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Triadic motifs are the smallest building blocks of higher-order interactions in complex networks and can be detected as over-occurrences with respect to null models with only pair-wise interactions. Recently, the motif structure of production networks has attracted attention in light of its possible role in the propagation of economic shocks. However, its characterization at the level of individual commodities is still poorly understood. Here we analyse both binary and weighted triadic motifs in the Dutch inter-industry production network disaggregated at the level of 187 commodity groups, using data from Statistics Netherlands. We introduce appropriate null models that filter out node heterogeneity and the strong effects of link reciprocity and find that, while the aggregate network that overlays all products is characterized by a multitude of triadic motifs, most single-product layers feature no significant motif, and roughly 80% of the layers feature only two motifs or less. This result paves the way for identifying a simple "triadic fingerprint" of each commodity and for reconstructing most product-specific networks from partial information in a pairwise fashion by controlling for their reciprocity structure. We discuss how these results can help statistical bureaus identify fine-grained information in structural analyses of interest for policymakers.

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Time-series datasets are central in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs), which are powerful mathematical tools that allow for probabilistic and interpretable learning on time series. Estimating the model parameters in SSMs is arguably one of the most complicated tasks, and the inclusion of prior knowledge is known to both ease the interpretation but also to complicate the inferential tasks. Very recent works have attempted to incorporate a graphical perspective on some of those model parameters, but they present notable limitations that this work addresses. More generally, existing graphical modeling tools are designed to incorporate either static information, focusing on statistical dependencies among independent random variables (e.g., graphical Lasso approach), or dynamic information, emphasizing causal relationships among time series samples (e.g., graphical Granger approaches). However, there are no joint approaches combining static and dynamic graphical modeling within the context of SSMs. This work proposes a novel approach to fill this gap by introducing a joint graphical modeling framework that bridges the static graphical Lasso model and a causal-based graphical approach for the linear-Gaussian SSM. We present DGLASSO (Dynamic Graphical Lasso), a new inference method within this framework that implements an efficient block alternating majorization-minimization algorithm. The algorithm's convergence is established by departing from modern tools from nonlinear analysis. Experimental validation on synthetic and real weather variability data showcases the effectiveness of the proposed model and inference algorithm.

Accurately predicting vapor pressure is vital for various industrial and environmental applications. However, obtaining accurate measurements for all compounds of interest is not possible due to the resource and labor intensity of experiments. The demand for resources and labor further multiplies when a temperature-dependent relationship for predicting vapor pressure is desired. In this paper, we propose PUFFIN (Path-Unifying Feed-Forward Interfaced Network), a machine learning framework that combines transfer learning with a new inductive bias node inspired by domain knowledge (the Antoine equation) to improve vapor pressure prediction. By leveraging inductive bias and transfer learning using graph embeddings, PUFFIN outperforms alternative strategies that do not use inductive bias or that use generic descriptors of compounds. The framework's incorporation of domain-specific knowledge to overcome the limitation of poor data availability shows its potential for broader applications in chemical compound analysis, including the prediction of other physicochemical properties. Importantly, our proposed machine learning framework is partially interpretable, because the inductive Antoine node yields network-derived Antoine equation coefficients. It would then be possible to directly incorporate the obtained analytical expression in process design software for better prediction and control of processes occurring in industry and the environment.

The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph $\boldsymbol{\beta}$-model for capturing degree heterogeneity in networks with higher-order (multi-way) interactions. In this paper we initiate the rigorous study of the hypergraph $\boldsymbol{\beta}$-model with multiple layers, which allows for hyperedges of different sizes across the layers. To begin with, we derive the rates of convergence of the maximum likelihood (ML) estimate and establish their minimax rate optimality. We also derive the limiting distribution of the ML estimate and construct asymptotically valid confidence intervals for the model parameters. Next, we consider the goodness-of-fit problem in the hypergraph $\boldsymbol{\beta}$-model. Specifically, we establish the asymptotic normality of the likelihood ratio (LR) test under the null hypothesis, derive its detection threshold, and also its limiting power at the threshold. Interestingly, the detection threshold of the LR test turns out to be minimax optimal, that is, all tests are asymptotically powerless below this threshold. The theoretical results are further validated in numerical experiments. In addition to developing the theoretical framework for estimation and inference for hypergraph $\boldsymbol{\beta}$-models, the above results fill a number of gaps in the graph $\boldsymbol{\beta}$-model literature, such as the minimax optimality of the ML estimates and the non-null properties of the LR test, which, to the best of our knowledge, have not been studied before.

Open and permissionless blockchains are distributed systems with thousands to tens of thousands of nodes, establishing novel platforms for decentralized applications. When realizing such an application, data might be stored and retrieved from one or more blockchains by distributed network nodes without relying on centralized coordination and trusted third parties. Data access could be provided through a query language such as SQL at the application level, establishing a unified view on application-level data that is verifiably stored. However, when accessing multiple blockchains through their node software and APIs, interoperability cannot be assumed today, resulting in challenges of inhomogeneous data access. In addition, different feature sets and trade-offs exist, e.g., regarding smart contract functionality, availability, distribution, scalability, and security. For increasing interoperability, the paper at hand suggests pursuing the development of a cross-chain query language at the application level. The language abstracts from implementation by providing a standardized syntax, an integrated data model, and a processing architecture for data queries. This research is an extended and updated paper demonstrating the language syntax, data model, and architecture with an evaluation of compatibility against the largest open and permissionless blockchains today.

The effectiveness of ad creatives is greatly influenced by their visual appearance. Advertising platforms can generate ad creatives with different appearances by combining creative elements provided by advertisers. However, with the increasing number of ad creative elements, it becomes challenging to select a suitable combination from the countless possibilities. The industry's mainstream approach is to select individual creative elements independently, which often overlooks the importance of interaction between creative elements during the modeling process. In response, this paper proposes a Cross-Element Combinatorial Selection framework for multiple creative elements, termed CECS. In the encoder process, a cross-element interaction is adopted to dynamically adjust the expression of a single creative element based on the current candidate creatives. In the decoder process, the creative combination problem is transformed into a cascade selection problem of multiple creative elements. A pointer mechanism with a cascade design is used to model the associations among candidates. Comprehensive experiments on real-world datasets show that CECS achieved the SOTA score on offline metrics. Moreover, the CECS algorithm has been deployed in our industrial application, resulting in a significant 6.02% CTR and 10.37% GMV lift, which is beneficial to the business.

Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information from its neighbors using a permutation-invariant aggregation function. Standard well-examined choices such as the mean or sum aggregation functions have limited capabilities, as they are not able to capture interactions among neighbors. In this work, we formalize these interactions using an information-theoretic framework that notably includes synergistic information. Driven by this definition, we introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. This is achieved by learning local node orderings via an attention mechanism and processing the ordered representations using a recurrent neural network aggregator. This design allows us to make use of a permutation-sensitive aggregator while maintaining the permutation-equivariance of the proposed GOAT layer. The GOAT model demonstrates its increased performance in modeling graph metrics that capture complex information, such as the betweenness centrality and the effective size of a node. In practical use-cases, its superior modeling capability is confirmed through its success in several real-world node classification benchmarks.

Graph neural networks (GNNs) have been a hot spot of recent research and are widely utilized in diverse applications. However, with the use of huger data and deeper models, an urgent demand is unsurprisingly made to accelerate GNNs for more efficient execution. In this paper, we provide a comprehensive survey on acceleration methods for GNNs from an algorithmic perspective. We first present a new taxonomy to classify existing acceleration methods into five categories. Based on the classification, we systematically discuss these methods and highlight their correlations. Next, we provide comparisons from aspects of the efficiency and characteristics of these methods. Finally, we suggest some promising prospects for future research.

Graph Convolution Networks (GCNs) manifest great potential in recommendation. This is attributed to their capability on learning good user and item embeddings by exploiting the collaborative signals from the high-order neighbors. Like other GCN models, the GCN based recommendation models also suffer from the notorious over-smoothing problem - when stacking more layers, node embeddings become more similar and eventually indistinguishable, resulted in performance degradation. The recently proposed LightGCN and LR-GCN alleviate this problem to some extent, however, we argue that they overlook an important factor for the over-smoothing problem in recommendation, that is, high-order neighboring users with no common interests of a user can be also involved in the user's embedding learning in the graph convolution operation. As a result, the multi-layer graph convolution will make users with dissimilar interests have similar embeddings. In this paper, we propose a novel Interest-aware Message-Passing GCN (IMP-GCN) recommendation model, which performs high-order graph convolution inside subgraphs. The subgraph consists of users with similar interests and their interacted items. To form the subgraphs, we design an unsupervised subgraph generation module, which can effectively identify users with common interests by exploiting both user feature and graph structure. To this end, our model can avoid propagating negative information from high-order neighbors into embedding learning. Experimental results on three large-scale benchmark datasets show that our model can gain performance improvement by stacking more layers and outperform the state-of-the-art GCN-based recommendation models significantly.

Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays an important role in graph classification. In this paper, we innovatively propose hierarchical graph capsule network (HGCN) that can jointly learn node embeddings and extract graph hierarchies. Specifically, disentangled graph capsules are established by identifying heterogeneous factors underlying each node, such that their instantiation parameters represent different properties of the same entity. To learn the hierarchical representation, HGCN characterizes the part-whole relationship between lower-level capsules (part) and higher-level capsules (whole) by explicitly considering the structure information among the parts. Experimental studies demonstrate the effectiveness of HGCN and the contribution of each component.

Traditional methods for link prediction can be categorized into three main types: graph structure feature-based, latent feature-based, and explicit feature-based. Graph structure feature methods leverage some handcrafted node proximity scores, e.g., common neighbors, to estimate the likelihood of links. Latent feature methods rely on factorizing networks' matrix representations to learn an embedding for each node. Explicit feature methods train a machine learning model on two nodes' explicit attributes. Each of the three types of methods has its unique merits. In this paper, we propose SEAL (learning from Subgraphs, Embeddings, and Attributes for Link prediction), a new framework for link prediction which combines the power of all the three types into a single graph neural network (GNN). GNN is a new type of neural network which directly accepts graphs as input and outputs their labels. In SEAL, the input to the GNN is a local subgraph around each target link. We prove theoretically that our local subgraphs also reserve a great deal of high-order graph structure features related to link existence. Another key feature is that our GNN can naturally incorporate latent features and explicit features. It is achieved by concatenating node embeddings (latent features) and node attributes (explicit features) in the node information matrix for each subgraph, thus combining the three types of features to enhance GNN learning. Through extensive experiments, SEAL shows unprecedentedly strong performance against a wide range of baseline methods, including various link prediction heuristics and network embedding methods.

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