Related papers: Error Bounds and Metric Subregularity
This paper is devoted to the study of the metric subregularity constraint qualification (MSCQ) for general optimization problems, with the emphasis on the nonconvex setting. We elaborate on notions of directional pseudo- and…
Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations…
This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely…
The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…
We revisit the well-established regularity estimates on harmonic maps on surfaces to question their independence with respect to the dimension of the target manifold. We are mainly interested in harmonic maps into target ellipsoids, that we…
Confronted with the challenge of identifying the most suitable metric to validate the merits of newly proposed models, the decision-making process is anything but straightforward. Given that comparing rankings introduces its own set of…
Assuming that the Standard Model is correct and taking into account the lower bound on M_H from direct searches, we discuss bounds on M_W, M_top, and Sin^2 theta_eff_lept at various confidence levels. This permits to identify theoretically…
The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
Many real-world classification problems are significantly class-imbalanced to detriment of the class of interest. The standard set of proper evaluation metrics is well-known but the usual assumption is that the test dataset imbalance equals…
The authors study Tikhonov regularization of linear ill-posed problems with a general convex penalty defined on a Banach space. It is well known that the error analysis requires smoothness assumptions. Here such assumptions are given in…
In this paper non-asymptotic exact exponential estimates are derived (under minimal conditions) for the tail of deviation of the MLE distribution in the so-called natural terms: natural function, natural distance, metric entropy, Banach…
An adjustable algorithm of exclusion of conditional equations with excessive residuals is proposed. The criteria applied in the algorithm use variable exclusion limits which decrease as the number of equations goes down. The algorithm is…
The problems connected with equivalent norms lie at the heart of Banach space theory. This is a short survey on some recent as well as classical results and open problems in renormings of Banach spaces.
Measurement error in multinomial data is a well-known and well-studied inferential problem that is encountered in many fields, including engineering, biomedical and omics research, ecology, finance, official statistics, and social sciences.…
Asymmetric systematic errors arise when there is a non-linear dependence of a result on a nuisance parameter. Their combination is traditionally done by adding positive and negative deviations separately in quadrature. There is no sound…
Parameter estimates in misspecified models converge to pseudo-true parameter values, which minimize a population objective function. Pseudo-true values often differ from quantities of economic interest, raising questions of how, if at all,…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…