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Finding non-Gaussian components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the " non-Gaussian subspace " within a very general semi-parametric framework. Our proposed method, called NGCA (Non-Gaussian Component Analysis), is essentially based on a… (More)

Diffusion Tensor Imaging (DTI) data is characterized by a high noise level. Thus, estimation errors of quantities like anisotropy indices or the main diffusion direction used for fiber tracking are relatively large and may significantly confound the accuracy of DTI in clinical or neuroscience applications. Besides pulse sequence optimization, noise… (More)

Non-gaussian component analysis (NGCA) introduced in [24] offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way. An important step of the NGCA procedure is identification of the non-Gaussian subspace using Principle Component… (More)

The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR subspace is proposed. Under mild assumptions, √ n-consistency of the proposed procedure is proved (up to a logarithmic… (More)

—This paper offers a new technique for spatially adap-tive estimation. The local likelihood is exploited for nonparametric modeling of observations and estimated signals. The approach is based on the assumption of a local homogeneity of the signal: for every point there exists a neighborhood in which the signal can be well approximated by a constant. The… (More)

We propose a new linear method for dimension reduction to identify non-Gaussian components in high dimensional data. Our method, NGCA (non-Gaussian component analysis), uses a very general semi-parametric framework. In contrast to existing projection methods we define what is uninteresting (Gaussian): by projecting out uninterestingness, we can estimate the… (More)

—We consider the problem of recovering edges of an image from noisy tomographic data. The original image is assumed to have a discontinuity jump (edge) along the boundary of a compact convex set. The Radon transform of the image is observed with noise, and the problem is to estimate the edge. We develop an estimation procedure which is based on recovering… (More)

In this article, we consider high-dimensional data which contains a low-dimensional non-Gaussian structure contaminated with Gaussian noise and propose a new linear method to identify the non-Gaussian subspace. Our method NGCA (Non-Gaussian Component Analysis) is based on a very general semi-parametric framework and has a theoretical guarantee that the… (More)

Obtaining the best linear unbiased estimator (BLUE) of noisy signals is a traditional but powerful approach to noise reduction. Explicitly computing BLUE usually requires the prior knowledge of the subspace to which the true signal belongs and the noise covariance matrix. However, such prior knowledge is often unavailable in reality, which prevents us from… (More)

Detection of recombination events in a bacterial genome is both important from the evolutionary point of view, and of practical interest. Indeed, homologous recombination (HR) plays a major role in the exchange of antigenic determinants between strains. There exist statistical methods to detect recently recombined segments in whole-genome sequences that use… (More)