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The problem of simple $M-$ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule…
This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…
As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world…
This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty…
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…
We elicit incomplete preferences over monetary gambles with subjective uncertainty. Subjects rank gambles, and these rankings are used to estimate preferences; payments are based on estimated preferences. About 40\% of subjects express…
A formalized and quantifiable responsibility score is a crucial component in many aspects of the development and application of multi-agent systems and autonomous agents. We can employ it to inform decision making processes based on ethical…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected…
Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims…
Traditional approaches to ensure group fairness in algorithmic decision making aim to equalize ``total'' error rates for different subgroups in the population. In contrast, we argue that the fairness approaches should instead focus only on…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide…
Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
Various measures can be used to estimate bias or unfairness in a predictor. Previous work has already established that some of these measures are incompatible with each other. Here we show that, when groups differ in prevalence of the…
Conformal prediction is a statistically rigorous method for quantifying uncertainty in models by having them output sets of predictions, with larger sets indicating more uncertainty. However, prediction sets are not inherently actionable;…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…