Related papers: Optimal monotone conditional error functions

In model checking for regressions, nonparametric estimation-based tests usually have tractable limiting null distributions and are sensitive to oscillating alternative models, but suffer from the curse of dimensionality. In contrast,…

Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…

We introduce a notion of inexact model of a convex objective function, which allows for errors both in the function and in its gradient. For this situation, a gradient method with an adaptive adjustment of some parameters of the model is…

The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a…

This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not…

We propose a batchwise monotone algorithm for dictionary learning. Unlike the state-of-the-art dictionary learning algorithms which impose sparsity constraints on a sample-by-sample basis, we instead treat the samples as a batch, and impose…

We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test…

This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these…

Second-order optimization methods exhibit fast convergence to critical points, however, in nonconvex optimization, these methods often require restrictive step-sizes to ensure a monotonically decreasing objective function. In the presence…

The optimization problems associated with training generative adversarial neural networks can be largely reduced to certain {\em non-monotone} variational inequality problems (VIPs), whereas existing convergence results are mostly based on…

This paper considers fault estimation in nonlinear fractional order systems in observer form. For this aim, a step by step second order sliding mode observer is used. By means of a fractional inequality, the stability of the observer…

We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is…

Two-stage robust optimization is a fundamental paradigm for modeling and solving optimization problems with uncertain parameters. A now classical method within this paradigm is finite adaptability, introduced by Bertsimas and Caramanis…

Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased…

The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as…

We propose a new criterion to analyse the order of phase transitions within a finite size scaling analysis. It refers to response functions like order parameter susceptibilities and the specific heat and states different monotony behaviour…

The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and…

In this paper we consider a composite optimization problem that minimizes the sum of a weakly smooth function and a convex function with either a bounded domain or a uniformly convex structure. In particular, we first present a…

We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…

In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic…