In recent advancements in Test Time Adaptation (TTA), most existing methodologies focus on updating normalization layers to adapt to the test domain. However, the reliance on normalization-based adaptation presents key challenges. First, normalization layers such as Batch Normalization (BN) are highly sensitive to small batch sizes, leading to unstable and inaccurate statistics. Moreover, normalizationbased adaptation is inherently constrained by the structure of the pre-trained model, as it relies on training-time statistics that may not generalize well to unseen domains. These issues limit the effectiveness of normalization-based TTA approaches, especially under significant domain shift.

Contrastive learning--a modern approach to extract useful representations from unlabeled data by training models to distinguish similar samples from dissimilar ones--has driven significant progress in foundation models. In this work, we develop a new theoretical framework for analyzing data augmentation-based contrastive learning, with a focus on SimCLR as a representative example. Our approach is based on the concept of approximate sufficient statistics, which we extend beyond its original definition in Oko et al. [28] for contrastive languageimage pretraining (CLIP) using KL-divergence. We generalize it to equivalent forms and general f-divergences, and show that minimizing SimCLR and other contrastive losses yields encoders that are approximately sufficient. Furthermore, we demonstrate that these near-sufficient encoders can be effectively adapted to downstream regression and classification tasks, with performance depending on their sufficiency and the error induced by data augmentation in contrastive learning. Concrete examples in linear regression and topic classification are provided to illustrate the broad applicability of our results.

The sparse additive model (SpAM) offers a trade-off between interpretability and flexibility, and hence is a powerful model for high-dimensional research. This paper focuses on the variable selection, i.e., the univariate function selection problem in SpAM. We establish the minimax separation rates from both the perspectives of sparse multiple testing (FDR + FNR control) and support recovery (wrong recovery probability control). We further study how adaptation to unknown smoothness affects the minimax separation rate, and propose an adaptive selection procedure. Finally, we discuss the difference between estimation and selection in SpAM: Procedures achieving optimal function estimation may fail to achieve optimal univariate function selection.

We prove that, given a mean-field location-scale variational family, black-box variational inference (BBVI) with the reparametrization gradient converges at a rate that is nearly independent of any explicit dimension dependence. Specifically, for a d-dimensional strongly log-concave and log-smooth target, the number of iterations for BBVI with a sub-Gaussian family to obtain a solution ϵ-close to the global optimum has an explicit dimension dependence no larger than O(logd). This is a significant improvement over the O(d)dependence of full-rank locationscale families. For heavy-tailed families, we prove a weaker O(d2/k)dependence, where kis the number of finite moments of the family. Additionally, if the Hessian of the target log-density is constant, the complexity is free of any explicit dimension dependence. We also prove that our bound on the gradient variance, which is key to our result, cannot be improved using only spectral bounds on the Hessian of the target log-density.

This position paper argues that post-deployment monitoring in clinical AI is underdeveloped and proposes statistically valid and label-efficient testing frameworks as a principled foundation for ensuring reliability and safety in real-world deployment. A recent review found that only 9% of FDA-registered AI-based healthcare tools include a post-deployment surveillance plan [1]. Existing monitoring approaches are often manual, sporadic, and reactive, making them ill-suited for the dynamic environments in which clinical models operate. We contend that post-deployment monitoring should be grounded in label-efficient and statistically valid testing frameworks, offering a principled alternative to current practices. We use the term "statistically valid" to refer to methods that provide explicit guarantees on error rates (e.g., Type I/II error), enable formal inference under pre-defined assumptions, and support reproducibility--features that align with regulatory requirements. Specifically, we propose that the detection of changes in the data and model performance degradation should be framed as distinct statistical hypothesis testing problems. Grounding monitoring in statistical rigor ensures a reproducible and scientifically sound basis for maintaining the reliability of clinical AI systems. Importantly, it also opens new research directions for the technical community--spanning theory, methods, and tools for statistically principled detection, attribution, and mitigation of post-deployment model failures in real-world settings.

We propose a generalized score-based diffusion framework for learning multivariate Gaussian mixture models with homoscedastic or heteroscedastic noise. Our goal is to nonparametrically estimate the latent location distribution and denoise the observations.

Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define heterogeneous subgroups and handling data that are missing not at random, a prevalent issue in fields like transcriptomics. While several notable methods have been proposed to address these problems, they typically tackle each issue in isolation, thereby limiting their flexibility and adaptability. This paper introduces a unified framework designed to address these challenges simultaneously. Our approach incorporates a data-driven penalty matrix into penalized clustering to enable more flexible variable selection, along with a mechanism that explicitly models the relationship between missingness and latent class membership. We demonstrate that, under certain regularity conditions, the proposed framework achieves both asymptotic consistency and selection consistency, even in the presence of missing data. This unified strategy significantly enhances the capability and efficiency of model-based clustering, advancing methodologies for identifying informative variables that define homogeneous subgroups in the presence of complex missing data patterns. The performance of the framework, including its computational efficiency, is evaluated through simulations and demonstrated using both synthetic and real-world transcriptomic datasets.

We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated learning, crowdsourcing, and sensor networks, yet existing robust estimators typically assume uniform or worst-case corruption, ignoring structural heterogeneity. For mean estimation for multivariate bounded distributions and univariate gaussian distributions, we give tight minimax rates for all heterogeneous corruption patterns. For multivariate gaussian mean estimation and linear regression, we establish the minimax rate for squared error up to a factor of d, where d is the dimension. Roughly, our findings suggest that samples beyond a certain corruption threshold may be discarded by the optimal estimators - this threshold is determined by the empirical distribution of the corruption rates given.

Large Vision-Language Models (LVLMs) pretrained on large-scale multimodal data have shown promising capabilities in Video Anomaly Detection (VAD). However, their ability to reason about abnormal events based on scene semantics remains underexplored. In this paper, we investigate LVLMs' behavior in VAD from a visual-textual co-occurrence perspective, focusing on whether their decisions are driven by statistical shortcuts between visual instances and textual phrases. By analyzing visual-textual co-occurrence in pretraining data and conducting experiments under different data settings, we reveal a hallucination phenomenon: LVLMs tend to rely on co-occurrence patterns between visual instances and textual phrases associated with either normality or abnormality, leading to incorrect predictions when these high-frequency objects appear in semantically mismatched contexts. To address this issue, we propose VAD-DPO, a direct preference optimization method supervised with counter-example pairs. By constructing visually similar but semantically contrasting video clips, VAD-DPO encourages the model to align its predictions with the semantics of scene rather than relying on co-occurrence patterns. Extensive experiments on six benchmark datasets demonstrate the effectiveness of VAD-DPO in enhancing both anomaly detection and reasoning performance, particularly in scene-dependent scenarios.

Recent work has shown that the generalization ability of image diffusion models arises from the locality properties of the trained neural network. In particular, when denoising a particular pixel, the model relies on a limited neighborhood of the input image around that pixel, which, according to the previous work, is tightly related to the ability of these models to produce novel images. Since locality is central to generalization, it is crucial to understand why diffusion models learn local behavior in the first place, as well as the factors that govern the properties of locality patterns. In this work, we present evidence that the locality in deep diffusion models emerges as a statistical property of the image dataset and is not due to the inductive bias of convolutional neural networks, as suggested in previous work. Specifically, we demonstrate that an optimal parametric linear denoiser exhibits similar locality properties to deep neural denoisers. We show, both theoretically and experimentally, that this locality arises directly from pixel correlations present in the image datasets. Moreover, locality patterns are drastically different on specialized datasets, approximating principal components of the data's covariance. We use these insights to craft an analytical denoiser that better matches scores predicted by a deep diffusion model than prior expert-crafted alternatives. Our key takeaway is that while neural network architectures influence generation quality, their primary role is to capture locality patterns inherent in the data.