Modern deep artificial neural networks have achieved great success in the domain of computer vision and beyond. However, their application to many real-world tasks is undermined by certain limitations, such as overconfident uncertainty estimates on out-of-distribution data or performance deterioration under data distribution shifts. Several types of deep learning models used for density estimation through probabilistic generative modeling have been shown to fail to detect out-of-distribution samples by assigning higher likelihoods to anomalous data.

Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm. Replacing the Kullback-Leibler divergence with a general $f$-divergence leads to a natural generalization. The case of divergences defined by superlinear functions was recently studied by Di Marino and Gerolin. Using convex analysis, we extend the theory developed so far to include all $f$-divergences defined by functions of Legendre type, and prove that under some mild conditions, strong duality holds, optimums in both the primal and dual problems are attained, the generalization of the $c$-transform is well-defined, and we give sufficient conditions for the generalized Sinkhorn algorithm to converge to an optimal solution.

For any standard Borel space , let denote the space of Borel probability measures on . In relation to a difficult problem of Aldous in exchangeability theory, and in connection with arithmetic combinatorics, Austin raised the question of describing the structure of affine-exchangeable probability measures on product spaces indexed by the vector space F, i.e., the measures in F that are invariant under the coordinate permutations on F induced by all affine automorphisms of F.

The National Laboratory for Artificial Intelligence (MILAB) aims to strengthen Hungary’s role in the field of AI. The European Union is making significant efforts to catch up with the development capabilities of the USA and China. The domestic research of artificial intelligence in Hungary is currently characterized by fragmentation, competition, and isolation. There is no unified AI umbrella over the large-scale, application-specific programs. Several universities and research institutions have good relations with business applicators, but societal innovation is also necessary for the acceptance of technological innovation.