This paper addresses structured out-of-distribution (OOD) testing in high-stakes machine learning applications. Traditional conformal methods rely on joint exchangeability, making it difficult to incorporate auxiliary information such as spatiotemporal or grouping structures. To overcome this limitation, we propose the structure-adaptive conformal q-value (SCQ), a significance index that integrates individual test evidence with structural patterns. We also develop pseudo-score-guided transductive automated model selection (P-TAMS), which adapts conformalized model selection to structured OOD testing across a toolbox of candidate models. Together, SCQ and P-TAMS form a unified framework under pairwise exchangeability, providing finite-sample error-rate control, improved power, and enhanced interpretability. Experiments on simulated and real data demonstrate that the proposed approach controls the false discovery rate and performs well across diverse settings.

Modern matrix completion problems often involve heterogeneous data whose rows simultaneously belong to many meta-categories, such as demographic and age groups in recommendation systems, or region and recording session labels in neural electrophysiological experiments. Standard low-rank estimators impose a single global latent geometry, which can recover average structure but may smooth away subgroup-specific variation, especially when observations are unevenly distributed across groups. We introduce Group-Aware Matrix Estimation (GAME), a convex estimator for overlapping subgroup-wise low-rank matrix estimation. GAME regularizes category-specific submatrices through overlapping nuclear-norm penalties, allowing related groups to borrow information while preserving local latent structure in a shared coordinate system. We provide finite-sample guarantees for both reconstruction error and subgroup-specific subspace recovery, showing how performance depends on sampling density, subgroup rank, and overlap structure. Experiments on synthetic, recommendation, ecological, and neuroscience datasets show that GAME is most beneficial in structured missingness regimes, where subgroup-aware regularization improves both reconstruction accuracy and latent subspace fidelity. Across these benchmarks, GAME is competitive or best among global low-rank, side-information, and modern imputation baselines, with the largest gains when subgroups exhibit distinct low-rank structure.

Low-rank matrix completion is a widely studied problem with many variants. Inductive matrix completion (IMC) incorporates row and column side information to significantly narrow the search space. Prior work falls into two regimes: methods that exploit this structure to achieve reduced sample complexity but only in noiseless settings, and methods that handle noise but require sample complexity matching the ambient matrix dimension, forfeiting the sample efficiency that side information should provide. In this paper, we close this gap by studying noisy IMC with a nonconvex projected gradient descent algorithm with spectral initialization. Our main technical contribution is establishing a regularity condition for the IMC loss function that holds at the reduced sample complexity determined by the effective problem size, scaling with the side information dimension a rather than the ambient dimension n. This directly yields linear convergence and an estimation error that both depend only on the effective problem size rather than the ambient matrix dimension. We further extend our analysis to the inexact side information setting, demonstrating that the reduced sample complexity is maintained and the estimation error is order-optimal with respect to the inexactness of the side information. Extensive simulations and real-world experiments on the MovieLens dataset validate our theoretical findings.

Neural Information Processing Systems http://nips.cc/

The Passive-Aggressive (PA) method is widely used in online regression problems for handling large-scale streaming data, typically updating model parameters in a passive-aggressive manner based on whether the error exceeds a predefined threshold. However, this approach struggles with determining optimal thresholds and adapting to complex scenarios with side information, where tracking accuracy is not the sole metric in the regression model. To address these challenges, we introduce a novel adaptive framework that allows finer adjustments to the weight vector in PA using side information. This framework adaptively selects the threshold parameter in PA, theoretically ensuring convergence to the optimal setting. Additionally, we present an efficient implementation of our algorithm that significantly reduces computational complexity. Numerical experiments show that our model achieves outstanding performance associated with the side information while maintaining low tracking error, demonstrating marked improvements over traditional PA methods across various scenarios.

Computer vision tasks often have side information available that is helpful to solve the task. For example, for crowd counting, the camera perspective (e.g., camera angle and height) gives a clue about the appearance and scale of people in the scene. While side information has been shown to be useful for counting systems using traditional hand-crafted features, it has not been fully utilized in counting systems based on deep learning. In order to incorporate the available side information, we propose an adaptive convolutional neural network (ACNN), where the convolution filter weights adapt to the current scene context via the side information.

Semi-supervised clustering algorithms have been proposed to identify data clusters that align with user perceived ones via the aid of side information such as seeds or pairwise constrains. However, traditional side information is mostly at the instance level and subject to the sampling bias, where non-randomly sampled instances in the supervision can mislead the algorithms to wrong clusters. In this paper, we propose learning from the feature-level supervision. We show that this kind of supervision can be easily obtained in the form of perception vectors in many applications. Then we present novel algorithms, called Perception Embedded (PE) clustering, that exploit the perception vectors as well as traditional side information to find clusters perceived by the user. Extensive experiments are conducted on real datasets and the results demonstrate the effectiveness of PE empirically.

Matrix completion methods can benefit from side information besides the partially observed matrix. The use of side features describing the row and column entities of a matrix has been shown to reduce the sample complexity for completing the matrix. We propose a novel sparse formulation that explicitly models the interaction between the row and column side features to approximate the matrix entries. Unlike early methods, this model does not require the low-rank condition on the model parameter matrix. We prove that when the side features can span the latent feature space of the matrix to be recovered, the number of observed entries needed for an exact recovery is $O(\log N)$ where $N$ is the size of the matrix. When the side features are corrupted latent features of the matrix with a small perturbation, our method can achieve an $\epsilon$-recovery with $O(\log N)$ sample complexity, and maintains a $\O(N^{3/2})$ rate similar to classfic methods with no side information. An efficient linearized Lagrangian algorithm is developed with a strong guarantee of convergence. Empirical results show that our approach outperforms three state-of-the-art methods both in simulations and on real world datasets.