Related papers: Convergence Analysis of Deterministic Kernel-Based…
Quantum kernel methods promise enhanced expressivity for learning structured data, but their usefulness has been limited by kernel concentration and barren plateaus. Both effects are mathematically equivalent and suppress trainability. We…
Existing guarantees for misspecified kernelized bandit optimization pay for misspecification through kernel complexity: in generic offline bounds, the misspecification level $\varepsilon$ is multiplied by $\sqrt{d_\mathrm{eff}}$, where…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
We establish well-posedness and maximal regularity estimates for linear parabolic SPDE in divergence form involving random coefficients that are merely bounded and measurable in the time, space, and probability variables. To reach this…
In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level $\lambda$. More precisely, it is assumed that the density (i) is smooth in a…
We consider minimization of indefinite quadratics with either trust-region (norm) constraints or cubic regularization. Despite the nonconvexity of these problems we prove that, under mild assumptions, gradient descent converges to their…
Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…
This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that…
Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…
In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of anyone of the four Chebyshev weights, considered by Gautschi and Li in \cite{gauli}. As it is well known, in the case of analytic integrands,…
The persistence of excitation (PE) condition is sufficient to ensure parameter convergence in adaptive estimation problems. Recent results on adaptive estimation in reproducing kernel Hilbert spaces (RKHS) introduce PE conditions for RKHS.…
The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say,…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
Structural uncertainties and unresolved features in fault zones hinder the assessment of leakage risks in subsurface CO2 storage. Understanding multi-scale uncertainties in fracture network conductivity is crucial for mitigating risks and…
We investigate the convergence theory of several known as well as new heuristic parameter choice rules for convex Tikhonov regularisation. The success of such methods is dependent on whether certain restrictions on the noise are satisfied.…
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global…
We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of…
Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates…