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Decomposition of digital signals and images into other basis or dictionaries than time or space domains is a very common approach in signal and image processing and analysis. Such a decomposition is commonly obtained using fixed transforms…

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…

Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these…

Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…

Motivated by the proliferation of observational datasets and the need to integrate non-randomized evidence with randomized controlled trials, causal inference researchers have recently proposed several new methodologies for combining biased…

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…

We investigate predictive densities for multivariate normal models with unknown mean vectors and known covariance matrices. Bayesian predictive densities based on shrinkage priors often have complex representations, although they are…

Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…

We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on a smoothing of the coefficients of the highest subbands. Specifically, we decompose the noisy microarray into…

Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through…

In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and in particular consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors…

We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a…

The `Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a…

In this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi-square random variable. We then consider the task of…

Gauss-Newton methods and their stochastic version have been widely used in machine learning and signal processing. Their nonsmooth counterparts, modified Gauss-Newton or prox-linear algorithms, can lead to contrasting outcomes when compared…

Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete…

Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding…

Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…

We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…