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We present an optimal uncertainty quantification (OUQ) framework for systems whose uncertain inputs are characterized by truncated moment constraints defined over subdomains. Based on this partial information, rigorous optimal upper and…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
Originating in the artificial intelligence literature, optimistic planning (OP) is an algorithm that generates near-optimal control inputs for generic nonlinear discrete-time systems whose input set is finite. This technique is therefore…
Confidence bounds are an essential tool for rigorously quantifying the uncertainty of predictions. They are a core component in many sequential learning and decision-making algorithms, with tighter confidence bounds giving rise to…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
Probabilistic programming languages aim to describe and automate Bayesian modeling and inference. Modern languages support programmable inference, which allows users to customize inference algorithms by incorporating guide programs to…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…
Off-policy evaluation (OPE) is a fundamental task in reinforcement learning (RL). In the classic setting of linear OPE, finite-sample guarantees often take the form $$ \textrm{Evaluation error} \le \textrm{poly}(C^\pi, d,…
In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…
Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI…
Providing finite-time probabilistic safety and reach-avoid guarantees is crucial for safety-critical stochastic systems. Existing state-of-the-art barrier methods often rely on a restrictive boundedness assumption for auxiliary functions,…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with…
While statistics focusses on hypothesis testing and on estimating (properties of) the true sampling distribution, in machine learning the performance of learning algorithms on future data is the primary issue. In this paper we bridge the…
A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…
Probabilistic programming (PP) is a programming paradigm that allows for writing statistical models like ordinary programs, performing simulations by running those programs, and analyzing and refining their statistical behavior using…
Probabilistic programs often trade accuracy for efficiency, and thus may, with a small probability, return an incorrect result. It is important to obtain precise bounds for the probability of these errors, but existing verification…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…