Accelerated Multiple Wasserstein Gradient Flows for Multi-objective Distributional Optimization

We study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of Wasserstein space to jointly optimize multiple objectives. Building on this approach, we propose an accelerated variant, A-MWGraD, inspired by Nesterov's acceleration. We analyze the continuous-time dynamics and establish convergence to weakly Pareto optimal points in probability space. Our theoretical results show that A-MWGraD achieves a convergence rate of O(1/t^2) for geodesically convex objectives and O(e^{-\sqrtβt}) for $β$-strongly geodesically convex objectives, improving upon the O(1/t) rate of MWGraD in the geodesically convex setting. We further introduce a practical kernel-based discretization for A-MWGraD and demonstrate through numerical experiments that it consistently outperforms MWGraD in convergence speed and sampling efficiency on multi-target sampling tasks.

Multiple Wasserstein Gradient Descent Algorithm for Multi-Objective Distributional Optimization

We address the optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions. This type of Multi-Objective Distributional Optimization commonly arises in machine learning and statistics, with applications in areas such as multiple target sampling, multi-task learning, and multi-objective generative modeling. To solve this problem, we propose an iterative particle-based algorithm, which we call Muliple Wasserstein Gradient Descent (MWGraD), which constructs a flow of intermediate empirical distributions, each being represented by a set of particles, which gradually minimize the multiple objective functionals simultaneously. Specifically, MWGraD consists of two key steps at each iteration. First, it estimates the Wasserstein gradient for each objective functional based on the current particles. Then, it aggregates these gradients into a single Wasserstein gradient using dynamically adjusted weights and updates the particles accordingly. In addition, we provide theoretical analysis and present experimental results on both synthetic and real-world datasets, demonstrating the effectiveness of MWGraD.

Wasserstein Gradient Flow over Variational Parameter Space for Variational Inference

Variational inference (VI) can be cast as an optimization problem in which the variational parameters are tuned to closely align a variational distribution with the true posterior. The optimization task can be approached through vanilla gradient descent in black-box VI or natural-gradient descent in natural-gradient VI. In this work, we reframe VI as the optimization of an objective that concerns probability distributions defined over a \textit{variational parameter space}. Subsequently, we propose Wasserstein gradient descent for tackling this optimization problem. Notably, the optimization techniques, namely black-box VI and natural-gradient VI, can be reinterpreted as specific instances of the proposed Wasserstein gradient descent. To enhance the efficiency of optimization, we develop practical methods for numerically solving the discrete gradient flows. We validate the effectiveness of the proposed methods through empirical experiments on a synthetic dataset, supplemented by theoretical analyses.

CentSmoothie: Central-Smoothing Hypergraph Neural Networks for Predicting Drug-Drug Interactions

Predicting drug-drug interactions (DDI) is the problem of predicting side effects (unwanted outcomes) of a pair of drugs using drug information and known side effects of many pairs. This problem can be formulated as predicting labels (i.e. side effects) for each pair of nodes in a DDI graph, of which nodes are drugs and edges are interacting drugs with known labels. State-of-the-art methods for this problem are graph neural networks (GNNs), which leverage neighborhood information in the graph to learn node representations. For DDI, however, there are many labels with complicated relationships due to the nature of side effects. Usual GNNs often fix labels as one-hot vectors that do not reflect label relationships and potentially do not obtain the highest performance in the difficult cases of infrequent labels. In this paper, we formulate DDI as a hypergraph where each hyperedge is a triple: two nodes for drugs and one node for a label. We then present CentSmoothie, a hypergraph neural network that learns representations of nodes and labels altogether with a novel central-smoothing formulation. We empirically demonstrate the performance advantages of CentSmoothie in simulations as well as real datasets.

Learning subtree pattern importance for Weisfeiler-Lehmanbased graph kernels

Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which measure the similaritybetween graphs and are plugged into a kernel machine such as a support vector machine.Weisfeiler-Lehman (WL) based graph kernels, which employ WL labeling scheme to extract subtree patterns and perform node embedding, are demonstrated to achieve great performance while being efficiently computable. However, one of the main drawbacks of ageneral kernel is the decoupling of kernel construction and learning process. For moleculargraphs, usual kernels such as WL subtree, based on substructures of the molecules, consider all available substructures having the same importance, which might not be suitable inpractice. In this paper, we propose a method to learn the weights of subtree patterns in the framework of WWL kernels, the state of the art method for graph classification task [14]. To overcome the computational issue on large scale data sets, we present an efficient learning algorithm and also derive a generalization gap bound to show its convergence. Finally, through experiments on synthetic and real-world data sets, we demonstrate the effectiveness of our proposed method for learning the weights of subtree patterns.

On Convex Clustering Solutions

Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However, it is not known whether convex clustering preserves desirable properties of these algorithms. A common expectation is that convex clustering may learn difficult cluster types such as non-convex ones. Current understanding of convex clustering is limited to only consistency results on well-separated clusters. We show new understanding of its solutions. We prove that convex clustering can only learn convex clusters. We then show that the clusters have disjoint bounding balls with significant gaps. We further characterize the solutions, regularization hyperparameters, inclusterable cases and consistency.

DIVERSE: bayesian Data IntegratiVE learning for precise drug ResponSE prediction

Detecting predictive biomarkers from multi-omics data is important for precision medicine, to improve diagnostics of complex diseases and for better treatments. This needs substantial experimental efforts that are made difficult by the heterogeneity of cell lines and huge cost. An effective solution is to build a computational model over the diverse omics data, including genomic, molecular, and environmental information. However, choosing informative and reliable data sources from among the different types of data is a challenging problem. We propose DIVERSE, a framework of Bayesian importance-weighted tri- and bi-matrix factorization(DIVERSE3 or DIVERSE2) to predict drug responses from data of cell lines, drugs, and gene interactions. DIVERSE integrates the data sources systematically, in a step-wise manner, examining the importance of each added data set in turn. More specifically, we sequentially integrate five different data sets, which have not all been combined in earlier bioinformatic methods for predicting drug responses. Empirical experiments show that DIVERSE clearly outperformed five other methods including three state-of-the-art approaches, under cross-validation, particularly in out-of-matrix prediction, which is closer to the setting of real use cases and more challenging than simpler in-matrix prediction. Additionally, case studies for discovering new drugs further confirmed the performance advantage of DIVERSE.

Scalable Probabilistic Matrix Factorization with Graph-Based Priors

In matrix factorization, available graph side-information may not be well suited for the matrix completion problem, having edges that disagree with the latent-feature relations learnt from the incomplete data matrix. We show that removing these $\textit{contested}$ edges improves prediction accuracy and scalability. We identify the contested edges through a highly-efficient graphical lasso approximation. The identification and removal of contested edges adds no computational complexity to state-of-the-art graph-regularized matrix factorization, remaining linear with respect to the number of non-zeros. Computational load even decreases proportional to the number of edges removed. Formulating a probabilistic generative model and using expectation maximization to extend graph-regularised alternating least squares (GRALS) guarantees convergence. Rich simulated experiments illustrate the desired properties of the resulting algorithm. On real data experiments we demonstrate improved prediction accuracy with fewer graph edges (empirical evidence that graph side-information is often inaccurate). A 300 thousand dimensional graph with three million edges (Yahoo music side-information) can be analyzed in under ten minutes on a standard laptop computer demonstrating the efficiency of our graph update.

AttentionXML: Extreme Multi-Label Text Classification with Multi-Label Attention Based Recurrent Neural Networks

Extreme multi-label text classification (XMTC) is a task for tagging each given text with the most relevant multiple labels from an extremely large-scale label set. This task can be found in many applications, such as product categorization,web page tagging, news annotation and so on. Many methods have been proposed so far for solving XMTC, while most of the existing methods use traditional bag-of-words (BOW) representation, ignoring word context as well as deep semantic information. XML-CNN, a state-of-the-art deep learning-based method, uses convolutional neural network (CNN) with dynamic pooling to process the text, going beyond the BOW-based appraoches but failing to capture 1) the long-distance dependency among words and 2) different levels of importance of a word for each label. We propose a new deep learning-based method, AttentionXML, which uses bidirectional long short-term memory (LSTM) and a multi-label attention mechanism for solving the above 1st and 2nd problems, respectively. We empirically compared AttentionXML with other six state-of-the-art methods over five benchmark datasets. AttentionXML outperformed all competing methods under all experimental settings except only a couple of cases. In addition, a consensus ensemble of AttentionXML with the second best method, Parabel, could further improve the performance over all five benchmark datasets.

Convex Coupled Matrix and Tensor Completion

We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, we propose a new completion algorithm based on the proposed norms. A key advantage of the proposed norms is that it is convex and can find a globally optimal solution, while existing methods for coupled learning are non-convex. Furthermore, we analyze the excess risk bounds of the completion model regularized by our proposed norms which show that our proposed norms can exploit the low rankness of coupled tensors leading to better bounds compared to uncoupled norms. Through synthetic and real-world data experiments, we show that the proposed completion algorithm compares favorably with existing completion algorithms.