We propose the data augmented bootstrap (DAB), a framework for constructing confidence intervals from approximately invariant transformations of the data. As special cases, DAB recovers popular methods that rely on exact group symmetries, such as conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics and the recently proposed SymmPI. Meanwhile, DAB also recovers the classical bootstrap method, which exploits the dataset's approximate invariance under uniform sampling of data indices as the dataset size grows. For all DAB methods, we establish theoretical coverage results that interpolate between finite-sample and asymptotic guarantees according to the strength of the invariance, and without assuming a group structure. The approximate invariance is measured in the Kolmogorov distance and, for statistics that satisfy Gaussian universality, reduces to conditional mean and variance matching. This allows us to incorporate data augmentation (DA), a widely used machine learning heuristic based on approximate invariances, into known statistical methods. We empirically test the performance of incorporating DA into bootstrap, wild bootstrap and conformal prediction for simulated settings as well as for image, language and scientific data.

In this paper, we explore semantic clustering properties of deep reinforcement learning (DRL) to improve its interpretability and deepen our understanding of its internal semantic organization. In this context, semantic clustering refers to the ability of neural networks to cluster inputs based on their semantic similarity in the feature space. We propose a DRL architecture that incorporates a novel semantic clustering module that combines feature dimensionality reduction with online clustering.

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals differ with high probability, and include tests of conditional moments or two-sample tests. Our key idea is to transform confidence bounds of a learning method into a test of conditional expectations.

In this paper, we propose a novel tube-wise local tensor compressed sensing (CS) model under the tensor product framework, where sensing operators are independently applied to each tube of a third-order tensor. To recover the low-rank ground truth tensor, we minimize a non-convex objective via Burer-Monteiro factorization and solve it using gradient descent (GD) with spectral initialization. We prove that this approach achieves exact recovery with a linear convergence rate. Notably, our method attains provably lower sample complexity than existing TCS methods if the low tubal rank ground truth tensor satisfies the defined incoherence condition. Our proof leverages the leave-one-out technique to show that gradient descent generates iterates implicitly biased towards solutions with bounded incoherence, which ensures contraction of optimization error in consecutive iterates. Empirical results validate the effectiveness of GD in solving the proposed local TCS model.

Latent variables (LVs) play a crucial role in encoder-decoder models by enabling effective data compression, prediction, and generation. Although their theoretical properties, such as generalization, have been extensively studied in supervised learning, similar analyses for unsupervised models such as variational autoencoders (VAEs) remain insufficiently explored. In this work, we extend informationtheoretic generalization analysis to vector-quantized (VQ) VAEs with discrete latent spaces, introducing a novel data-dependent prior to rigorously analyze the relationship among LVs, generalization, and data generation. We derive a novel generalization error bound of the reconstruction loss of VQ-VAEs, which depends solely on the complexity of LVs and the encoder, independent of the decoder. Additionally, we provide the upper bound of the 2-Wasserstein distance between the distributions of the true data and the generated data, explaining how the regularization of the LVs contributes to the data generation performance.

Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges proportionally to their effective resistances, but require expensive preprocessing to estimate these resistances. We study whether uniform edge sampling--a simple, structure-agnostic strategy--can suffice for spectral clustering. Our main result shows that for graphs admitting a well-separated k-clustering, characterized by a large structure ratio Υ(k) = λk+1/ρG(k), uniform sampling preserves the spectral subspace used for clustering. Specifically, we prove that uniformly sampling O(γ2nlogn/ε2) edges, where γ is the Laplacian condition number, yields a sparsifier whose top (n k)dimensional eigenspace is approximately orthogonal to the cluster indicators.

Class-imbalanced learning (CIL) on tabular data is important in many realworld applications where the minority class holds the critical but rare outcomes.

Recently, 3DGaussian Splatting (3DGS) has achieved state-of-the-art rendering results. However, its efficiency relies on simplifications that disregard the thickness of Gaussian primitives and their overlapping interactions. These simplifications can lead to popping artifacts due to inaccurate sorting, thereby affecting the rendering quality. In this paper, we propose Screen-Aligned Primitives (SAP), an anisotropic kernel that generates primitives parallel to the image plane for each view. Our rasterization pipeline enables full per-pixel ordering in real time. Since the primitives are parallel for a given viewpoint, a single global sorting operation suffices for correct per-pixel depth ordering. We formulate 3D reconstruction as a combination of a 3D-consistent decoder and 2D view-specific primitives, and further propose a highly efficient decoder to ensure 3D consistency. Moreover, within our framework, the primitive function values remain consistent between view space and screen space, allowing arbitrary radial basis functions (RBFs) to represent the scene without introducing projection errors. Experiments on diverse datasets demonstrate that our method achieves state-of-the-art rendering quality while maintaining real-time performance.

Graph transfer learning, especially in unsupervised domain adaptation, aims to transfer knowledge from a label-abundant source graph to an unlabeled target graph. However, most existing approaches overlook the common issue of label imbalance in the source domain, typically assuming a balanced label distribution that rarely holds in practice. Moreover, they face challenges arising from biased knowledge in the source graph and substantial domain distribution shifts. To remedy the above challenges, we propose a dual-branch prototype-enhanced contrastive framework for graph domain adaptation under a class-imbalanced scenario. Specifically, we introduce a dual-branch graph encoder to capture both local and global information, generating class-specific prototypes from a distilled anchor set. Then, a prototypeenhanced contrastive learning framework is introduced. On the one hand, we encourage class alignment between the two branches based on constructed prototypes to alleviate the bias introduced by class imbalance. On the other hand, we infer the pseudo-labels for the target domain and align sample pairs across domains that share similar semantics to reduce domain discrepancies. Experimental results show that our ImGDA outperforms the state-of-the-art methods across multiple datasets and settings.

Data valuation quantifies the impact of individual data points on model performance, and Shapley values provide a principled approach to this important task due to their desirable axiomatic properties, albeit with high computational complexity. Recent breakthroughs have enabled fast computation of exact Shapley values for unweighted k-nearest neighbor (kNN) classifiers. However, extending this to weighted kNN models has remained a significant open challenge. The state-of-theart methods either require quadratic time complexity or resort to approximation via sampling. In this paper, we show that a conceptually simple but overlooked approach -- data duplication -- can be applied to this problem, yielding a natural variant of weighted kNN-Shapley. However, a straightforward application of the data-duplication idea leads to increased data size and prohibitive computational and memory costs. We develop an efficient algorithm that avoids materializing the duplicated dataset by exploiting the structural properties of weighted kNN models, reducing the complexity to near-linear time in the original data size. Besides, we establish theoretical foundations for this approach through axiomatic characterization of the resulting values, and empirically validate the effectiveness and efficiency of our method.