Our results are corroborated with experiments.

Neural Information Processing Systems http://nips.cc/

We then follow the proof of Theorem 3 in Farnia and Tse [2016]. Our formulation differs from Nowak-Vila et al. [2020] in the fact that we allow probabilistic prediction to be ground truth. Proposition 4. Let G be a multi-graph. We follow the proof of Friesen [2019] for simple graphs. Proposition 5. Let G be a multi-graph.

Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.

Our results are corroborated with experiments.

In this paper, we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework.

Distributionally robust optimization has become a powerful tool for prediction and decision-making under model uncertainty. By focusing on the local worst-case risk, it enhances robustness by identifying the most unfavorable distribution within a predefined ambiguity set. While extensive research has been conducted in parametric settings, studies on nonparametric frameworks remain limited. This paper studies the generalization properties of Wasserstein distributionally robust nonparametric estimators, with particular attention to the impact of model misspecification, where non-negligible discrepancies between the estimation function space and target function can impair generalization performance. We establish non-asymptotic error bounds for the excess local worst-case risk by analyzing the regularization effects induced by distributional perturbations and employing feedforward neural networks with Lipschitz constraints. These bounds illustrate how uncertainty levels and neural network structures influence generalization performance and are applicable to both Lipschitz and quadratic loss functions. Furthermore, we investigate the Lagrangian relaxation of the local worst-case risk and derive corresponding non-asymptotic error bounds for these estimators. The robustness of the proposed estimator is evaluated through simulation studies and illustrated with an application to the MNIST dataset.

A fundamental task in AI is providing performance guarantees for predictions made in unseen domains. In practice, there can be substantial uncertainty about the distribution of new data, and corresponding variability in the performance of existing predictors. Building on the theory of partial identification and transportability, this paper introduces new results for bounding the value of a functional of the target distribution, such as the generalization error of a classifier, given data from source domains and assumptions about the data generating mechanisms, encoded in causal diagrams. Our contribution is to provide the first general estimation technique for transportability problems, adapting existing parameterization schemes such Neural Causal Models to encode the structural constraints necessary for cross-population inference. We demonstrate the expressiveness and consistency of this procedure and further propose a gradient-based optimization scheme for making scalable inferences in practice. Our results are corroborated with experiments.

Certifying the robustness of model performance under bounded data distribution drifts has recently attracted intensive interest under the umbrella of distributional robustness. However, existing techniques either make strong assumptions on the model class and loss functions that can be certified, such as smoothness expressed via Lipschitz continuity of gradients, or require to solve complex optimization problems. As a result, the wider application of these techniques is currently limited by its scalability and flexibility -- these techniques often do not scale to large-scale datasets with modern deep neural networks or cannot handle loss functions which may be non-smooth such as the 0-1 loss. In this paper, we focus on the problem of certifying distributional robustness for blackbox models and bounded loss functions, and propose a novel certification framework based on the Hellinger distance. Our certification technique scales to ImageNet-scale datasets, complex models, and a diverse set of loss functions. We then focus on one specific application enabled by such scalability and flexibility, i.e., certifying out-of-domain generalization for large neural networks and loss functions such as accuracy and AUC. We experimentally validate our certification method on a number of datasets, ranging from ImageNet, where we provide the first non-vacuous certified out-of-domain generalization, to smaller classification tasks where we are able to compare with the state-of-the-art and show that our method performs considerably better.