Related papers: Warped Wavelet and Vertical Thresholding

This paper deals with near-best approximation of a given bivariate function using elements of quarkonial tensor frames. For that purpose we apply anisotropic tensor products of the univariate B-spline quarklets introduced around 2017 by…

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

Given a random sample from some unknown density $f_0: \mathbb R \to [0, \infty)$ we devise Haar wavelet estimators for $f_0$ with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen, and Spokoiny…

We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \langle X,w^* \rangle + \epsilon$ (with $X \in \mathbb{R}^d$ and $\epsilon$ independent), in…

In a typical two-phase design, a random sample is drawn from the target population in phase 1, during which only a subset of variables is collected. In phase 2, a subsample of the phase-1 cohort is selected, and additional variables are…

In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution…

Predictive models make mistakes. Hence, there is a need to quantify the uncertainty associated with their predictions. Conformal inference has emerged as a powerful tool to create statistically valid prediction regions around point…

We develop unbalanced Haar (UH) wavelet tree ensembles for regression on triangulable manifolds. Given data sampled on a triangulated manifold, we construct UH wavelet trees whose atoms are supported on geodesic triangles and form an…

Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an…

Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…

We study the convergence of the predictive surface of regression trees and forests. To support our analysis we introduce a notion of adaptive concentration for regression trees. This approach breaks tree training into a model selection…

Variational inference (VI) has become a widely used approach for scalable Bayesian inference, but its performance strongly depends on the flexibility of the chosen variational family. In this work, we propose a novel variational family that…

This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…

Random graph mixture models are now very popular for modeling real data networks. In these setups, parameter estimation procedures usually rely on variational approximations, either combined with the expectation-maximisation (\textsc{em})…

In this article, we developed and analyzed a thresholding method in which soft thresholding estimators are independently expanded by empirical scaling values. The scaling values have a common hyper-parameter that is an order of expansion of…

We develop a skew-adaptive extension of split conformal prediction for regression. The method starts from an asymmetric interval family centered at a point prediction and uses the gauge approach to deduce the conformity score induced by…

In the presence of sufficiently weak overlap, it is known that no regular root-n-consistent estimators exist and standard estimators may fail to be asymptotically normal. This paper shows that a thresholded version of the standard doubly…

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…

In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…

We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and…