Subgraph neural networks have recently gained prominence for various subgraph-level predictive tasks. However, existing methods either \emph{1)} apply simple standard pooling over graph convolutional networks, failing to capture essential subgraph properties, or \emph{2)} rely on rigid subgraph definitions, leading to suboptimal performance. Moreover, these approaches fail to model long-range dependencies both between and within subgraphs—a critical limitation, as many real-world networks contain subgraphs of varying sizes and connectivity patterns. In this paper, we propose a novel implicit subgraph neural network, the first of its kind, designed to capture dependencies across subgraphs. Our approach also integrates label-aware subgraph-level information. We formulate implicit subgraph learning as a bilevel optimization problem and develop a provably convergent algorithm that requires fewer gradient estimations than standard bilevel optimization methods. We evaluate our approach on real-world networks against state-of-the-art baselines, demonstrating its effectiveness and superiority.

Predicting the edge weights of a graph is a critical task across many domains. Some examples include predicting traffic flow in transportation networks, strength of interactions in protein-protein networks, and collaboration frequency in co-authorship networks. Graph Neural Networks have been very successful in edge-weight prediction tasks. However, these predictions lack rigorous statistical uncertainty quantification. Recent work has demonstrated the efficacy of conformal inference in quantifying the uncertainties of the predictions made by graph neural networks. However, there has been limited research in conformal inference for edge-weight prediction.

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the oversmoothing of learned embeddings and long-range dependency being more pronounced in dynamic graphs, as features are aggregated both across neighborhood and time, no prior work has proposed an implicit graph neural model in a dynamic setting.

The problem of urban event ranking aims at predicting the top-$k$ most risky locations of future events such as traffic accidents and crimes. This problem is of fundamental importance to public safety and urban administration especially when limited resources are available. The problem is, however, challenging due to complex and dynamic spatio-temporal correlations between locations, uneven distribution of urban events in space, and the difficulty to correctly rank nearby locations with similar features. Prior works on event forecasting mostly aim at accurately predicting the actual risk score or counts of events for all the locations. Rankings obtained as such usually have low quality due to prediction errors. Learning-to-rank methods directly optimize measures such as Normalized Discounted Cumulative Gain (NDCG), but cannot handle the spatiotemporal autocorrelation existing among locations. Due to the common assumption that items are independent. In this paper, we bridge the gap by proposing a novel spatial event ranking approach named SpatialRank. SpatialRank features adaptive graph convolution layers that dynamically learn the spatiotemporal dependencies across locations from data. In addition, the model optimizes through surrogates a hybrid NDCG loss with a spatial component to better rank neighboring spatial locations. We design an importance-sampling with a spatial filtering algorithm to effectively evaluate the loss during training. Comprehensive experiments on three real-world datasets demonstrate that SpatialRank can effectively identify the top riskiest locations of crimes and traffic accidents and outperform state-of-art methods in terms of NDCG by up to 12.7%.

NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to optimize NDCG and its top-$K$ variant. First, we formulate a novel compositional optimization problem for optimizing the NDCG surrogate, and a novel bilevel compositional optimization problem for optimizing the top-$K$ NDCG surrogate. Then, we develop efficient stochastic algorithms with provable convergence guarantees for the non-convex objectives. Different from existing NDCG optimization methods, the per-iteration complexity of our algorithms scales with the mini-batch size instead of the number of total items. To improve the effectiveness for deep learning, we further propose practical strategies by using initial warm-up and stop gradient operator. Experimental results on multiple datasets demonstrate that our methods outperform prior ranking approaches in terms of NDCG. To the best of our knowledge, this is the first time that stochastic algorithms are proposed to optimize NDCG with a provable convergence guarantee. Our proposed methods are implemented in the LibAUC library at https://libauc.org.

In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual variables and lower level problems. Due to the intertwined multi-block min-max bilevel structure, the computational cost at each iteration could be prohibitively high, especially with a large number of blocks. To tackle this challenge, we present two single-loop randomized stochastic algorithms, which require updates for only a constant number of blocks at each iteration. Under some mild assumptions on the problem, we establish their sample complexity of $\mathcal{O}(1/\epsilon^4)$ for finding an $\epsilon$-stationary point. This matches the optimal complexity order for solving stochastic nonconvex optimization under a general unbiased stochastic oracle model. Moreover, we provide two applications of the proposed method in multi-task deep AUC (area under ROC curve) maximization. Experimental results validate our theory and demonstrate the effectiveness of our method.

Investigating correlation between example features and example labels is essential to solve classification problems. However, identification and calculation of the correlation between features and labels can be rather difficult for high-dimensional multi-label data. Both feature embedding and label embedding have been developed to tackle this challenge, and a shared subspace for both labels and features are usually learned by existing embedding methods to simultaneously reduce dimensionality of features and labels. In contrast, this paper suggests to learn separated subspaces for features and labels by maximizing the independence between components in each subspace and maximizing the correlation between these two subspaces. The learned independent label components indicates fundamental combinations of labels in multi-label datasets, which thus helps to reveals the correlation between labels. On the other hand, the learned independent feature components lead to a compact representation of example features. The connections between the proposed algorithm and existing embedding methods have been discussed. Experimental results on real-world multi-label datasets demonstrate the necessity of exploring independence components from multi-label data and the effectiveness of the proposed algorithm.