Understanding the evolving dependence between two sets of multivariate signals is fundamental in neuroscience and other domains where sub-networks in a system interact dynamically over time. Despite the growing interest in multivariate time series analysis, existing methods for between-clusters dependence typically rely on the assumption of stationarity and lack the temporal resolution to capture transient, frequency-specific interactions. To overcome this limitation, we propose scale-specific wavelet canonical coherence (WaveCanCoh), a novel framework that extends canonical coherence analysis to the nonstationary setting by leveraging the multivariate locally stationary wavelet model. The proposed WaveCanCoh enables the estimation of time-varying canonical coherence between clusters, providing interpretable insight into scale-specific time-varying interactions between clusters. Through extensive simulation studies, we demonstrate that WaveCanCoh accurately recovers true coherence structures under both locally stationary and general nonstationary conditions. Application to local field potential (LFP) activity data recorded from the hippocampus reveals distinct dynamic coherence patterns between correct and incorrect memory-guided decisions, illustrating the capacity of the method to detect behaviorally relevant neural coordination.

Unsupervised Graph Domain Adaptation has become a promising paradigm for transferring knowledge from a fully labeled source graph to an unlabeled target graph. Existing graph domain adaptation models primarily focus on the closed-set setting, where the source and target domains share the same label spaces. However, this assumption might not be practical in the real-world scenarios, as the target domain might include classes that are not present in the source domain. In this paper, we investigate the problem of unsupervised open-set graph domain adaptation, where the goal is to not only correctly classify target nodes into the known classes, but also recognize previously unseen node types into the unknown class. Towards this end, we propose a novel framework called GraphRTA, which conducts reprogramming on both the graph and model sides. Specifically, we reprogram the graph by modifying target graph structure and node features, which facilitates better separation of known and unknown classes. Meanwhile, we also perform model reprogramming by pruning domain-specific parameters to reduce bias towards the source graph while preserving parameters that capture transferable patterns across graphs. Additionally, we extend the classifier with an extra dimension for the unknown class, thus eliminating the need of manually specified threshold in open-set recognition. Comprehensive experiments on several public datasets demonstrate that our proposed model can achieve satisfied performance compared with recent state-of-the-art baselines.

The goal is to find representations (e.g., embeddings in Rd or a tree metric) where anchors are placed closer to positive than to negative examples. While finding global optima of contrastive objectives is NP-hard, the complexity of finding local optima--representations that do not improve by local search algorithms such as gradient-based methods--remains open. Our work settles the complexity of finding local optima in various contrastive learning problems by proving PLS-hardness in discrete settings (e.g., maximize satisfied triplets) and CLS-hardness in continuous settings (e.g., minimize Triplet Loss), where PLS(Polynomial Local Search) and CLS(Continuous Local Search) are well-studied complexity classes capturing local search dynamics in discrete and continuous optimization, respectively. Our results imply that no polynomial time algorithm (local search or otherwise) can find a local optimum for various contrastive learning problems, unless PLS P(or CLS P for continuous problems). Even in the unlikely scenario that PLS P(or CLS P), our reductions imply that there exist instances where local search algorithms need exponential time to reach a local optimum, even for d = 1(embeddings on a line).

Extant studies predominantly address catastrophic forgetting within a simplified continual learning paradigm, typically confined to a singular data domain. Conversely, real-world applications frequently encompass multiple, evolving data domains, wherein models often struggle to retain many critical past information, thereby leading to performance degradation. This paper addresses this complex scenario by introducing a novel dynamic expansion approach called Learning Expandable and Adaptable Representations (LEAR). This framework orchestrates a collaborative backbone structure, comprising global and local backbones, designed to capture both general and task-specific representations. Leveraging this collaborative backbone, the proposed framework dynamically creates a lightweight expert to delineate decision boundaries for each novel task, thereby facilitating the prediction process. To enhance new task learning, we introduce a novel Mutual Information-Based Prediction Alignment approach, which incrementally optimizes the global backbone via a mutual information metric, ensuring consistency in the prediction patterns of historical experts throughout the optimization phase.

Neural simulation-based inference (SBI) is a popular set of methods for Bayesian inference when models are only available in the form of a simulator. These methods are widely used in the sciences and engineering, where writing down a likelihood can be significantly more challenging than constructing a simulator. However, the performance of neural SBI can suffer when simulators are computationally expensive, thereby limiting the number of simulations that can be performed. In this paper, we propose a novel approach to neural SBI which leverages multilevel Monte Carlo techniques for settings where several simulators of varying cost and fidelity are available. We demonstrate through both theoretical analysis and extensive experiments that our method can significantly enhance the accuracy of SBI methods given a fixed computational budget.

Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and provide new theoretical insights. In particular, we show the kernelizability and outof-sample applicability for a PCA-like family of problems. Moreover, we uncover that simultaneous iteration, which is connected to the classical QR algorithm, is an instance of the difference-of-convex algorithm (DCA), offering an optimization perspective on this longstanding method. Further, we describe new algorithms for PCA and empirically compare them with state-of-the-art methods. Lastly, we introduce a kernelizable dual formulation for a robust variant of PCA that minimizes the l1-deviation of the reconstruction errors.

Data deviations in electronic health records (EHR) refer to discrepancies between recorded entries and a patient's actual physiological state, indicating a decline in EHR data fidelity. Such deviations can result from pre-analytical variability, documentation errors, or unvalidated data sources. Effectively detecting data deviations is clinically valuable for identifying erroneous records, excluding them from downstream clinical workflows, and informing corrective actions. Despite its importance and practical relevance, this problem remains largely underexplored in existing research. To bridge this gap, we propose a bi-level knowledge distillation approach centered on a task-agnostic formulation of EHR data fidelity as an intrinsic measure of data reliability. Our approach performs layered knowledge distillation in two levels: from a computation-intensive, task-specific data Shapley oracle to a neural oracle for individual tasks, and then to a unified EHR data fidelity predictor. This design enables the integration of task-specific insights into a holistic assessment of a patient's EHR data fidelity from a multi-task perspective. By tracking the outputs of this learned predictor, we detect potential data deviations in EHR data.

Limited labeling budget severely impedes data-driven research, such as medical analysis, remote sensing and population census, and active inference is a solution to this problem. Prior works utilizing independent sampling have achieved improvements over uniform sampling, but its insufficient usage of available information undermines its statistical efficiency. In this paper, we propose balanced active inference, a novel algorithm that incorporates balancing constraints based on model uncertainty utilizing the cube method for label selection. Under regularity conditions, we establish its asymptotic properties and also prove that the statistical efficiency of the proposed algorithm is higher than its alternatives. Various numerical experiments, including regression and classification in both synthetic setups and real data analysis, demonstrate that the proposed algorithm outperforms its alternatives while guaranteeing nominal coverage. Our code is available at: https://github.com/Uninfty/Balanced_Active_Inference

We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic Gradient Descent (SGD) based solvers have demonstrated strong empirical performance in recent machine learning applications, yet their theoretical guarantee to approximate the OT map is an open question. In this work, we answer it positively by providing both computational and statistical convergence guarantees of SGD. Specifically, we show that SGD methods can estimate the OT map with a minimax convergence rate of $\mathcal{O}(1/\sqrt{n})$, where $n$ is the number of samples drawn from $\mu$. To establish this result, we study the averaged projected SGD algorithm, and identify a suitable projection set that contains a minimizer of the objective, even when the source measure is not compactly supported. Our analysis holds under mild assumptions on the source measure and applies to MTW cost functions,whic include $\|\cdot\|^p$ for $p \in (1, \infty)$. We finally provide numerical evidence for our theoretical results.

View missing remains a significant challenge in graph-based multi-view semisupervised learning, hindering their real-world applications. To address this issue, traditional methods introduce a missing indicator matrix and focus on mining partial structure among existing samples in each view for label propagation (LP). However, we argue that these disregarded missing samples sometimes induce discontinuous local structures, i.e., sub-clusters, breaking the fundamental smoothness assumption in LP. Consequently, such a Sub-Cluster Problem (SCP) would distort graph fusion and degrade classification performance. To alleviate SCP, we propose a novel incomplete multi-view semi-supervised learning method, termed AGF-TI.