相关论文: Decision making via generalized Bajraktarevi\'c me…

We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…

Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…

Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian…

We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…

In the field of Judgment Aggrgation, a domain, that is a subset of a Cartesian power of $\{0,1\}$, is considered to reflect abstract rationality restrictions on vectors of two-valued judgments on a number of issues. We are interested in the…

Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit…

Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…

We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for level $\ell$ highest weight modules over an affine Kac-Moody algebra with exactly one highest weight being taken for each equivalence class, in a way…

We take a geometrical viewpoint and present a unifying view on supervised deep learning with the Bregman divergence loss function - this entails frequent classification and prediction tasks. Motivated by simulations we suggest that there is…

This article characterizes conjugates and subdifferentials of convex integral functionals over linear spaces of cadlag stochastic processes. The approach is based on new measurability results on the Skorokhod space and new interchange rules…

We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…

Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…

The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign…

This work introduces a novel cause-effect relation in Markov decision processes using the probability-raising principle. Initially, sets of states as causes and effects are considered, which is subsequently extended to regular path…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

In this work, we propose the concept of Construction Defining Functionality (CDF), which characterizes functions by the structural spaces they generate through iteration,recursion, and logical application. By viewing functions as generators…

In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs…

The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…

Category, or property generalization is a central function in the human cognition. It plays a crucial role in a variety of domains, such as learning, everyday reasoning, specialized reasoning, and decision making. Judging the content of a…