Related papers: Deconvolution density estimation with penalised ML…
Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular non-differentiable…
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…
We consider the problem of estimating the density $g$ of identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$ and $\sigma \epsilon\_i$ is a noise independent of $X\_i$…
Conditional density estimation (CDE) is the task of estimating the probability of an event conditioned on some inputs. A neural network (NN) can also be used to compute the output distribution for continuous-domain, which can be viewed as…
We consider the problem of estimating a density $f_X$ using a sample $Y_1,...,Y_n$ from $f_Y=f_X\star f_{\epsilon}$, where $f_{\epsilon}$ is an unknown density. We assume that an additional sample $\epsilon_1,...,\epsilon_m$ from…
The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density…
Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
In the present paper we consider the problem of Laplace deconvolution with noisy discrete observations. The study is motivated by Dynamic Contrast Enhanced imaging using a bolus of contrast agent, a procedure which allows considerable…
We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…
We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…
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…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
Fluorescence microscopy is widely used for the study of biological specimens. Deconvolution can significantly improve the resolution and contrast of images produced using fluorescence microscopy; in particular, Bayesian-based methods have…
Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language…
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
We introduce a new procedure to select the optimal cutoff parameter for Fourier density estimators that leads to adaptive rate optimal estimators, up to a logarithmic factor. This adaptive procedure applies for different inverse problems.…
For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…