the dimension $D$. In this paper we establish stronger and more general approximation guarantees. First of all, we show that the number of hidden units only needs to be larger than a quantity dependent on the regularity properties of the data, and independent of the dimensions. Next, we generalize this analysis to the case of unbounded activation functions, which was not covered by earlier bounds. We extend our results to noisy stochastic gradient descent. Finally, we show that kernel ridge regression can be recovered as a special limit of the mean field analysis.

This paper considers the subject of information losses arising from finite datasets used in the training of neural classifiers. It proves a relationship between such losses and the product of the expected total variation of the estimated neural model with the information about the feature space contained in the hidden representation of that model. It then shows that this total variation drops extremely quickly with sample size. It ultimately obtains bounds on information losses that are less sensitive to input compression and much tighter than existing bounds. This brings about a tighter relevance of information theory to the training of neural networks, so a review of techniques for information estimation and control is provided. The paper then explains some potential uses of these bounds in the field of active learning, and then uses them to explain some recent experimental findings of information compression in neural networks which cannot be explained by previous work. It then uses the bounds to justify an information regularization term in the training of neural networks for low entropy feature space problems. Finally, the paper shows that, not only are these bounds much tighter than existing ones, but that these bounds correspond with experiments as well.

In many machine learning applications, one needs to interactively select a sequence of items (e.g., recommending movies based on a user's feedback) or make sequential decisions in certain orders (e.g., guiding an agent through a series of states). Not only do sequences already pose a dauntingly large search space, but we must take into account past observations, as well as the uncertainty of future outcomes. Without further structure, finding an optimal sequence is notoriously challenging, if not completely intractable. In this paper, we introduce adaptive sequence submodularity, a rich framework that generalizes the notion of submodularity to adaptive policies that explicitly consider sequential dependencies between items. We show that once such dependencies are encoded by a directed graph, an adaptive greedy policy is guaranteed to achieve a constant factor approximation guarantee, where the constant naturally depends on the structural properties of the underlying graph. Additionally, to demonstrate the practical utility of our results, we run experiments on Amazon product recommendation and Wikipedia link prediction tasks.

The Bayesian Optimisation Algorithm (BOA) is an Estimation of Distribution Algorithm (EDA) that uses a Bayesian network as probabilistic graphical model (PGM). Determining the optimal Bayesian network structure given a solution sample is an NP-hard problem. This step should be completed at each iteration of BOA, resulting in a very time-consuming process. For this reason most implementations use greedy estimation algorithms such as K2. However, we show in this paper that significant changes in PGM structure do not occur so frequently, and can be particularly sparse at the end of evolution. A statistical study of BOA is thus presented to characterise a pattern of PGM adjustments that can be used as a guide to reduce the frequency of PGM updates during the evolutionary process. This is accomplished by proposing a new BOA-based optimisation approach (FBOA) whose PGM is not updated at each iteration. This new approach avoids the computational burden usually found in the standard BOA. The results compare the performances of both algorithms on an NK-landscape optimisation problem using the correlation between the ruggedness and the expected runtime over enumerated instances. The experiments show that FBOA presents competitive results while significantly saving computational time.

In real-world scenarios, the observation data for reinforcement learning with continuous control is commonly noisy and part of it may be dynamically missing over time, which violates the assumption of many current methods developed for this. We addressed the issue within the framework of partially observable Markov Decision Process (POMDP) using a model-based method, in which the transition model is estimated from the incomplete and noisy observations using a newly proposed surrogate loss function with local approximation, while the policy and value function is learned with the help of belief imputation. For the latter purpose, a generative model is constructed and is seamlessly incorporated into the belief updating procedure of POMDP, which enables robust execution even under a significant incompleteness and noise. The effectiveness of the proposed method is verified on a collection of benchmark tasks, showing that our approach outperforms several compared methods under various challenging scenarios.

Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve mixing/convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain Monte Carlo. Nonetheless, introducing appropriate auxiliary variables while preserving the initial target probability distribution cannot be conducted in a systematic way but highly depends on the considered problem. To deal with such issues, this paper draws a unified framework, namely asymptotically exact data augmentation (AXDA), which encompasses several well-established but also more recent approximate augmented models. Benefiting from a much more general perspective, it delivers some additional qualitative and quantitative insights concerning these schemes. In particular, general properties of AXDA along with non-asymptotic theoretical results on the approximation that is made are stated. Close connections to existing Bayesian methods (e.g. mixture modeling, robust Bayesian models and approximate Bayesian computation) are also drawn. All the results are illustrated with examples and applied to standard statistical learning problems.

The deep network model, with the majority built on neural networks, has been proved to be a powerful framework to represent complex data for high performance machine learning. In recent years, more and more studies turn to nonneural network approaches to build diverse deep structures, and the Deep Stacking Network (DSN) model is one of such approaches that uses stacked easy-to-learn blocks to build a parameter-training-parallelizable deep network. In this paper, we propose a novel SVM-based Deep Stacking Network (SVM-DSN), which uses the DSN architecture to organize linear SVM classifiers for deep learning. A BP-like layer tuning scheme is also proposed to ensure holistic and local optimizations of stacked SVMs simultaneously. Some good math properties of SVM, such as the convex optimization, is introduced into the DSN framework by our model. From a global view, SVM-DSN can iteratively extract data representations layer by layer as a deep neural network but with parallelizability, and from a local view, each stacked SVM can converge to its optimal solution and obtain the support vectors, which compared with neural networks could lead to interesting improvements in anti-saturation and interpretability. Experimental results on both image and text data sets demonstrate the excellent performances of SVM-DSN compared with some competitive benchmark models.

In this paper we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction on the discriminative function space commonly suffer from the problem that the gradient produced by the discriminator is uninformative to guide the generator. By contrast, Wasserstein GAN (WGAN), where the discriminative function is restricted to $1$-Lipschitz, does not suffer from such a gradient uninformativeness problem. We further show in the paper that the model with a compact dual form of Wasserstein distance, where the Lipschitz condition is relaxed, also suffers from this issue. This implies the importance of Lipschitz condition and motivates us to study the general formulation of GANs with Lipschitz constraint, which leads to a new family of GANs that we call Lipschitz GANs (LGANs). We show that LGANs guarantee the existence and uniqueness of the optimal discriminative function as well as the existence of a unique Nash equilibrium. We prove that LGANs are generally capable of eliminating the gradient uninformativeness problem. According to our empirical analysis, LGANs are more stable and generate consistently higher quality samples compared with WGAN.

While neural networks have achieved vastly enhanced performance over traditional iterative methods in many cases, they are generally empirically designed and the underlying structures are difficult to interpret. The algorithm unrolling approach has helped connect iterative algorithms to neural network architectures. However, such connections have not been made yet for blind image deblurring. In this paper, we propose a neural network architecture that advances this idea. We first present an iterative algorithm that may be considered a generalization of the traditional total-variation regularization method on the gradient domain, and subsequently unroll the half-quadratic splitting algorithm to construct a neural network. Our proposed deep network achieves significant practical performance gains while enjoying interpretability at the same time. Experimental results show that our approach outperforms many state-of-the-art methods.