Related papers: Lipschitz Interpolation: Non-parametric Convergenc…
One classical measure of the quality of an interpolating function is its Lipschitz constant. In this paper we consider interpolants with additional smoothness requirements, in particular that their derivatives be Lipschitz. We show that…
This manuscript bridges nonparametric smoothness-based and shape-restricted estimation, which may appear as two disjoint paradigms in the field. The proposed approach is motivated by a conceptually simple observation: every Lipschitz…
Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a…
The Lipschitz bound, a technique from robust statistics, can limit the maximum changes in the output concerning the input, taking into account associated irrelevant biased factors. It is an efficient and provable method for examining the…
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
Stochastic gradient descent is one of the most common iterative algorithms used in machine learning and its convergence analysis is a rich area of research. Understanding its convergence properties can help inform what modifications of it…
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…
Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and…
The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…
This work establishes a Lipschitz stability result for identifying unknown polygonal inclusions along with their unknown constant conductivity values, given boundary measurements encoded in the Dirichlet-to-Neumann map.
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…
The present work provides a systematic approach for the design of sampled-data observers to a wide class of 1-D, parabolic PDEs with non-local outputs. The studied class of parabolic PDEs allows the presence of globally Lipschitz nonlinear…
In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…
The superiority of symplectic methods for stochastic Hamiltonian systems has been widely recognized, yet the probabilistic mechanism behind this superiority remains incompletely understood. This paper studies the superiority of symplectic…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…
Stochastic approximation is a powerful class of algorithms with celebrated success. However, a large body of previous analysis focuses on stochastic approximations driven by contractive operators, which is not applicable in some important…
Techniques known as Nonlinear Set Membership prediction, Lipschitz Interpolation or Kinky Inference are approaches to machine learning that utilise presupposed Lipschitz properties to compute inferences over unobserved function values.…
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
In this paper we present a stability proof of model predictive control without stabilizing terminal constraints of cost which are subject to unknown but measurable disturbances. To this end, a relaxed Lyapunov argument on the nominal system…