Related papers: Resolvent estimates with mild trapping
Modern neural networks are undeniably successful. Numerous works study how the curvature of loss landscapes can affect the quality of solutions. In this work we study the loss landscape by considering the Hessian matrix during network…
Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance we note that…
This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations.…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
The stabilizing effects of local enrichment are revisited. Diffusively coupled host-parasitoid and predator-prey metapopulations are shown to admit a stable fixed point, limit cycle or stable torus with a rich bifurcation structure. A…
In this paper, we investigate the impact of test-time adversarial attacks on linear regression models and determine the optimal level of robustness that any model can reach while maintaining a given level of standard predictive performance…
In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as…
Galaxy modelling is greatly simplified by assuming the existence of a global system of angle-action coordinates. Unfortunately, global angle-action coordinates do not exist because some orbits become trapped by resonances, especially where…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on $\mathbb{R}^d$ using the variational approach. This includes well-posedness of (possibly degenerate) linear rough PDE's in…
In this paper, we prove strong consistency of an estimator by the truncated singular value decomposition for a multivariate errors-in-variables linear regression model with collinearity. This result is an extension of Gleser's proof of the…
Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
The principle of optimism in the face of uncertainty is prevalent throughout sequential decision making problems such as multi-armed bandits and reinforcement learning (RL). To be successful, an optimistic RL algorithm must over-estimate…
Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…
We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft…
Regression discontinuity (RD) designs are a popular approach to estimating a treatment effect of cutoff-based interventions. Two current estimation approaches dominate the literature. One fits separate regressions on either side of the…
In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing…