The classic Cluster Editing problem (also known as Correlation Clustering) asks to transform a given graph into a disjoint union of cliques (clusters) by a small number of edge modifications. When applied to vertex-colored graphs (the colors representing subgroups), standard algorithms for the NP-hard Cluster Editing problem may yield solutions that are biased towards subgroups of data (e.g., demographic groups), measured in the number of modifications incident to the members of the subgroups. We propose a modification fairness constraint which ensures that the number of edits incident to each subgroup is proportional to its size. To start with, we study Modification-Fair Cluster Editing for graphs with two vertex colors. We show that the problem is NP-hard even if one may only insert edges within a subgroup; note that in the classic "non-fair" setting, this case is trivially polynomial-time solvable. However, in the more general editing form, the modification-fair variant remains fixed-parameter tractable with respect to the number of edge edits. We complement these and further theoretical results with an empirical analysis of our model on real-world social networks where we find that the price of modification-fairness is surprisingly low, that is, the cost of optimal modification-fair solutions differs from the cost of optimal "non-fair" solutions only by a small percentage.

Recent advances in depthwise-separable convolutional neural networks (DS-CNNs) have led to novel architectures, that surpass the performance of classical CNNs, by a considerable scalability and accuracy margin. This paper reveals another striking property of DS-CNN architectures: discernible and explainable patterns emerge in their trained depthwise convolutional kernels in all layers. Through an extensive analysis of millions of trained filters, with different sizes and from various models, we employed unsupervised clustering with autoencoders, to categorize these filters. Astonishingly, the patterns converged into a few main clusters, each resembling the difference of Gaussian (DoG) functions, and their first and second-order derivatives. Notably, we were able to classify over 95\% and 90\% of the filters from state-of-the-art ConvNextV2 and ConvNeXt models, respectively. This finding is not merely a technological curiosity; it echoes the foundational models neuroscientists have long proposed for the vision systems of mammals. Our results thus deepen our understanding of the emergent properties of trained DS-CNNs and provide a bridge between artificial and biological visual processing systems. More broadly, they pave the way for more interpretable and biologically-inspired neural network designs in the future.

Solving large-scale capacity expansion problems (CEPs) is central to cost-effective decarbonization of regional-scale energy systems. To ensure the intended outcomes of CEPs, modeling uncertainty due to weather-dependent variable renewable energy (VRE) supply and energy demand becomes crucially important. However, the resulting stochastic optimization models are often less computationally tractable than their deterministic counterparts. Here, we propose a learning-assisted approximate solution method to tractably solve two-stage stochastic CEPs. Our method identifies low-cost planning decisions by constructing and solving a sequence of tractable temporally aggregated surrogate problems. We adopt a Bayesian optimization approach to searching the space of time series aggregation hyperparameters and compute approximate solutions that minimize costs on a validation set of supply-demand projections. Importantly, we evaluate solved planning outcomes on a held-out set of test projections. We apply our approach to generation and transmission expansion planning for a joint power-gas system spanning New England. We show that our approach yields an estimated cost savings of up to 3.8% in comparison to benchmark time series aggregation approaches.

Discrete distribution clustering (D2C) was often solved by Wasserstein barycenter methods. These methods are under a common assumption that clusters can be well represented by barycenters, which may not hold in many real applications. In this work, we propose a simple yet effective framework based on spectral clustering and distribution affinity measures (e.g., maximum mean discrepancy and Wasserstein distance) for D2C. To improve the scalability, we propose to use linear optimal transport to construct affinity matrices efficiently on large datasets. We provide theoretical guarantees for the success of the proposed methods in clustering distributions. Experiments on synthetic and real data show that our methods outperform the baselines largely in terms of both clustering accuracy and computational efficiency.

In industry, Bayesian optimization (BO) is widely applied in the human-AI collaborative parameter tuning of cyber-physical systems. However, BO's solutions may deviate from human experts' actual goal due to approximation errors and simplified objectives, requiring subsequent tuning. The black-box nature of BO limits the collaborative tuning process because the expert does not trust the BO recommendations. Current explainable AI (XAI) methods are not tailored for optimization and thus fall short of addressing this gap. To bridge this gap, we propose TNTRules (TUNE-NOTUNE Rules), a post-hoc, rule-based explainability method that produces high quality explanations through multiobjective optimization. Our evaluation of benchmark optimization problems and real-world hyperparameter optimization tasks demonstrates TNTRules' superiority over state-of-the-art XAI methods in generating high quality explanations. This work contributes to the intersection of BO and XAI, providing interpretable optimization techniques for real-world applications.

Federated learning (FL) has attracted vivid attention as a privacy-preserving distributed learning framework. In this work, we focus on cross-silo FL, where clients become the model owners after training and are only concerned about the model's generalization performance on their local data. Due to the data heterogeneity issue, asking all the clients to join a single FL training process may result in model performance degradation. To investigate the effectiveness of collaboration, we first derive a generalization bound for each client when collaborating with others or when training independently. We show that the generalization performance of a client can be improved only by collaborating with other clients that have more training data and similar data distribution. Our analysis allows us to formulate a client utility maximization problem by partitioning clients into multiple collaborating groups. A hierarchical clustering-based collaborative training (HCCT) scheme is then proposed, which does not need to fix in advance the number of groups. We further analyze the convergence of HCCT for general non-convex loss functions which unveils the effect of data similarity among clients. Extensive simulations show that HCCT achieves better generalization performance than baseline schemes, whereas it degenerates to independent training and conventional FL in specific scenarios.

We define a distance between temporal graphs based on graph embeddings built using time-respecting random walks. We study both the case of matched graphs, when there exists a known relation between the nodes, and the unmatched case, when such a relation is unavailable and the graphs may be of different sizes. We illustrate the interest of our distance definition, using both real and synthetic temporal network data, by showing its ability to discriminate between graphs with different structural and temporal properties. Leveraging state-of-the-art machine learning techniques, we propose an efficient implementation of distance computation that is viable for large-scale temporal graphs.

Speaker diarization, the task of segmenting an audio recording based on speaker identity, constitutes an important speech pre-processing step for several downstream applications. The conventional approach to diarization involves multiple steps of embedding extraction and clustering, which are often optimized in an isolated fashion. While end-to-end diarization systems attempt to learn a single model for the task, they are often cumbersome to train and require large supervised datasets. In this paper, we propose an end-to-end supervised hierarchical clustering algorithm based on graph neural networks (GNN), called End-to-end Supervised HierARchical Clustering (E-SHARC). The E-SHARC approach uses front-end mel-filterbank features as input and jointly learns an embedding extractor and the GNN clustering module, performing representation learning, metric learning, and clustering with end-to-end optimization. Further, with additional inputs from an external overlap detector, the E-SHARC approach is capable of predicting the speakers in the overlapping speech regions. The experimental evaluation on several benchmark datasets like AMI, VoxConverse and DISPLACE, illustrates that the proposed E-SHARC framework improves significantly over the state-of-art diarization systems.

Successive proposals of several self-supervised training schemes continue to emerge, taking one step closer to developing a universal foundation model. In this process, the unsupervised downstream tasks are recognized as one of the evaluation methods to validate the quality of visual features learned with a self-supervised training scheme. However, unsupervised dense semantic segmentation has not been explored as a downstream task, which can utilize and evaluate the quality of semantic information introduced in patch-level feature representations during self-supervised training of a vision transformer. Therefore, this paper proposes a novel data-driven approach for unsupervised semantic segmentation (DatUS^2) as a downstream task. DatUS^2 generates semantically consistent and dense pseudo annotate segmentation masks for the unlabeled image dataset without using any visual-prior or synchronized data. We compare these pseudo-annotated segmentation masks with ground truth masks for evaluating recent self-supervised training schemes to learn shared semantic properties at the patch level and discriminative semantic properties at the segment level. Finally, we evaluate existing state-of-the-art self-supervised training schemes with our proposed downstream task, i.e., DatUS^2. Also, the best version of DatUS^2 outperforms the existing state-of-the-art method for the unsupervised dense semantic segmentation task with 15.02% MiOU and 21.47% Pixel accuracy on the SUIM dataset. It also achieves a competitive level of accuracy for a large-scale and complex dataset, i.e., the COCO dataset.

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work, we build on widely adopted $k$-center clustering and model its input background knowledge as must-link (ML) and cannot-link (CL) constraint sets. However, most clustering problems including $k$-center are inherently $\mathcal{NP}$-hard, while the more complex constrained variants are known to suffer severer approximation and computation barriers that significantly limit their applicability. By employing a suite of techniques including reverse dominating sets, linear programming (LP) integral polyhedron, and LP duality, we arrive at the first efficient approximation algorithm for constrained $k$-center with the best possible ratio of 2. We also construct competitive baseline algorithms and empirically evaluate our approximation algorithm against them on a variety of real datasets. The results validate our theoretical findings and demonstrate the great advantages of our algorithm in terms of clustering cost, clustering quality, and running time.