Related papers: Convergence bounds for local least squares approxi…
We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly…
We consider the problem of estimating curvature where the data can be viewed as a noisy sample from an underlying manifold. For manifolds of dimension greater than one there are multiple definitions of local curvature, each suggesting a…
Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required…
We study neural network compressibility by using singular learning theory to extend the minimum description length (MDL) principle to singular models like neural networks. Through extensive experiments on the Pythia suite with quantization,…
Weight sharing, equivariance, and local filters, as in convolutional neural networks, are believed to contribute to the sample efficiency of neural networks. However, it is not clear how each one of these design choices contributes to the…
We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade-off between closeness to the true function and complexity penalization of the estimator,…
A local projection model is defined by a set of linear regressions that account for the associations between exogenous variables and an endogenous variable observed at different time points. While it is standard practice to separately…
We provide several new results on the sample complexity of vector-valued linear predictors (parameterized by a matrix), and more generally neural networks. Focusing on size-independent bounds, where only the Frobenius norm distance of the…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
We study the problem of learning nonparametric distributions in a finite mixture, and establish tight bounds on the sample complexity for learning the component distributions in such models. Namely, we are given i.i.d. samples from a pdf…
Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second.…
We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…
The \(L_1/L_2\) norm ratio has gained significant attention as a measure of sparsity due to three merits: sharper approximation to the \(L_0\) norm compared to the \(L_1\) norm, being parameter-free and scale-invariant, and exceptional…
We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is…