相关论文: Why Do We Need Foundations for Modelling Uncertain…
We develop a fast algorithm to construct the robustness degradation function, which describes quantitatively the relationship between the proportion of systems guaranteeing the robustness requirement and the radius of the uncertainty set.…
We discuss when and why custom multi-factor risk models are warranted and give source code for computing some risk factors. Pension/mutual funds do not require customization but standardization. However, using standardized risk models in…
We formalize the idea of probability distributions that lead to reliable predictions about some, but not all aspects of a domain. The resulting notion of `safety' provides a fresh perspective on foundational issues in statistics, providing…
A large family of deployable filamentary structures can be built by connecting two elastic rods along their length. The resulting structure has interesting shapes that can be stabilized by tuning the material properties of each rod. To…
This paper advocates the usefulness of new theories of uncertainty for the purpose of modeling some facets of uncertain knowledge, especially vagueness, in AI. It can be viewed as a partial reply to Cheeseman's (among others) defense of…
As natural language becomes the default interface for human-AI interaction, there is a need for LMs to appropriately communicate uncertainties in downstream applications. In this work, we investigate how LMs incorporate confidence in…
Homeowners around the world elevate houses to manage flood risks. Deciding how high to elevate a house poses a nontrivial decision problem. The U.S. Federal Emergency Management Agency (FEMA) recommends elevating existing houses to the Base…
Recent advances in artificial intelligence have witnessed the emergence of large-scale deep learning models capable of interpreting and generating both textual and imaging data. Such models, typically referred to as foundation models, are…
The release of ChatGPT, Gemini, and other large language model has drawn huge interests on foundations models. There is a broad consensus that foundations models will be the fundamental building blocks for future AI systems. However, there…
Despite several (accepted) standards, core notions typically employed in information technology or system engineering architectures lack the precise and exact foundations encountered in logic, algebra, and other branches of mathematics. In…
Obtaining deep networks that are robust against adversarial examples and generalize well is an open problem. A recent hypothesis even states that both robust and accurate models are impossible, i.e., adversarial robustness and…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
This paper studies the design of mechanisms that are robust to misspecification. We introduce a novel notion of robustness that connects a variety of disparate approaches and study its implications in a wide class of mechanism design…
A lot of mathematical knowledge has been formalized and stored in repositories by now: different mathematical theorems and theories have been taken into consideration and included in mathematical repositories. Applications more distant from…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
Demands on the disaster response capacity of the European Union are likely to increase, as the impacts of disasters continue to grow both in size and frequency. This has resulted in intensive research on issues concerning spatially-explicit…
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…
Multiple hypotheses/models have been put forward regarding the cooling history of the Earth. The search for life beyond Earth has brought these models into a new light as they connect to one of the two energy sources life can tap. The…
Effectively measuring and modeling the reliability of a trained model is essential to the real-world deployment of monocular depth estimation (MDE) models. However, the intrinsic ill-posedness and ordinal-sensitive nature of MDE pose major…