We address the problem of non-parametric multiple model comparison: given $l$ candidate models, decide whether each candidate is as good as the best one(s) or worse than it. We propose two statistical tests, each controlling a different notion of decision errors. The first test, building on the post selection inference framework, provably controls the number of best models that are wrongly declared worse (false positive rate). The second test is based on multiple correction, and controls the proportion of the models declared worse but are in fact as good as the best (false discovery rate). We prove that under appropriate conditions the first test can yield a higher true positive rate than the second. Experimental results on toy and real (CelebA, Chicago Crime data) problems show that the two tests have high true positive rates with well-controlled error rates. By contrast, the naive approach of choosing the model with the lowest score without correction leads to more false positives.

Given samples lying on any of a number of subspaces, subspace clustering is the task of grouping the samples based on the their corresponding subspaces. Many subspace clustering methods operate by assigning a measure of affinity to each pair of points and feeding these affinities into a graph clustering algorithm. This paper proposes a new paradigm for subspace clustering that computes affinities based on the corresponding conic geometry. The proposed conic subspace clustering (CSC) approach considers the convex hull of a collection of normalized data points and the corresponding tangent cones. The union of subspaces underlying the data imposes a strong association between the tangent cone at a sample x and the original subspace containing x . In addition to describing this novel geometric perspective, this paper provides a practical algorithm for subspace clustering that leverages this perspective, where a tangent cone membership test is used to estimate the affinities. This algorithm is accompanied with deterministic and stochastic guarantees on the properties of the learned affinity matrix, on the true and false positive rates and spread, which directly translate into the overall clustering accuracy.

We enourage readers to consult the more complete manuscript on the arXiv.

Machine learning technologies have permeated everyday life and it is common nowadays that an automated system makes decisions for/about us, such as who is going to get bank credit.

As AI systems become more capable, deceptive behaviors can undermine evaluation and mislead users at deployment. Recent work has shown that lie detectors can accurately classify deceptive behavior, but they are not typically used in the training pipeline due to concerns around contamination and objective hacking. We examine these concerns by incorporating a lie detector into the labelling step of LLM post-training and evaluating whether the learned policy is genuinely more honest, or instead learns to fool the lie detector while remaining deceptive. Using DolusChat, a novel 65k-example dataset with paired truthful/deceptive responses, we identify three key factors that determine the honesty of learned policies: amount of exploration during preference learning, lie detector accuracy, and KL regularization strength. We find that preference learning with lie detectors and GRPO can lead to policies which evade lie detectors, with deception rates of over 85\%. However, if the lie detector true positive rate (TPR) or KL regularization is sufficiently high, GRPO learns honest policies. In contrast, off-policy algorithms (DPO) consistently lead to deception rates under 25\% for realistic TPRs. Our results illustrate a more complex picture than previously assumed: depending on the context, lie-detector-enhanced training can be a powerful tool for scalable oversight, or a counterproductive method encouraging undetectable misalignment.