Related papers: Backward Error Analysis for Perturbation Methods

When performing supervised learning with the model selected using validation error from sample splitting and cross validation, the minimum value of the validation error can be biased downward. We propose two simple methods that use the…

Deep Neural Networks have been widely used in many fields. However, studies have shown that DNNs are easily attacked by adversarial examples, which have tiny perturbations and greatly mislead the correct judgment of DNNs. Furthermore, even…

Advances in the effectiveness of machine learning models have come at the cost of enormous complexity resulting in a poor understanding of how they function. Local surrogate methods have been used to approximate the workings of these…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

To reinforce the quality of code delivery, especially to improve future coding quality, one global Information and Communication Technology (ICT) enterprise has institutionalized a retrospective style inspection (namely retro-inspection),…

In this research we propose a new method for training predictive machine learning models for prescriptive applications. This approach, which we refer to as coupled validation, is based on tweaking the validation step in the standard…

Program errors can occur in any type of programming, and can manifest in a variety of ways, such as unexpected output, crashes, or performance issues. And program error diagnosis can often be too abstract or technical for developers to…

Background: Measurement errors in terms of quantification or classification frequently occur in epidemiologic data and can strongly impact inference. Measurement errors may occur when ascertaining, recording or extracting data. Although the…

We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…

Counterfactual explanations are emerging as an attractive option for providing recourse to individuals adversely impacted by algorithmic decisions. As they are deployed in critical applications (e.g. law enforcement, financial lending), it…

Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…

The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…

Cross-validation is the standard approach for tuning parameter selection in many non-parametric regression problems. However its use is less common in change-point regression, perhaps as its prediction error-based criterion may appear to…

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…

Perturbative approaches have often been used to include the effects of ground-state correlations in extended theories of the random-phase approximation. Validity of such approaches is investigated for a solvable model where comparison with…

Backtracking (i.e., reverse execution) helps the user of a debugger to naturally think backwards along the execution path of a program, and thinking backwards makes it easy to locate the origin of a bug. So far backtracking has been…

Our aim in the current article is to extend the developments in Kruger, Ngai & Th\'era, SIAM J. Optim. 20(6), 3280-3296 (2010) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error…

We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…

In the last few years, many explanation methods based on the perturbations of input data have been introduced to improve our understanding of decisions made by black-box models. The goal of this work is to introduce a novel perturbation…