The paper shows that the optimal rule for such metrics has the form of sign(P(y|x)-\delta^*), where \delta^* is a threshold that is metric dependent. This unified framework recovers many results for metrics studied in the literature. Authors devise 2 simple algorithms for estimating p(y|x) and the threshold delta^*. Bayes and statistical consistency of the proposed algorithms is then analyzed.

There are many natural models for noise.

Machine learning models developed from real-world data can inherit pre-existing bias in the dataset. When these models are used to inform decisions involving humans, it may exhibit similar discrimination against sensitive attributes (e.g., gender and race) [

Neural Networks can perform poorly when the training label distribution is heavily imbalanced, as well as when the testing data differs from the training distribution. In order to deal with shift in the testing label distribution, which imbalance causes, we motivate the problem from the perspective of an optimal Bayes classifier and derive a post-training prior rebalancing technique that can be solved through a KL-divergence based optimization. This method allows a flexible post-training hyper-parameter to be efficiently tuned on a validation set and effectively modify the classifier margin to deal with this imbalance. We further combine this method with existing likelihood shift methods, re-interpreting them from the same Bayesian perspective, and demonstrating that our method can deal with both problems in a unified way.

In criminal justice, the "risk-needs-responsivity" model emphasizes matching the level of

Symmetry-aware methods for machine learning, such as data augmentation and equivariant architectures, encourage correct model behavior on all transformations (e.g. rotations or permutations) of the original dataset. These methods can improve generalization and sample efficiency, under the assumption that the transformed datapoints are highly probable, or "important", under the test distribution. In this work, we develop a method for critically evaluating this assumption. In particular, we propose a metric to quantify the amount of anisotropy, or symmetry-breaking, in a dataset, via a two-sample neural classifier test that distinguishes between the original dataset and its randomly augmented equivalent. We validate our metric on synthetic datasets, and then use it to uncover surprisingly high degrees of alignment in several benchmark point cloud datasets. We show theoretically that distributional symmetry-breaking can actually prevent invariant methods from performing optimally even when the underlying labels are truly invariant, as we show for invariant ridge regression in the infinite feature limit. Empirically, we find that the implication for symmetry-aware methods is dataset-dependent: equivariant methods still impart benefits on some anisotropic datasets, but not others. Overall, these findings suggest that understanding equivariance -- both when it works, and why -- may require rethinking symmetry biases in the data.

We study the problem of determining whether a piece of text has been authored by a human or by a large language model (LLM). Existing state of the art logits-based detectors make use of statistics derived from the log-probability of the observed text evaluated using the distribution function of a given source LLM. However, relying solely on log probabilities can be sub-optimal. In response, we introduce AdaDetectGPT -- a novel classifier that adaptively learns a witness function from training data to enhance the performance of logits-based detectors. We provide statistical guarantees on its true positive rate, false positive rate, true negative rate and false negative rate. Extensive numerical studies show AdaDetectGPT nearly uniformly improves the state-of-the-art method in various combination of datasets and LLMs, and the improvement can reach up to 58%. A python implementation of our method is available at https://github.com/Mamba413/AdaDetectGPT.

Linking textual values in tabular data to their corresponding entities in a Knowledge Base is a core task across a variety of data integration and enrichment applications. Although Large Language Models (LLMs) have shown State-of-The-Art performance in Entity Linking (EL) tasks, their deployment in real-world scenarios requires not only accurate predictions but also reliable uncertainty estimates, which require resource-demanding multi-shot inference, posing serious limits to their actual applicability. As a more efficient alternative, we investigate a self-supervised approach for estimating uncertainty from single-shot LLM outputs using token-level features, reducing the need for multiple generations. Evaluation is performed on an EL task on tabular data across multiple LLMs, showing that the resulting uncertainty estimates are highly effective in detecting low-accuracy outputs. This is achieved at a fraction of the computational cost, ultimately supporting a cost-effective integration of uncertainty measures into LLM-based EL workflows. The method offers a practical way to incorporate uncertainty estimation into EL workflows with limited computational overhead.