Daniel Průša

Vojtech Franc, Daniel Prusa, Jakub Paplham

The optimal prediction strategy for out-of-distribution (OOD) setups is a fundamental question in machine learning. In this paper, we address this question and present several contributions. We propose three reject option models for OOD setups: the Cost-based model, the Bounded TPR-FPR model, and the Bounded Precision-Recall model. These models extend the standard reject option models used in non-OOD setups and define the notion of an optimal OOD selective classifier. We establish that all the proposed models, despite their different formulations, share a common class of optimal strategies. Motivated by the optimal strategy, we introduce double-score OOD methods that leverage uncertainty scores from two chosen OOD detectors: one focused on OOD/ID discrimination and the other on misclassification detection. The experimental results consistently demonstrate the superior performance of this simple strategy compared to state-of-the-art methods. Additionally, we propose novel evaluation metrics derived from the definition of the optimal strategy under the proposed OOD rejection models. These new metrics provide a comprehensive and reliable assessment of OOD methods without the deficiencies observed in existing evaluation approaches.

Vojtech Franc, Jakub Paplham, Daniel Prusa

This paper addresses the problem of designing reliable prediction models that abstain from predictions when faced with uncertain or out-of-distribution samples - a recently proposed problem known as Selective Classification in the presence of Out-of-Distribution data (SCOD). We make three key contributions to SCOD. Firstly, we demonstrate that the optimal SCOD strategy involves a Bayes classifier for in-distribution (ID) data and a selector represented as a stochastic linear classifier in a 2D space, using i) the conditional risk of the ID classifier, and ii) the likelihood ratio of ID and out-of-distribution (OOD) data as input. This contrasts with suboptimal strategies from current OOD detection methods and the Softmax Information Retaining Combination (SIRC), specifically developed for SCOD. Secondly, we establish that in a distribution-free setting, the SCOD problem is not Probably Approximately Correct learnable when relying solely on an ID data sample. Third, we introduce POSCOD, a simple method for learning a plugin estimate of the optimal SCOD strategy from both an ID data sample and an unlabeled mixture of ID and OOD data. Our empirical results confirm the theoretical findings and demonstrate that our proposed method, POSCOD, out performs existing OOD methods in effectively addressing the SCOD problem.

Tomáš Werner, Daniel Průša

(Block-)coordinate minimization is an iterative optimization method which in every iteration finds a global minimum of the objective over a variable or a subset of variables, while keeping the remaining variables constant. While for some problems, coordinate minimization converges to a global minimum (e.g., convex differentiable objective), for general (non-differentiable) convex problems this may not be the case. Despite this drawback, (block-)coordinate minimization can be an acceptable option for large-scale non-differentiable convex problems; an example is methods to solve the linear programming relaxation of the discrete energy minimization problem (MAP inference in graphical models). When block-coordinate minimization is applied to a general convex problem, in every iteration the minimizer over the current coordinate block need not be unique and therefore a single minimizer must be chosen. We propose that this minimizer be chosen from the relative interior of the set of all minimizers over the current block. We show that this rule is not worse, in a certain precise sense, than any other rule.