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We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence…
Machine-learning techniques have become fundamental in high-energy physics and, for new physics searches, it is crucial to know their performance in terms of experimental sensitivity, understood as the statistical significance of the…
In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp…
A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…
This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…
We propose two new conformity scores for conformal prediction, in a general multivariate regression framework. The underlying score functions are based on a covariance analysis of the residuals and the input points. We give theoretical…
We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…
Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…
Broadband wireless channels usually have the sparse nature. Based on the assumption of Gaussian noise model, adaptive filtering algorithms for reconstruction sparse channels were proposed to take advantage of channel sparsity. However,…
Adaptive spectral (AS) decompositions associated with a piecewise constant function $u$ yield small subspaces where the characteristic functions comprising $u$ are well approximated. When combined with Newton-like optimization methods for…
We study a high-dimensional regression setting under the assumption of known covariate distribution. We aim at estimating the amount of explained variation in the response by the best linear function of the covariates (the signal level). In…
Multireference alignment (MRA) problem is to estimate an underlying signal from a large number of noisy circularly-shifted observations. The existing methods are always proposed under the hypothesis of a single Gaussian noise. However, the…
We present a framework for the optimal filtering of spherical signals contaminated by realizations of an additive, zero-mean, uncorrelated and anisotropic noise process on the sphere. Filtering is performed in the wavelet domain given by…
We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging…
Exploiting intrinsic structures in sparse signals underpins the recent progress in compressive sensing (CS). The key for exploiting such structures is to achieve two desirable properties: generality (\ie, the ability to fit a wide range of…
In real-time applications the characteristics and properties of a signal vary inconsistently. So, to maintain the integrity of such signals there is a need for effective adaptive filters. The conventional Least Mean Squared(LMS) algorithm…
High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two…
We describe ways to define and calculate $L_1$-norm signal subspaces which are less sensitive to outlying data than $L_2$-calculated subspaces. We focus on the computation of the $L_1$ maximum-projection principal component of a data matrix…