Recent works have extended notions of feature importance to semantic concepts that are inherently interpretable to the users interacting with a black-box predictive model. Yet, precise statistical guarantees such as false positive rate and false discovery rate control are needed to communicate findings transparently, and to avoid unintended consequences in real-world scenarios. In this paper, we formalize the global (i.e., over a population) and local (i.e., for a sample) statistical importance of semantic concepts for the predictions of opaque models by means of conditional independence, which allows for rigorous testing. We use recent ideas of sequential kernelized independence testing to induce a rank of importance across concepts, and we showcase the effectiveness and flexibility of our framework on synthetic datasets as well as on image classification using several vision-language models.

Sparse ridge regression problems play a significant role across various domains. To solve sparse ridge regression, Liu et al. (2023) recently propose an advanced algorithm, Scalable Optimal K -Sparse Ridge Regression (OKRidge), which is both faster and more accurate than existing approaches. However, the absence of theoretical analysis on the error of OKRidge impedes its large-scale applications. In this paper, we reframe the estimation error of OKRidge as a Primary Optimization ( \textbf{PO}) problem and employ the Convex Gaussian min-max theorem (CGMT) to simplify the \textbf{PO} problem into an Auxiliary Optimization ( \textbf{AO}) problem. Subsequently, we provide a theoretical error analysis for OKRidge based on the \textbf{AO} problem. This error analysis improves the theoretical reliability of OKRidge.

Out-of-distribution (OOD) detection is crucial for the safe deployment of neural networks. Existing CLIP-based approaches perform OOD detection by devising novel scoring functions or sophisticated fine-tuning methods. In this work, we propose SeTAR, a novel, training-free OOD detection method that leverages selective low-rank approximation of weight matrices in vision-language and vision-only models. SeTAR enhances OOD detection via post-hoc modification of the model's weight matrices using a simple greedy search algorithm. Based on SeTAR, we further propose SeTAR FT, a fine-tuning extension optimizing model performance for OOD detection tasks.

Adaptation of pretrained vision-language models such as CLIP to various downstream tasks have raised great interest in recent researches. Previous works have proposed a variety of test-time adaptation (TTA) methods to achieve strong generalization without any knowledge of the target domain. However, existing training-required TTA approaches like TPT necessitate entropy minimization that involves large computational overhead, while training-free methods like TDA overlook the potential for information mining from the test samples themselves.In this paper, we break down the design of existing popular training-required and training-free TTA methods and bridge the gap between them within our framework.Specifically, we maintain a light-weight key-value memory for feature retrieval from instance-agnostic historical samples and instance-aware boosting samples. The historical samples are filtered from the testing data stream and serve to extract useful information from the target distribution, while the boosting samples are drawn from regional bootstrapping and capture the knowledge of the test sample itself.We theoretically justify the rationality behind our method and empirically verify its effectiveness on both the out-of-distribution and the cross-domain datasets, showcasing its applicability in real-world situations.

We introduce One-Shot Label-Only (OSLO) membership inference attacks (MIAs), which accurately infer a given sample's membership in a target model's training set with high precision using just a single query, where the target model only returns the predicted hard label. This is in contrast to state-of-the-art label-only attacks which require \sim6000 queries, yet get attack precisions lower than OSLO's. The core idea is that a member sample exhibits more resistance to adversarial perturbations than a non-member. We compare OSLO against state-of-the-art label-only attacks and demonstrate that, despite requiring only one query, our method significantly outperforms previous attacks in terms of precision and true positive rate (TPR) under the same false positive rates (FPR). For example, compared to previous label-only MIAs, OSLO achieves a TPR that is at least 7 \times higher under a 1\% FPR and at least 22 \times higher under a 0.1\% FPR on CIFAR100 for a ResNet18 model.

Many modern data analyses benefit from explicitly modeling dependence structure in data -- such as measurements across time or space, ordered words in a sentence, or genes in a genome. A gold standard evaluation technique is structured cross-validation (CV), which leaves out some data subset (such as data within a time interval or data in a geographic region) in each fold. But CV here can be prohibitively slow due to the need to re-run already-expensive learning algorithms many times. Previous work has shown approximate cross-validation (ACV) methods provide a fast and provably accurate alternative in the setting of empirical risk minimization. But this existing ACV work is restricted to simpler models by the assumptions that (i) data across CV folds are independent and (ii) an exact initial model fit is available. In structured data analyses, both these assumptions are often untrue.

Bayesian neural networks (BNNs) treat neural network weights as random variables, which aim to provide posterior uncertainty estimates and avoid overfitting by performing inference on the posterior weights. However, the selection of appropriate prior distributions remains a challenging task, and BNNs may suffer from catastrophic inflated variance or poor predictive performance when poor choices are made for the priors. Existing BNN designs apply different priors to weights, while the behaviours of these priors make it difficult to sufficiently shrink noisy signals or they are prone to overshrinking important signals in the weights. To alleviate this problem, we propose a novel R2D2-Net, which imposes the R^2-induced Dirichlet Decomposition (R2D2) prior to the BNN weights. The R2D2-Net can effectively shrink irrelevant coefficients towards zero, while preventing key features from over-shrinkage. To approximate the posterior distribution of weights more accurately, we further propose a variational Gibbs inference algorithm that combines the Gibbs updating procedure and gradient-based optimization. This strategy enhances stability and consistency in estimation when the variational objective involving the shrinkage parameters is non-convex. We also analyze the evidence lower bound (ELBO) and the posterior concentration rates from a theoretical perspective. Experiments on both natural and medical image classification and uncertainty estimation tasks demonstrate satisfactory performance of our method.

We present a weighted version of Leave-One-Out (LOO) cross-validation for estimating the Integrated Squared Error (ISE) when approximating an unknown function by a predictor that depends linearly on evaluations of the function over a finite collection of sites. The method relies on the construction of the best linear estimator of the squared prediction error at an arbitrary unsampled site based on squared LOO residuals, assuming that the function is a realization of a Gaussian Process (GP). A theoretical analysis of performance of the ISE estimator is presented, and robustness with respect to the choice of the GP kernel is investigated first analytically, then through numerical examples. Overall, the estimation of ISE is significantly more precise than with classical, unweighted, LOO cross validation. Application to model selection is briefly considered through examples.

Prediction-Powered Inference (PPI) is a popular strategy for combining gold-standard and possibly noisy pseudo-labels to perform statistical estimation. Prior work has shown an asymptotic "free lunch" for PPI++, an adaptive form of PPI, showing that the *asymptotic* variance of PPI++ is always less than or equal to the variance obtained from using gold-standard labels alone. Notably, this result holds *regardless of the quality of the pseudo-labels*. In this work, we demystify this result by conducting an exact finite-sample analysis of the estimation error of PPI++ on the mean estimation problem. We give a "no free lunch" result, characterizing the settings (and sample sizes) where PPI++ has provably worse estimation error than using gold-standard labels alone. Specifically, PPI++ will outperform if and only if the correlation between pseudo- and gold-standard is above a certain level that depends on the number of labeled samples ($n$). In some cases our results simplify considerably: For Gaussian data, the correlation must be at least $1/\sqrt{n - 2}$ in order to see improvement, and a similar result holds for binary labels. In experiments, we illustrate that our theoretical findings hold on real-world datasets, and give insights into trade-offs between single-sample and sample-splitting variants of PPI++.

In this paper, we analyze the classical $K$-means alternating-minimization algorithm, also known as Lloyd's algorithm (Lloyd, 1956), for a mixture of Gaussians in a data-distributed setting that incorporates local iteration steps. Assuming unlabeled data distributed across multiple machines, we propose an algorithm, LocalKMeans, that performs Lloyd's algorithm in parallel in the machines by running its iterations on local data, synchronizing only every $L$ of such local steps. We characterize the cost of these local iterations against the non-distributed setting, and show that the price paid for the local steps is a higher required signal-to-noise ratio. While local iterations were theoretically studied in the past for gradient-based learning methods, the analysis of unsupervised learning methods is more involved owing to the presence of latent variables, e.g. cluster identities, than that of an iterative gradient-based algorithm. To obtain our results, we adapt a virtual iterate method to work with a non-convex, non-smooth objective function, in conjunction with a tight statistical analysis of Lloyd steps.