We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs), a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers.

However, the labeling process can be tedious, costly, and error-prone in practice. In this paper, we propose to unify active learning (AL) and message passing towards minimizing labeling costs, e.g.,making useoffewandunreliable labels thatcan beobtainedcheaply.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper present a heuristic for node selection in Branch and Bound for Mixed Integer Programs based on machine learning. Although machine learning used for node selection is not new the paper present a new approach (to the best of my knowledge). They utilize a classifier together with an oracle for training two aspects: a node selection policy and a node pruning policy. The first one is used to enforce a linear order/priority on the current open nodes of the Branch and Bound while the second one is used to further shrink the list of open nodes by pruning the unpromising ones.

We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs), a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers. We evaluate L2C on challenging MPE queries involving high-treewidth PGMs. Experiments show that our learned heuristic significantly reduces the search space while maintaining or improving solution quality over state-of-the-art methods.

Combinatorial optimization (CO) is one of the most fundamental mathematical models in real-world applications. Traditional CO solvers, such as Branch-and-Bound (B&B) solvers, heavily rely on expert-designed heuristics, which are reliable but require substantial manual tuning. Recent studies have leveraged deep learning (DL) models as an alternative to capture rich feature patterns for improved performance on GPU machines. Nonetheless, the drawbacks of high training and inference costs, as well as limited interpretability, severely hinder the adoption of DL methods in real-world applications. To address these challenges, we propose a novel deep symbolic optimization learning framework that combines their advantages. Specifically, we focus on the node selection module within B&B solvers -- namely, deep symbolic optimization for node selection (Dso4NS). With data-driven approaches, Dso4NS guides the search for mathematical expressions within the high-dimensional discrete symbolic space and then incorporates the highest-performing mathematical expressions into a solver. The data-driven model captures the rich feature information in the input data and generates symbolic expressions, while the expressions deployed in solvers enable fast inference with high interpretability. Experiments demonstrate the effectiveness of Dso4NS in learning high-quality expressions, outperforming existing approaches on a CPU machine. Encouragingly, the learned CPU-based policies consistently achieve performance comparable to state-of-the-art GPU-based approaches.

In this paper, we introduce Conditional Gumbel-Softmax as a method to perform end-to-end learning of the optimal feature subset for a given task and deep neural network (DNN) model, while adhering to certain pairwise constraints between the features. We do this by conditioning the selection of each feature in the subset on another feature. We demonstrate how this approach can be used to select the task-optimal nodes composing a wireless sensor network (WSN) while ensuring that none of the nodes that require communication between one another have too large of a distance between them, limiting the required power spent on this communication. We validate this approach on an emulated Wireless Electroencephalography (EEG) Sensor Network (WESN) solving a motor execution task. We analyze how the performance of the WESN varies as the constraints are made more stringent and how well the Conditional Gumbel-Softmax performs in comparison with a heuristic, greedy selection method. While the application focus of this paper is on wearable brain-computer interfaces, the proposed methodology is generic and can readily be applied to node deployment in wireless sensor networks and constrained feature selection in other applications as well.

This study investigates the robustness of graph embedding methods for community detection in the face of network perturbations, specifically edge deletions. Graph embedding techniques, which represent nodes as low-dimensional vectors, are widely used for various graph machine learning tasks due to their ability to capture structural properties of networks effectively. However, the impact of perturbations on the performance of these methods remains relatively understudied. The research considers state-of-the-art graph embedding methods from two families: matrix factorization (e.g., LE, LLE, HOPE, M-NMF) and random walk-based (e.g., DeepWalk, LINE, node2vec). Through experiments conducted on both synthetic and real-world networks, the study reveals varying degrees of robustness within each family of graph embedding methods. The robustness is found to be influenced by factors such as network size, initial community partition strength, and the type of perturbation. Notably, node2vec and LLE consistently demonstrate higher robustness for community detection across different scenarios, including networks with degree and community size heterogeneity. These findings highlight the importance of selecting an appropriate graph embedding method based on the specific characteristics of the network and the task at hand, particularly in scenarios where robustness to perturbations is crucial.

Graph Neural Networks (GNNs) have seen significant success in tasks such as node classification, largely contingent upon the availability of sufficient labeled nodes. Yet, the excessive cost of labeling large-scale graphs led to a focus on active learning on graphs, which aims for effective data selection to maximize downstream model performance. Notably, most existing methods assume reliable graph topology, while real-world scenarios often present noisy graphs. Given this, designing a successful active learning framework for noisy graphs is highly needed but challenging, as selecting data for labeling and obtaining a clean graph are two tasks naturally interdependent: selecting high-quality data requires clean graph structure while cleaning noisy graph structure requires sufficient labeled data. Considering the complexity mentioned above, we propose an active learning framework, GALClean, which has been specifically designed to adopt an iterative approach for conducting both data selection and graph purification simultaneously with best information learned from the prior iteration. Importantly, we summarize GALClean as an instance of the Expectation-Maximization algorithm, which provides a theoretical understanding of its design and mechanisms. This theory naturally leads to an enhanced version, GALClean+. Extensive experiments have demonstrated the effectiveness and robustness of our proposed method across various types and levels of noisy graphs.

This paper presents an integrated algorithmic framework for minimising product delivery costs in e-commerce (known as the cost-to-serve or C2S). One of the major challenges in e-commerce is the large volume of spatio-temporally diverse orders from multiple customers, each of which has to be fulfilled from one of several warehouses using a fleet of vehicles. This results in two levels of decision-making: (i) selection of a fulfillment node for each order (including the option of deferral to a future time), and then (ii) routing of vehicles (each of which can carry multiple orders originating from the same warehouse). We propose an approach that combines graph neural networks and reinforcement learning to train the node selection and vehicle routing agents. We include real-world constraints such as warehouse inventory capacity, vehicle characteristics such as travel times, service times, carrying capacity, and customer constraints including time windows for delivery. The complexity of this problem arises from the fact that outcomes (rewards) are driven both by the fulfillment node mapping as well as the routing algorithms, and are spatio-temporally distributed. Our experiments show that this algorithmic pipeline outperforms pure heuristic policies.