Identifying the maximum edge biclique in bipartite graphs, a complete bipartite subgraph with the largest number of edges, plays a crucial role in uncovering densely-connected communities and has significant applications in domains such as recommendation systems and biological network analysis. However, this problem is NP-hard, and existing methods face inefficiencies both in practice and theory. In this paper, we propose two novel algorithms with distinct branching strategies and provable time guarantees for solving the maximum edge biclique search problem. The first is a refined pivot-based branching algorithm that systematically exploits vertex adjacency relationships to bound the search for the maximum edge biclique, achieving a time complexity of O ( m 1.348 n ). The second is a cover-based algorithm that uncovers a novel duality between maximal bicliques and minimal vertex covers in bipartite graphs, attaining a complexity of O ( m 1.381 n ). To the best of our knowledge, these two algorithms achieve the best-known worst-case time complexities for this problem. Notably, while the cover-based algorithm has a marginally higher theoretical complexity, it typically provides superior practical performance on dense graphs due to its inherent pruning efficiency. To further enhance performance, we introduce advanced pruning techniques, including polynomial-time solvable graph cases, neighbor and non-neighbor constraint-based upper bounds, vertex cover constraint-driven upper bounds, heuristic prioritization, and an improved progressive bounding approach. Additionally, we propose a hybrid framework that deploys the pivot-based approach for sparse graph regions and the cover-based approach for dense regions, balancing efficiency across varying graph structures. Extensive experiments on 12 real-world bipartite graphs demonstrate that our hybrid framework outperforms the state-of-the-art baseline by up to four orders of magnitude and achieves speedups of several times to orders of magnitude over the pivot-based approach on dense graphs.

One primary problem for supervised ML is data scarcity, which refers to the inadequacy of well-labeled training data. Recently, deep generative models have shown the capability of generating data objects that closely resemble real data for datasets in different modalities, including images, natural language, and tabular data. Naturally, a promising approach for tackling data scarcity involves training a generative model to produce a collection of data objects, and then employing machine-labeling solutions (e.g., weak supervision or semi-supervised learning) to incorporate these generated data objects for supervised ML. However, it is important to note that because the provided training data may exhibit a different data distribution compared to the validation (or unseen testing) data, the generative model learned from these seen training data cannot guarantee the generation of high-quality data relative to this ML task. To address this challenge, we introduce an iterative approach that gradually calibrates the generative model by interacting with an environment that tells whether generated tuples are good or bad, by using a validation dataset that is not exposed to the generative model. In each iteration, we first use a pre-trained generative model to create unlabeled data objects, label them, and integrate this freshly generated data into the learning process. Afterwards, the model will be tested in the environment to assess the quality of the generated data. The iterative framework can be naturally controlled using reinforcement learning (RL), where an agent generates and labels tuples, an environment tests the generated tuples and sends reward back to the agent to progressively enhance the generative model for a specific supervised ML task. Experimental results over 8 datasets and multiple baselines demonstrate that our RL guided data synthesis, together with off-the-shelf semi-automatic labeling solutions, can significantly improve the performance of supervised ML models.

Outlier detection is crucial for preventing financial fraud, network intrusions, and device failures. Users often expect systems to automatically summarize and interpret outlier detection results to reduce human effort and convert outliers into actionable insights. However, existing methods fail to effectively assist users in identifying the root causes of outliers, as they only pinpoint data attributes without considering outliers in the same subspace may have different causes. To fill this gap, we propose STAIR, which learns concise and human-understandable rules to summarize and explain outlier detection results with finer granularity. These rules consider both attributes and associated values. STAIR employs an interpretation-aware optimization objective to generate a small number of rules with minimal complexity for strong interpretability. The learning algorithm of STAIR produces a rule set by iteratively splitting the large rules and is optimal in maximizing this objective in each iteration. Moreover, to effectively handle high dimensional, highly complex data sets that are hard to summarize with simple rules, we propose a localized STAIR approach, called L-STAIR. Taking data locality into consideration, it simultaneously partitions data and learns a set of localized rules for each partition. Our experimental study on many outlier benchmark datasets shows that STAIR significantly reduces the complexity of the rules required to summarize the outlier detection results, thus more amenable for humans to understand and evaluate.