Let k (,) be the ν = 2 .5 Matérn kernel.

The "folk wisdom" in the literature is that the focus on local optimization sidesteps the curse of dimensionality;

A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas Bayesian inference requires the assumption of a specific model. A fundamental question is then whether GNN has a high accuracy in addition to this flexibility.

Our contributions are twofold: First, we establish a statistically rigorous definition of competence that generalizesthecommon notion ofclassifier confidence; second, wepresent theALICE (Accurate Layerwise Interpretable Competence Estimation) Score, a pointwise competence estimator foranyclassifier.

How to develop slim and accurate deep neural networks has become crucial for real-world applications, especially for those employed in embedded systems.

In this paper, we develop and analyze a new model-based approach that computes a safe policy, given an inaccurate model of the system's

A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas Bayesian inference requires the assumption of a specific model. A fundamental question is then whether GNN has a high accuracy in addition to this flexibility. Moreover, whether the achieved performance is predominately a result of the backpropagation or the architecture itself is a matter of considerable interest. To gain a better insight into these questions, a mean-field theory of a minimal GNN architecture is developed for the graph partitioning problem. This demonstrates a good agreement with numerical experiments.

We consider training and testing on mixture distributions with different training and test proportions. We show that in many settings, and in some sense generically, distribution shift can be beneficial, and test performance can improve due to mismatched training proportions, even if the components are unrelated and with no transfer between components. In a variety of scenarios, we identify the optimal training proportions and the extent to which such distribution shift can be beneficial. We show how the same analysis applies also to a compositional setting with differing distribution of component "skills'' at training and test.