Related papers: Bagging cross-validated bandwidths with applicatio…

We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To…

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…

Randomized smoothing (RS) has successfully been used to improve the robustness of predictions for deep neural networks (DNNs) by adding random noise to create multiple variations of an input, followed by deciding the consensus. To…

Bayesian neural networks (BNNs) provide a formalism to quantify and calibrate uncertainty in deep learning. Current inference approaches for BNNs often resort to few-sample estimation for scalability, which can harm predictive performance,…

There is an intense and partly recent literature focussing on the problem of selecting the bandwidth parameter for kernel density estimators. Available methods are largely `very nonparametric', in the sense of not requiring any knowledge…

The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets---which are increasingly prevalent---the computation of bootstrap-based quantities can be prohibitively…

In this paper, we propose a general framework for the asymptotic analysis of node-based verification-based algorithms. In our analysis we tend the signal length $n$ to infinity. We also let the number of non-zero elements of the signal $k$…

In classification problems, the datasets are usually imbalanced, noisy or complex. Most sampling algorithms only make some improvements to the linear sampling mechanism of the synthetic minority oversampling technique (SMOTE). Nevertheless,…

Choosing models from a hypothesis space is a frequent task in approximation theory and inverse problems. Cross-validation is a classical tool in the learner's repertoire to compare the goodness of fit for different reconstruction models.…

Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically…

We present a technique of proving lower bounds for noisy computations. This is achieved by a theorem connecting computations on a kind of randomized decision trees and sampling based algorithms. This approach is surprisingly powerful, and…

It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…

The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets, the computation of bootstrap-based quantities can be prohibitively demanding. As an alternative, we…

Certifying whether an arbitrary quantum system is entangled or not, is, in general, an NP-hard problem. Though various necessary and sufficient conditions have already been explored in this regard for lower dimensional systems, it is hard…

We define a general V-fold cross-validation type method based on robust tests, which is an extension of the hold-out defined by Birg{\'e} [7, Section 9]. We give some theoretical results showing that, under some weak assumptions on the…

Gaussian boson sampling (GBS), a computational problem conjectured to be hard to simulate on a classical machine, has been at the forefront of recent years' experimental and theoretical efforts to demonstrate quantum advantage. The…

Allthough nonparametric kernel density estimation with bias reduce is nowadays a standard technique in explorative data-analysis, there is still a big dispute on how to assess the quality of the estimate and which choice of bandwidth is…

We consider the problem of detecting an elevated mean on an interval with unknown location and length in the univariate Gaussian sequence model. Recent results have shown that using scale-dependent critical values for the scan statistic…