Multivariate relations are general in various types of networks, such as biological networks, social networks, transportation networks, and academic networks. Due to the principle of ternary closures and the trend of group formation, the multivariate relationships in social networks are complex and rich. Therefore, in graph learning tasks of social networks, the identification and utilization of multivariate relationship information are more important. Existing graph learning methods are based on the neighborhood information diffusion mechanism, which often leads to partial omission or even lack of multivariate relationship information, and ultimately affects the accuracy and execution efficiency of the task. To address these challenges, this paper proposes the multivariate relationship aggregation learning (MORE) method, which can effectively capture the multivariate relationship information in the network environment. By aggregating node attribute features and structural features, MORE achieves higher accuracy and faster convergence speed. We conducted experiments on one citation network and five social networks. The experimental results show that the MORE model has higher accuracy than the GCN (Graph Convolutional Network) model in node classification tasks, and can significantly reduce time cost.
Human emotion is expressed, perceived and captured using a variety of dynamic data modalities, such as speech (verbal), videos (facial expressions) and motion sensors (body gestures). We propose a generalized approach to emotion recognition that can adapt across modalities by modeling dynamic data as structured graphs. The motivation behind the graph approach is to build compact models without compromising on performance. To alleviate the problem of optimal graph construction, we cast this as a joint graph learning and classification task. To this end, we present the Learnable Graph Inception Network (L-GrIN) that jointly learns to recognize emotion and to identify the underlying graph structure in the dynamic data. Our architecture comprises multiple novel components: a new graph convolution operation, a graph inception layer, learnable adjacency, and a learnable pooling function that yields a graph-level embedding. We evaluate the proposed architecture on five benchmark emotion recognition databases spanning three different modalities (video, audio, motion capture), where each database captures one of the following emotional cues: facial expressions, speech and body gestures. We achieve state-of-the-art performance on all five databases outperforming several competitive baselines and relevant existing methods. Our graph architecture shows superior performance with significantly fewer parameters (compared to convolutional or recurrent neural networks) promising its applicability to resource-constrained devices.
We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued function on its state space. Our result gives exponentially decreasing bounds on the tail distributions of the extreme eigenvalues of the sample mean matrix. Our proof is based on the matrix expander (regular undirected graph) Chernoff bound [Garg et al. STOC '18] and scalar Chernoff-Hoeffding bounds for Markov chains [Chung et al. STACS '12]. Our matrix Chernoff bound for Markov chains can be applied to analyze the behavior of co-occurrence statistics for sequential data, which have been common and important data signals in machine learning. We show that given a regular Markov chain with $n$ states and mixing time $\tau$, we need a trajectory of length $O(\tau (\log{(n)}+\log{(\tau)})/\epsilon^2)$ to achieve an estimator of the co-occurrence matrix with error bound $\epsilon$. We conduct several experiments and the experimental results are consistent with the exponentially fast convergence rate from theoretical analysis. Our result gives the first bound on the convergence rate of the co-occurrence matrix and the first sample complexity analysis in graph representation learning.
To address the problem of data inconsistencies among different facial expression recognition (FER) datasets, many cross-domain FER methods (CD-FERs) have been extensively devised in recent years. Although each declares to achieve superior performance, fair comparisons are lacking due to the inconsistent choices of the source/target datasets and feature extractors. In this work, we first analyze the performance effect caused by these inconsistent choices, and then re-implement some well-performing CD-FER and recently published domain adaptation algorithms. We ensure that all these algorithms adopt the same source datasets and feature extractors for fair CD-FER evaluations. We find that most of the current leading algorithms use adversarial learning to learn holistic domain-invariant features to mitigate domain shifts. However, these algorithms ignore local features, which are more transferable across different datasets and carry more detailed content for fine-grained adaptation. To address these issues, we integrate graph representation propagation with adversarial learning for cross-domain holistic-local feature co-adaptation by developing a novel adversarial graph representation adaptation (AGRA) framework. Specifically, it first builds two graphs to correlate holistic and local regions within each domain and across different domains, respectively. Then, it extracts holistic-local features from the input image and uses learnable per-class statistical distributions to initialize the corresponding graph nodes. Finally, two stacked graph convolution networks (GCNs) are adopted to propagate holistic-local features within each domain to explore their interaction and across different domains for holistic-local feature co-adaptation. We conduct extensive and fair evaluations on several popular benchmarks and show that the proposed AGRA framework outperforms previous state-of-the-art methods.
Domain adaptation techniques, which focus on adapting models between distributionally different domains, are rarely explored in the video recognition area due to the significant spatial and temporal shifts across the source (i.e. training) and target (i.e. test) domains. As such, recent works on visual domain adaptation which leverage adversarial learning to unify the source and target video representations and strengthen the feature transferability are not highly effective on the videos. To overcome this limitation, in this paper, we learn a domain-agnostic video classifier instead of learning domain-invariant representations, and propose an Adversarial Bipartite Graph (ABG) learning framework which directly models the source-target interactions with a network topology of the bipartite graph. Specifically, the source and target frames are sampled as heterogeneous vertexes while the edges connecting two types of nodes measure the affinity among them. Through message-passing, each vertex aggregates the features from its heterogeneous neighbors, forcing the features coming from the same class to be mixed evenly. Explicitly exposing the video classifier to such cross-domain representations at the training and test stages makes our model less biased to the labeled source data, which in-turn results in achieving a better generalization on the target domain. To further enhance the model capacity and testify the robustness of the proposed architecture on difficult transfer tasks, we extend our model to work in a semi-supervised setting using an additional video-level bipartite graph. Extensive experiments conducted on four benchmarks evidence the effectiveness of the proposed approach over the SOTA methods on the task of video recognition.
Endogeneity bias and instrument variable validation have always been important topics in statistics and econometrics. In the era of big data, such issues typically combine with dimensionality issues and, hence, require even more attention. In this paper, we merge two well-known tools from machine learning and biostatistics---variable selection algorithms and probablistic graphs---to estimate house prices and the corresponding causal structure using 2010 data on Sydney. The estimation uses a 200-gigabyte ultrahigh dimensional database consisting of local school data, GIS information, census data, house characteristics and other socio-economic records. Using "big data", we show that it is possible to perform a data-driven instrument selection efficiently and purge out the invalid instruments. Our approach improves the sparsity of variable selection, stability and robustness in the presence of high dimensionality, complicated causal structures and the consequent multicollinearity, and recovers a sparse and intuitive causal structure. The approach also reveals an efficiency and effectiveness in endogeneity detection, instrument validation, weak instrument pruning and the selection of valid instruments. From the perspective of machine learning, the estimation results both align with and confirms the facts of Sydney house market, the classical economic theories and the previous findings of simultaneous equations modeling. Moreover, the estimation results are consistent with and supported by classical econometric tools such as two-stage least square regression and different instrument tests. All the code may be found at \url{https://github.com/isaac2math/solar_graph_learning}.
In this paper we focus on the empirical variable-selection peformance of subsample-ordered least angle regression (Solar) -- a novel ultrahigh dimensional redesign of lasso -- on the empirical data with complicated dependence structures and, hence, severe multicollinearity and grouping effect issues. Previous researches show that Solar largely alleviates several known high-dimensional issues with least-angle regression and $\mathcal{L}_1$ shrinkage. Also, With the same computation load, solar yields substantiali mprovements over two lasso solvers (least-angle regression for lasso and coordinate-descent) in terms of the sparsity (37-64\% reduction in the average number of selected variables), stability and accuracy of variable selection. Simulations also demonstrate that solar enhances the robustness of variable selection to different settings of the irrepresentable condition and to variations in the dependence structures assumed in regression analysis. To confirm that the improvements are also available for empirical researches, we choose the prostate cancer data and the Sydney house price data and apply two lasso solvers, elastic net and Solar on them for comparison. The results shows that (i) lasso is affected by the grouping effect and randomly drop variables with high correlations, resulting unreliable and uninterpretable results; (ii) elastic net is more robust to grouping effect; however, it completely lose variable-selection sparsity when the dependence structure of the data is complicated; (iii) solar demonstrates its superior robustness to complicated dependence structures and grouping effect, returning variable-selection results with better stability and sparsity. The code can be found at https://github.com/isaac2math/solar_application
How can we find the right graph for semi-supervised learning? In real world applications, the choice of which edges to use for computation is the first step in any graph learning process. Interestingly, there are often many types of similarity available to choose as the edges between nodes, and the choice of edges can drastically affect the performance of downstream semi-supervised learning systems. However, despite the importance of graph design, most of the literature assumes that the graph is static. In this work, we present Grale, a scalable method we have developed to address the problem of graph design for graphs with billions of nodes. Grale operates by fusing together different measures of(potentially weak) similarity to create a graph which exhibits high task-specific homophily between its nodes. Grale is designed for running on large datasets. We have deployed Grale in more than 20 different industrial settings at Google, including datasets which have tens of billions of nodes, and hundreds of trillions of potential edges to score. By employing locality sensitive hashing techniques,we greatly reduce the number of pairs that need to be scored, allowing us to learn a task specific model and build the associated nearest neighbor graph for such datasets in hours, rather than the days or even weeks that might be required otherwise. We illustrate this through a case study where we examine the application of Grale to an abuse classification problem on YouTube with hundreds of million of items. In this application, we find that Grale detects a large number of malicious actors on top of hard-coded rules and content classifiers, increasing the total recall by 89% over those approaches alone.
Predicting interactions among heterogenous graph structured data has numerous applications such as knowledge graph completion, recommendation systems and drug discovery. Often times, the links to be predicted belong to rare types such as the case in repurposing drugs for novel diseases. This motivates the task of few-shot link prediction. Typically, GCNs are ill-equipped in learning such rare link types since the relation embedding is not learned in an inductive fashion. This paper proposes an inductive RGCN for learning informative relation embeddings even in the few-shot learning regime. The proposed inductive model significantly outperforms the RGCN and state-of-the-art KGE models in few-shot learning tasks. Furthermore, we apply our method on the drug-repurposing knowledge graph (DRKG) for discovering drugs for Covid-19. We pose the drug discovery task as link prediction and learn embeddings for the biological entities that partake in the DRKG. Our initial results corroborate that several drugs used in clinical trials were identified as possible drug candidates. The method in this paper are implemented using the efficient deep graph learning (DGL)
Recently there was an increasing interest in applications of graph neural networks in non-Euclidean geometry; however, are non-Euclidean representations always useful for graph learning tasks? For different problems such as node classification and link prediction we compute hyperbolic embeddings and conclude that for tasks that require global prediction consistency it might be useful to use non-Euclidean embeddings, while for other tasks Euclidean models are superior. To do so we first fix an issue of the existing models associated with the optimization process at zero curvature. Current hyperbolic models deal with gradients at the origin in ad-hoc manner, which is inefficient and can lead to numerical instabilities. We solve the instabilities of kappa-Stereographic model at zero curvature cases and evaluate the approach of embedding graphs into the manifold in several graph representation learning tasks.
Graph Identification (GI) has long been researched in graph learning and is essential in certain applications (e.g. social community detection). Specifically, GI requires to predict the label/score of a target graph given its collection of node features and edge connections. While this task is common, more complex cases arise in practice---we are supposed to do the inverse thing by, for example, grouping similar users in a social network given the labels of different communities. This triggers an interesting thought: can we identify nodes given the labels of the graphs they belong to? Therefore, this paper defines a novel problem dubbed Inverse Graph Identification (IGI), as opposed to GI. Upon a formal discussion of the variants of IGI, we choose a particular case study of node clustering by making use of the graph labels and node features, with an assistance of a hierarchical graph that further characterizes the connections between different graphs. To address this task, we propose Gaussian Mixture Graph Convolutional Network (GMGCN), a simple yet effective method that makes the node-level message passing process using Graph Attention Network (GAT) under the protocol of GI and then infers the category of each node via a Gaussian Mixture Layer (GML). The training of GMGCN is further boosted by a proposed consensus loss to take advantage of the structure of the hierarchical graph. Extensive experiments are conducted to test the rationality of the formulation of IGI. We verify the superiority of the proposed method compared to other baselines on several benchmarks we have built up. We will release our codes along with the benchmark data to facilitate more research attention to the IGI problem.
Graph Convolutional Network (GCN) has experienced great success in graph analysis tasks. It works by smoothing the node features across the graph. The current GCN models overwhelmingly assume that the node feature information is complete. However, real-world graph data are often incomplete and containing missing features. Traditionally, people have to estimate and fill in the unknown features based on imputation techniques and then apply GCN. However, the process of feature filling and graph learning are separated, resulting in degraded and unstable performance. This problem becomes more serious when a large number of features are missing. We propose an approach that adapts GCN to graphs containing missing features. In contrast to traditional strategy, our approach integrates the processing of missing features and graph learning within the same neural network architecture. Our idea is to represent the missing data by Gaussian Mixture Model (GMM) and calculate the expected activation of neurons in the first hidden layer of GCN, while keeping the other layers of the network unchanged. This enables us to learn the GMM parameters and network weight parameters in an end-to-end manner. Notably, our approach does not increase the computational complexity of GCN and it is consistent with GCN when the features are complete. We demonstrate through extensive experiments that our approach significantly outperforms the imputation-based methods in node classification and link prediction tasks. We show that the performance of our approach for the case with a low level of missing features is even superior to GCN for the case with complete features.
The Travelling Salesman Problem (TSP) is a challenging graph task in combinatorial optimization that requires reasoning about both local node neighborhoods and global graph structure. In this paper, we propose to use the novel Graph Learning Network (GLN), a generative approach, to approximately solve the TSP. GLN model learns directly the pattern of TSP instances as training dataset, encodes the graph properties, and merge the different node embeddings to output node-to-node an optimal tour directly or via graph search technique that validates the final tour. The preliminary results of the proposed novel approach proves its applicability to this challenging problem providing a low optimally gap with significant computation saving compared to the optimal solution.
Graph neural networks (GNNs) have emerged as a powerful approach for solving many network mining tasks. However, learning on large graphs remains a challenge - many recently proposed scalable GNN approaches rely on an expensive message-passing procedure to propagate information through the graph. We present the PPRGo model which utilizes an efficient approximation of information diffusion in GNNs resulting in significant speed gains while maintaining state-of-the-art prediction performance. In addition to being faster, PPRGo is inherently scalable, and can be trivially parallelized for large datasets like those found in industry settings. We demonstrate that PPRGo outperforms baselines in both distributed and single-machine training environments on a number of commonly used academic graphs. To better analyze the scalability of large-scale graph learning methods, we introduce a novel benchmark graph with 12.4 million nodes, 173 million edges, and 2.8 million node features. We show that training PPRGo from scratch and predicting labels for all nodes in this graph takes under 2 minutes on a single machine, far outpacing other baselines on the same graph. We discuss the practical application of PPRGo to solve large-scale node classification problems at Google.
Graph representation learning is gaining popularity in a wide range of applications, such as social networks analysis, computational biology, and recommender systems. However, different with positive results from many academic studies, applying graph neural networks (GNNs) in a real-world application is still challenging due to non-stationary environments. The underlying distribution of streaming data changes unexpectedly, resulting in different graph structures (a.k.a., concept drift). Therefore, it is essential to devise a robust graph learning technique so that the model does not overfit to the training graphs. In this work, we present Hop Sampling, a straightforward regularization method that can effectively prevent GNNs from overfishing. The hop sampling randomly selects the number of propagation steps rather than fixing it, and by doing so, it encourages the model to learn meaningful node representation for all intermediate propagation layers and to experience a variety of plausible graphs that are not in the training set. Particularly, we describe the use case of our method in recommender systems, a representative example of the real-world non-stationary case. We evaluated hop sampling on a large-scale real-world LINE dataset and conducted an online A/B/n test in LINE Coupon recommender systems of LINE Wallet Tab. Experimental results demonstrate that the proposed scheme improves the prediction accuracy of GNNs. We observed hop sampling provides 7.97% and 16.93% improvements for NDCG and MAP compared to non-regularized GNN models in our online service. Furthermore, models using hop sampling alleviate the oversmoothing issue in GNNs enabling a deeper model as well as more diversified representation.
Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often constructed based on inaccurate modelling assumptions and/or noisy data. As a result, it fails to represent the true relationships between nodes. A Bayesian framework which targets posterior inference of the graph by considering it as a random quantity can be beneficial. In this paper, we propose a novel non-parametric graph model for constructing the posterior distribution of graph adjacency matrices. The proposed model is flexible in the sense that it can effectively take into account the output of graph-based learning algorithms that target specific tasks. In addition, model inference scales well to large graphs. We demonstrate the advantages of this model in three different problem settings: node classification, link prediction and recommendation.
Today, there are two major understandings for graph convolutional networks, i.e., in the spectral and spatial domain. But both lack transparency. In this work, we introduce a new understanding for it -- data augmentation, which is more transparent than the previous understandings. Inspired by it, we propose a new graph learning paradigm -- Monte Carlo Graph Learning (MCGL). The core idea of MCGL contains: (1) Data augmentation: propagate the labels of the training set through the graph structure and expand the training set; (2) Model training: use the expanded training set to train traditional classifiers. We use synthetic datasets to compare the strengths of MCGL and graph convolutional operation on clean graphs. In addition, we show that MCGL's tolerance to graph structure noise is weaker than GCN on noisy graphs (four real-world datasets). Moreover, inspired by MCGL, we re-analyze the reasons why the performance of GCN becomes worse when deepened too much: rather than the mainstream view of over-smoothing, we argue that the main reason is the graph structure noise, and experimentally verify our view. The code is available at https://github.com/DongHande/MCGL.
In this paper, we propose an end-to-end graph learning framework, namely Iterative Deep Graph Learning (IDGL), for jointly and iteratively learning graph structure and graph embedding. The key rationale of IDGL is to learn a better graph structure based on better node embeddings, and vice versa (i.e., better node embeddings based on a better graph structure). Our iterative method dynamically stops when the learned graph structure approaches close enough to the graph optimized for the downstream prediction task. In addition, we cast the graph learning problem as a similarity metric learning problem and leverage adaptive graph regularization for controlling the quality of the learned graph. Finally, combining the anchor-based approximation technique, we further propose a scalable version of IDGL, namely IDGL-Anch, which significantly reduces the time and space complexity of IDGL without compromising the performance. Our extensive experiments on nine benchmarks show that our proposed IDGL models can consistently outperform or match the state-of-the-art baselines. Furthermore, IDGL can be more robust to adversarial graphs and cope with both transductive and inductive learning.
The problem of inferring unknown graph edges from numerical data at a graph's nodes appears in many forms across machine learning. We study a version of this problem that arises in the field of \emph{landscape genetics}, where genetic similarity between organisms living in a heterogeneous landscape is explained by a weighted graph that encodes the ease of dispersal through that landscape. Our main contribution is an efficient algorithm for \emph{inverse landscape genetics}, which is the task of inferring this graph from measurements of genetic similarity at different locations (graph nodes). Inverse landscape genetics is important in discovering impediments to species dispersal that threaten biodiversity and long-term species survival. In particular, it is widely used to study the effects of climate change and human development. Drawing on influential work that models organism dispersal using graph \emph{effective resistances} (McRae 2006), we reduce the inverse landscape genetics problem to that of inferring graph edges from noisy measurements of these resistances, which can be obtained from genetic similarity data. Building on the NeurIPS 2018 work of Hoskins et al. 2018 on learning edges in social networks, we develop an efficient first-order optimization method for solving this problem. Despite its non-convex nature, experiments on synthetic and real genetic data establish that our method provides fast and reliable convergence, significantly outperforming existing heuristics used in the field. By providing researchers with a powerful, general purpose algorithmic tool, we hope our work will have a positive impact on accelerating work on landscape genetics.
Domain shift is a fundamental problem in visual recognition which typically arises when the source and target data follow different distributions. The existing domain adaptation approaches which tackle this problem work in the closed-set setting with the assumption that the source and the target data share exactly the same classes of objects. In this paper, we tackle a more realistic problem of open-set domain shift where the target data contains additional classes that are not present in the source data. More specifically, we introduce an end-to-end Progressive Graph Learning (PGL) framework where a graph neural network with episodic training is integrated to suppress underlying conditional shift and adversarial learning is adopted to close the gap between the source and target distributions. Compared to the existing open-set adaptation approaches, our approach guarantees to achieve a tighter upper bound of the target error. Extensive experiments on three standard open-set benchmarks evidence that our approach significantly outperforms the state-of-the-arts in open-set domain adaptation.