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In this work we introduce a novel weighted message-passing algorithm based on the cavity method to estimate volume-related properties of random polytopes, properties which are relevant in various research fields ranging from metabolic…
Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the…
The weak measurements based amplification of ultra-small phase was proposed in our previous work. Due to the technical imperfections, the ability of amplification is usually limited in practice. Here we introduce the concept of cascaded…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
In this paper, we address a data dependent modification of the moving least squares (MLS) problem. We propose a novel approach by replacing the traditional weight functions with new functions that assign smaller weights to nodes that are…
In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…
We consider scattered data approximation in samplet coordinates with $\ell_1$-regularization. The application of an $\ell_1$-regularization term enforces sparsity of the coefficients with respect to the samplet basis. Samplets are…
In the heteroscedastic linear model, the weighted least squares (WLS) estimate of the model coefficients is more efficient than the ordinary least squares (OLS) esti- mate. However, the practical application of WLS is challenging because it…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
This paper investigates the possibility of improving radio interferometric images using an algorithm inspired by an optical method known as "lucky imaging", which would give more weight to the best-calibrated visibilities used to make a…
Cluster-weighted modeling (CWM) is a mixture approach for modeling the joint probability of a response variable and a set of explanatory variables. The parameters are estimated by means of the expectation-maximization algorithm according to…
We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented…
Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis…
We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally…
Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method,…
We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…