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Sparsity-based methods have a long history in the field of signal processing and have been successfully applied to various image reconstruction problems. The involved sparsifying transformations or dictionaries are typically either pre-trained using a model which reflects the assumed properties of the signals or adaptively learned during the reconstruction - yielding so-called blind Compressed Sensing approaches. However, by doing so, the transforms are never explicitly trained in conjunction with the physical model which generates the signals. In addition, properly choosing the involved regularization parameters remains a challenging task. Another recently emerged training-paradigm for regularization methods is to use iterative neural networks (INNs) - also known as unrolled networks - which contain the physical model. In this work, we construct an INN which can be used as a supervised and physics-informed online convolutional dictionary learning algorithm. We evaluated the proposed approach by applying it to a realistic large-scale dynamic MR reconstruction problem and compared it to several other recently published works. We show that the proposed INN improves over two conventional model-agnostic training methods and yields competitive results also compared to a deep INN. Further, it does not require to choose the regularization parameters and - in contrast to deep INNs - each network component is entirely interpretable.

Graph Neural Networks (GNNs) have achieved great success in various graph mining tasks.However, drastic performance degradation is always observed when a GNN is stacked with many layers. As a result, most GNNs only have shallow architectures, which limits their expressive power and exploitation of deep neighborhoods.Most recent studies attribute the performance degradation of deep GNNs to the \textit{over-smoothing} issue. In this paper, we disentangle the conventional graph convolution operation into two independent operations: \textit{Propagation} (\textbf{P}) and \textit{Transformation} (\textbf{T}).Following this, the depth of a GNN can be split into the propagation depth ($D_p$) and the transformation depth ($D_t$). Through extensive experiments, we find that the major cause for the performance degradation of deep GNNs is the \textit{model degradation} issue caused by large $D_t$ rather than the \textit{over-smoothing} issue mainly caused by large $D_p$. Further, we present \textit{Adaptive Initial Residual} (AIR), a plug-and-play module compatible with all kinds of GNN architectures, to alleviate the \textit{model degradation} issue and the \textit{over-smoothing} issue simultaneously. Experimental results on six real-world datasets demonstrate that GNNs equipped with AIR outperform most GNNs with shallow architectures owing to the benefits of both large $D_p$ and $D_t$, while the time costs associated with AIR can be ignored.

The analysis of cyber-physical systems (CPS) is challenging due to the large state space and the continuous changes occurring in its parts. Design practices favor modularity to help reducing the complexity. In a previous work, we proposed a discrete semantic model for CPS that captures both cyber and physical aspects as streams of discrete observations, which ultimately form the behavior of a component. This semantic model is denotational and compositional, where each composition operator algebraically models the interaction between a pair of components. In this paper, we propose a specification of some components as rewrite systems. The specification is operational and executable, and we study conditions for its semantics as components to be compositional. We demonstrate our framework on modeling a coordination of robots moving on a shared field. We show that the system of robots can be coordinated by a protocol in order to exhibit emerging behavior. We use an implementation of our framework in Maude to give some practical results.

Gaussian processes provide an elegant framework for specifying prior and posterior distributions over functions. They are, however, also computationally expensive, and limited by the expressivity of their covariance function. We propose Neural Diffusion Processes (NDPs), a novel approach based upon diffusion models, that learn to sample from distributions over functions. Using a novel attention block, we can incorporate properties of stochastic processes, such as exchangeability, directly into the NDP's architecture. We empirically show that NDPs are able to capture functional distributions that are close to the true Bayesian posterior of a Gaussian process. This enables a variety of downstream tasks, including hyperparameter marginalisation and Bayesian optimisation.

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.

Learning disentanglement aims at finding a low dimensional representation which consists of multiple explanatory and generative factors of the observational data. The framework of variational autoencoder (VAE) is commonly used to disentangle independent factors from observations. However, in real scenarios, factors with semantics are not necessarily independent. Instead, there might be an underlying causal structure which renders these factors dependent. We thus propose a new VAE based framework named CausalVAE, which includes a Causal Layer to transform independent exogenous factors into causal endogenous ones that correspond to causally related concepts in data. We further analyze the model identifiabitily, showing that the proposed model learned from observations recovers the true one up to a certain degree. Experiments are conducted on various datasets, including synthetic and real word benchmark CelebA. Results show that the causal representations learned by CausalVAE are semantically interpretable, and their causal relationship as a Directed Acyclic Graph (DAG) is identified with good accuracy. Furthermore, we demonstrate that the proposed CausalVAE model is able to generate counterfactual data through "do-operation" to the causal factors.

Deep learning methods for graphs achieve remarkable performance on many node-level and graph-level prediction tasks. However, despite the proliferation of the methods and their success, prevailing Graph Neural Networks (GNNs) neglect subgraphs, rendering subgraph prediction tasks challenging to tackle in many impactful applications. Further, subgraph prediction tasks present several unique challenges, because subgraphs can have non-trivial internal topology, but also carry a notion of position and external connectivity information relative to the underlying graph in which they exist. Here, we introduce SUB-GNN, a subgraph neural network to learn disentangled subgraph representations. In particular, we propose a novel subgraph routing mechanism that propagates neural messages between the subgraph's components and randomly sampled anchor patches from the underlying graph, yielding highly accurate subgraph representations. SUB-GNN specifies three channels, each designed to capture a distinct aspect of subgraph structure, and we provide empirical evidence that the channels encode their intended properties. We design a series of new synthetic and real-world subgraph datasets. Empirical results for subgraph classification on eight datasets show that SUB-GNN achieves considerable performance gains, outperforming strong baseline methods, including node-level and graph-level GNNs, by 12.4% over the strongest baseline. SUB-GNN performs exceptionally well on challenging biomedical datasets when subgraphs have complex topology and even comprise multiple disconnected components.

The chronological order of user-item interactions can reveal time-evolving and sequential user behaviors in many recommender systems. The items that users will interact with may depend on the items accessed in the past. However, the substantial increase of users and items makes sequential recommender systems still face non-trivial challenges: (1) the hardness of modeling the short-term user interests; (2) the difficulty of capturing the long-term user interests; (3) the effective modeling of item co-occurrence patterns. To tackle these challenges, we propose a memory augmented graph neural network (MA-GNN) to capture both the long- and short-term user interests. Specifically, we apply a graph neural network to model the item contextual information within a short-term period and utilize a shared memory network to capture the long-range dependencies between items. In addition to the modeling of user interests, we employ a bilinear function to capture the co-occurrence patterns of related items. We extensively evaluate our model on five real-world datasets, comparing with several state-of-the-art methods and using a variety of performance metrics. The experimental results demonstrate the effectiveness of our model for the task of Top-K sequential recommendation.

In recent years, Graph Neural Networks (GNNs), which can naturally integrate node information and topological structure, have been demonstrated to be powerful in learning on graph data. These advantages of GNNs provide great potential to advance social recommendation since data in social recommender systems can be represented as user-user social graph and user-item graph; and learning latent factors of users and items is the key. However, building social recommender systems based on GNNs faces challenges. For example, the user-item graph encodes both interactions and their associated opinions; social relations have heterogeneous strengths; users involve in two graphs (e.g., the user-user social graph and the user-item graph). To address the three aforementioned challenges simultaneously, in this paper, we present a novel graph neural network framework (GraphRec) for social recommendations. In particular, we provide a principled approach to jointly capture interactions and opinions in the user-item graph and propose the framework GraphRec, which coherently models two graphs and heterogeneous strengths. Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed framework GraphRec. Our code is available at \url{//github.com/wenqifan03/GraphRec-WWW19}

Many recent state-of-the-art recommender systems such as D-ATT, TransNet and DeepCoNN exploit reviews for representation learning. This paper proposes a new neural architecture for recommendation with reviews. Our model operates on a multi-hierarchical paradigm and is based on the intuition that not all reviews are created equal, i.e., only a select few are important. The importance, however, should be dynamically inferred depending on the current target. To this end, we propose a review-by-review pointer-based learning scheme that extracts important reviews, subsequently matching them in a word-by-word fashion. This enables not only the most informative reviews to be utilized for prediction but also a deeper word-level interaction. Our pointer-based method operates with a novel gumbel-softmax based pointer mechanism that enables the incorporation of discrete vectors within differentiable neural architectures. Our pointer mechanism is co-attentive in nature, learning pointers which are co-dependent on user-item relationships. Finally, we propose a multi-pointer learning scheme that learns to combine multiple views of interactions between user and item. Overall, we demonstrate the effectiveness of our proposed model via extensive experiments on \textbf{24} benchmark datasets from Amazon and Yelp. Empirical results show that our approach significantly outperforms existing state-of-the-art, with up to 19% and 71% relative improvement when compared to TransNet and DeepCoNN respectively. We study the behavior of our multi-pointer learning mechanism, shedding light on evidence aggregation patterns in review-based recommender systems.