In our article, we describe a method for generating counterfactual explanations in high-dimensional spaces using four steps that involve fitting our dataset to a model, finding the decision boundary, determining constraints on the problem, and computing the closest point (counterfactual explanation) from that boundary. We propose a discretized approach where we find many discrete points on the boundary and then identify the closest feasible counterfactual explanation. This method, which we later call $\textit{Segmented Sampling for Boundary Approximation}$ (SSBA), applies binary search to find decision boundary points and then searches for the closest boundary point. Across four datasets of varying dimensionality, we show that our method can outperform current methods for counterfactual generation with reductions in distance between $5\%$ to $50\%$ in terms of the $L_2$ norm. Our method can also handle real-world constraints by restricting changes to immutable and categorical features, such as age, gender, sex, height, and other related characteristics such as the case for a health-based dataset. In terms of runtime, the SSBA algorithm generates decision boundary points on multiple orders of magnitude in the same given time when we compare to a grid-based approach. In general, our method provides a simple and effective model-agnostic method that can compute nearest feasible (i.e. realistic with constraints) counterfactual explanations. All of our results and code are available at: https://github.com/dsin85691/SSBA_For_Counterfactuals

Clustering is a fundamental task in machine learning and data analysis, but it frequently fails to provide fair representation for various marginalized communities defined by multiple protected attributes -- a shortcoming often caused by biases in the training data. As a result, there is a growing need to enhance the fairness of clustering outcomes, ideally by making minimal modifications, possibly as a post-processing step after conventional clustering. Recently, Chakraborty et al. [COLT'25] initiated the study of \emph{closest fair clustering}, though in a restricted scenario where data points belong to only two groups. In practice, however, data points are typically characterized by many groups, reflecting diverse protected attributes such as age, ethnicity, gender, etc. In this work, we generalize the study of the \emph{closest fair clustering} problem to settings with an arbitrary number (more than two) of groups. We begin by showing that the problem is NP-hard even when all groups are of equal size -- a stark contrast with the two-group case, for which an exact algorithm exists. Next, we propose near-linear time approximation algorithms that efficiently handle arbitrary-sized multiple groups, thereby answering an open question posed by Chakraborty et al. [COLT'25]. Leveraging our closest fair clustering algorithms, we further achieve improved approximation guarantees for the \emph{fair correlation clustering} problem, advancing the state-of-the-art results established by Ahmadian et al. [AISTATS'20] and Ahmadi et al. [2020]. Additionally, we are the first to provide approximation algorithms for the \emph{fair consensus clustering} problem involving multiple (more than two) groups, thus addressing another open direction highlighted by Chakraborty et al. [COLT'25].

We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and testability have largely been examined only in discrete or restricted settings -- typically with respect to the Hamming distance, which is ill-suited for real-valued functions. In contrast, we study these problems in high dimensions under the standard Gaussian measure, assuming sample access to the function and a mild smoothness condition, namely Lipschitzness. A smoothness assumption is natural and, in fact, necessary even in one dimension: without it, convexity cannot be inferred from finitely many samples. As our main results, we give: - Learning Convex Functions: An agnostic proper learning algorithm for Lipschitz convex functions that achieves error $\varepsilon$ using $n^{O(1/\varepsilon^2)}$ samples, together with a complementary lower bound of $n^{\mathrm{poly}(1/\varepsilon)}$ samples in the \emph{correlational statistical query (CSQ)} model. - Testing Convex Functions: A tolerant (two-sided) tester for convexity of Lipschitz functions with the same sample complexity (as a corollary of our learning result), and a one-sided tester (which never rejects convex functions) using $O(\sqrt{n}/\varepsilon)^n$ samples.

There has been a prevalence of applying AI software in both high-stakes public-sector and industrial contexts. However, the lack of transparency has raised concerns about whether these data-informed AI software decisions secure fairness against people of all racial, gender, or age groups. Despite extensive research on emerging fairness-aware AI software, up to now most efforts to solve this issue have been dedicated to binary classification tasks. Fairness in regression is relatively underexplored. In this work, we adopted a mutual information-based metric to assess separation violations. The metric is also extended so that it can be directly applied to both classification and regression problems with both binary and continuous sensitive attributes. Inspired by the Reweighing algorithm in fair classification, we proposed a FairReweighing pre-processing algorithm based on density estimation to ensure that the learned model satisfies the separation criterion. Theoretically, we show that the proposed FairReweighing algorithm can guarantee separation in the training data under a data independence assumption. Empirically, on both synthetic and real-world data, we show that FairReweighing outperforms existing state-of-the-art regression fairness solutions in terms of improving separation while maintaining high accuracy.

Spatial transcriptomics enables gene expression profiling with spatial context, offering unprecedented insights into the tissue microenvironment. However, most computational models treat genes as isolated numerical features, ignoring the rich biological semantics encoded in their symbols. This prevents a truly deep understanding of critical biological characteristics. To overcome this limitation, we present SemST, a semantic-guided deep learning framework for spatial transcriptomics data clustering. SemST leverages Large Language Models (LLMs) to enable genes to "speak" through their symbolic meanings, transforming gene sets within each tissue spot into biologically informed embeddings. These embeddings are then fused with the spatial neighborhood relationships captured by Graph Neural Networks (GNNs), achieving a coherent integration of biological function and spatial structure. We further introduce the Fine-grained Semantic Modulation (FSM) module to optimally exploit these biological priors. The FSM module learns spot-specific affine transformations that empower the semantic embeddings to perform an element-wise calibration of the spatial features, thus dynamically injecting high-order biological knowledge into the spatial context. Extensive experiments on public spatial transcriptomics datasets show that SemST achieves state-of-the-art clustering performance. Crucially, the FSM module exhibits plug-and-play versatility, consistently improving the performance when integrated into other baseline methods.

Natural language data, such as text and speech, have become readily available through social networking services and chat platforms. By leveraging human observations expressed in natural language, this paper addresses the problem of state estimation for physical systems, in which humans act as sensing agents. To this end, we propose a Language-Aided Particle Filter (LAPF), a particle filter framework that structures human observations via natural language processing and incorporates them into the update step of the state estimation. Finally, the LAPF is applied to the water level estimation problem in an irrigation canal and its effectiveness is demonstrated.

Fine-grained knowledge is crucial for vision-language models to obtain a better understanding of the real world. While there has been work trying to acquire this kind of knowledge in the space of vision and language, it has mostly focused on aligning the image patches with the tokens on the language side. However, image patches do not have any meaning to the human eye, and individual tokens do not necessarily carry groundable information in the image. It is groups of tokens which describe different aspects of the scene. In this work, we propose a model which groups the caption tokens as part of its architecture in order to capture a fine-grained representation of the language. We expect our representations to be at the level of objects present in the image, and therefore align our representations with the output of an image encoder trained to discover objects. We show that by learning to group the tokens, the vision-language model has a better fine-grained understanding of vision and language. In addition, the token groups that our model discovers are highly similar to groundable phrases in text, both qualitatively and quantitatively.

Attributed graphs, typically characterized by irregular topologies and a mix of numerical and categorical attributes, are ubiquitous in diverse domains such as social networks, bioinformatics, and cheminformatics. While graph kernels provide a principled framework for measuring graph similarity, existing kernel methods often struggle to simultaneously capture heterogeneous attribute semantics and neighborhood information in attributed graphs. In this work, we propose the Neighborhood-Aware Star Kernel (NASK), a novel graph kernel designed for attributed graph learning. NASK leverages an exponential transformation of the Gower similarity coefficient to jointly model numerical and categorical features efficiently, and employs star substructures enhanced by Weisfeiler-Lehman iterations to integrate multi-scale neighborhood structural information. We theoretically prove that NASK is positive definite, ensuring compatibility with kernel-based learning frameworks such as SVMs. Extensive experiments are conducted on eleven attributed and four large-scale real-world graph benchmarks. The results demonstrate that NASK consistently achieves superior performance over sixteen state-of-the-art baselines, including nine graph kernels and seven Graph Neural Networks.

Split Federated Learning (SFL) is an emerging paradigm for privacy-preserving distributed learning. However, it remains vulnerable to sophisticated data poisoning attacks targeting local features, labels, smashed data, and model weights. Existing defenses, primarily adapted from traditional Federated Learning (FL), are less effective under SFL due to limited access to complete model updates. This paper presents HealSplit, the first unified defense framework tailored for SFL, offering end-to-end detection and recovery against five sophisticated types of poisoning attacks. HealSplit comprises three key components: (1) a topology-aware detection module that constructs graphs over smashed data to identify poisoned samples via topological anomaly scoring (TAS); (2) a generative recovery pipeline that synthesizes semantically consistent substitutes for detected anomalies, validated by a consistency validation student; and (3) an adversarial multi-teacher distillation framework trains the student using semantic supervision from a Vanilla Teacher and anomaly-aware signals from an Anomaly-Influence Debiasing (AD) Teacher, guided by the alignment between topological and gradient-based interaction matrices. Extensive experiments on four benchmark datasets demonstrate that HealSplit consistently outperforms ten state-of-the-art defenses, achieving superior robustness and defense effectiveness across diverse attack scenarios.

The prevalence of real-world multi-view data makes incomplete multi-view clustering (IMVC) a crucial research. The rapid development of Graph Neural Networks (GNNs) has established them as one of the mainstream approaches for multi-view clustering. Despite significant progress in GNNs-based IMVC, some challenges remain: (1) Most methods rely on the K-Nearest Neighbors (KNN) algorithm to construct static graphs from raw data, which introduces noise and diminishes the robustness of the graph topology. (2) Existing methods typically utilize the Mean Squared Error (MSE) loss between the reconstructed graph and the sparse adjacency graph directly as the graph reconstruction loss, leading to substantial gradient noise during optimization. To address these issues, we propose a novel \textbf{D}ynamic Deep \textbf{G}raph Learning for \textbf{I}ncomplete \textbf{M}ulti-\textbf{V}iew \textbf{C}lustering with \textbf{M}asked Graph Reconstruction Loss (DGIMVCM). Firstly, we construct a missing-robust global graph from the raw data. A graph convolutional embedding layer is then designed to extract primary features and refined dynamic view-specific graph structures, leveraging the global graph for imputation of missing views. This process is complemented by graph structure contrastive learning, which identifies consistency among view-specific graph structures. Secondly, a graph self-attention encoder is introduced to extract high-level representations based on the imputed primary features and view-specific graphs, and is optimized with a masked graph reconstruction loss to mitigate gradient noise during optimization. Finally, a clustering module is constructed and optimized through a pseudo-label self-supervised training mechanism. Extensive experiments on multiple datasets validate the effectiveness and superiority of DGIMVCM.