Related papers: Valuations and Metrics on Partially Ordered Sets

In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…

This paper discusses the challenge when evaluating multi-objective optimisation algorithms under noise, and argues that decision maker preferences need to be taken into account. It demonstrates that commonly used performance metrics are…

Despite the growing body of work in interpretable machine learning, it remains unclear how to evaluate different explainability methods without resorting to qualitative assessment and user-studies. While interpretability is an inherently…

We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…

We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…

This article reformulates the theory of computable physical models, previously introduced by the author, as a branch of applied model theory in first-order logic. It provides a semantic approach to the philosophy of science that…

We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…

In markets where algorithmic data processing is increasingly prevalent, recommendation algorithms can substantially affect trade and welfare. We consider a setting in which an algorithm recommends a product based on its value to the buyer…

Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…

Evaluation plays a crucial role in development of Machine translation systems. In order to judge the quality of an existing MT system i.e. if the translated output is of human translation quality or not, various automatic metrics exist. We…

The game-theoretic notion of the semivalue offers a popular framework for credit attribution and data valuation in machine learning. Semivalues have been proposed for a variety of high-stakes decisions involving data, such as determining…

Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several…

We describe all weights which are appropriated for the unitarization of linear representations of primitive partially ordered sets of finite type.

Post-hoc global/local feature attribution methods are progressively being employed to understand the decisions of complex machine learning models. Yet, because of limited amounts of data, it is possible to obtain a diversity of models with…

Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…

Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…

Current practice for evaluating recommender systems typically focuses on point estimates of user-oriented effectiveness metrics or business metrics, sometimes combined with additional metrics for considerations such as diversity and…

The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…

Decisions in organizations are about evaluating alternatives and choosing the one that would best serve organizational goals. To the extent that the evaluation of alternatives could be formulated as a predictive task with appropriate…

In this paper we address a unified mathematical optimization framework to compute a wide range of measures used in most operations research and data science contexts. The goal is to embed such metrics within general optimization models…