Related papers: Data-Driven Reachable Set Computation using Adapti…

We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

Inferential models (IMs) offer prior-free, Bayesian-like posterior degrees of belief designed for statistical inference, which feature a frequentist-like calibration property that ensures reliability of said inferences. The catch is that…

We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with…

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…

Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…

We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update…

In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…

We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…

Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…

This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…

This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global…

In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…

We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…

In this paper, we present an analytical approach for the synthesis of ellipsoidal probabilistic reachable sets of saturated systems subject to unbounded additive noise. Using convex optimization methods, we compute a contraction factor of…

In this paper, we propose a novel approach for computing robust backward reachable sets from noisy data for unknown constrained linear systems subject to bounded disturbances. In particular, we develop an algorithm for obtaining zonotopic…