Related papers: Generalization error of minimum weighted norm and …
Motivated by surprisingly good generalization properties of learned deep neural networks in overparameterized scenarios and by the related double descent phenomenon, this paper analyzes the relation between smoothness and low generalization…
This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning where data from diverse distributions are available. Min-norm interpolators emerge naturally as implicit regularized limits of…
We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a…
One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in…
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still…
We analyze the convergence of generalized kernel-based interpolation methods. This is done under minimalistic assumptions on both the kernel and the target function. On these grounds, we further prove convergence of popular greedy data…
Generalization beyond a training dataset is a main goal of machine learning, but theoretical understanding of generalization remains an open problem for many models. The need for a new theory is exacerbated by recent observations in deep…
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…
Prior information can be incorporated in matrix completion to improve estimation accuracy and extrapolate the missing entries. Reproducing kernel Hilbert spaces provide tools to leverage the said prior information, and derive more reliable…
We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape for the various scalings of $d = n^{\alpha}$, $\alpha\in(0,1)$, for the input…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
This paper provides elementary analyses of the regret and generalization of minimum-norm interpolating classifiers (MNIC). The MNIC is the function of smallest Reproducing Kernel Hilbert Space norm that perfectly interpolates a label…
Modern neural networks are often operated in a strongly overparametrized regime: they comprise so many parameters that they can interpolate the training set, even if actual labels are replaced by purely random ones. Despite this, they…
We investigate how shallow ReLU networks interpolate between known regions. Our analysis shows that empirical risk minimizers converge to a minimum norm interpolant as the number of data points and parameters tends to infinity when a weight…
In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the…
We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to…
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
This article develops a general theory for minimum norm interpolating estimators and regularized empirical risk minimizers (RERM) in linear models in the presence of additive, potentially adversarial, errors. In particular, no conditions on…