Related papers: Certified Roundoff Error Bounds using Bernstein Ex…
Finding optimal policies for Partially Observable Markov Decision Processes (POMDPs) is challenging due to their uncountable state spaces when transformed into fully observable Markov Decision Processes (MDPs) using belief states.…
This paper presents preliminary work on computing upper bounds on the estimation error covariance in the framework of the extended Kalman filter. The approach taken is using quadratic constraints to bound the dynamic nonlinearities and use…
Probabilistic model checking computes probabilities and expected values related to designated behaviours of interest in Markov models. As a formal verification approach, it is applied to critical systems; thus we trust that probabilistic…
In this paper, we present BERN-NN as an efficient tool to perform bound propagation of Neural Networks (NNs). Bound propagation is a critical step in wide range of NN model checkers and reachability analysis tools. Given a bounded input…
In this paper, we examine linear programming (LP) relaxations based on Bernstein polynomials for polynomial optimization problems (POPs). We present a progression of increasingly more precise LP relaxations based on expressing the given…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
Precision tuning or customized precision number representations is emerging, in these recent years, as one of the most promising techniques that has a positive impact on the footprint of programs concerning energy consumption, bandwidth…
We present two improved randomized neural network methods, namely RNN-Scaling and RNN-Boundary-Processing (RNN-BP) methods, for solving elliptic equations such as the Poisson equation and the biharmonic equation. The RNN-Scaling method…
We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating…
This work focuses on assessing the information-theoretic limits of scene parameter estimation in plenoptic imaging systems. A general framework to compute lower bounds on the parameter estimation error from noisy plenoptic observations is…
We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the precision. We present a systematic recurrence for a martingale…
In this paper, we present a study of an a posteriori estimator for the discretization error of a non-standard finite difference scheme applied to boundary value problems defined on an infinite interval. In particular, we show how…
It is well known that the computation of accurate trajectories of the Lorenz system is a difficult problem. Computed solutions are very sensitive to the discretization error determined by the time step size and polynomial order of the…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
Stochastic processes are often represented through orthonormal series expansions, a framework originating in the classical works of Lo\`eve and Karhunen and widely used for simulation and numerical approximation. While truncation error in…
In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results…
Many of today's probabilistic programming languages (PPLs) have brittle inference performance: the performance of the underlying inference algorithm is very sensitive to the precise way in which the probabilistic program is written. A…
In finite element methods (FEMs), the accuracy of the solution cannot increase indefinitely because the round-off error increases when the number of degrees of freedom (DoFs) is large enough. This means that the accuracy that can be reached…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…