Related papers: Response surface methodology: Asymptotic normality…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…
We discuss several aspects of the loss landscape of regularized neural networks: the structure of stationary points, connectivity of optimal solutions, path with nonincreasing loss to arbitrary global optimum, and the nonuniqueness of…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
Generalizing the well-known relations on characteristic functions on a plane to the case of a one-dimensional regular surface (curve) with compact support, we establish implicit equations for these functions. Introducing an approximation,…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optical methods. By…
Asymptotic post-buckling theory is applied to sizing and topology optimization of trusses and frames, exploring its potential and current computational difficulties. We show that a designs' post-buckling response can be controlled by…
Stochastic Gradient Descent (SGD) is one of the most popular algorithms in statistical and machine learning due to its computational and memory efficiency. Various averaging schemes have been proposed to accelerate the convergence of SGD in…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous…
The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also…
A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in…
In this paper, we investigate the asymptotic symmetry and monotonicity of positive solutions to a reaction-diffusion equation in the unit ball, utilizing techniques from elliptic geometry. Firstly, we discuss the properties of solutions in…
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit of this…