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The paper considers regression problems with uni-variate design points. The design points are irregular and no assumptions on their distribution are imposed. The regression function is retrieved by a wavelet based reproducing kernel Hilbert space (RKHS) technique with the penalty equal to the sum of blockwise RKHS norms. In order to simplify numerical… (More)

The problem of estimating a density g based on a sample X 1 X 2 X n from p = q * g is considered. Linear and nonlinear wavelet estima-tors based on Meyer-type wavelets are constructed. The estimators are asymptotically optimal and adaptive if g belongs to the Sobolev space H α. Moreover, the estimators considered in this paper adjust automatically to the… (More)

Deep neural networks have achieved remarkable performance in both image classification and object detection problems, at the cost of a large number of parameters and computational complexity. In this work, we show how to reduce the redundancy in these parameters using a sparse decomposition. Maximum sparsity is obtained by exploiting both inter-channel and… (More)

- Felix Abramovich, Vadim Grinshtein, Marianna Pensky
- 2007

We consider a problem of recovering a high-dimensional vector µ observed in white noise, where the unknown vector µ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of l 0-type penalties. The penalties are associated with various choices of the prior distributions π n (·) on the number of… (More)

The problem of estimating the log-spectrum of a stationary Gaussian time series by Bayesianly induced shrinkage of empirical wavelet coefficients is studied. A model in the wavelet domain that accounts for distributional properties of the log-periodogram at levels of fine detail and approximate normality at coarse levels in the wavelet decomposition, is… (More)

BACKGROUND
Gene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular… (More)

The objective of the present paper is to develop a truly functional Bayesian method specifically designed for time series microarray data. The method allows one to identify differentially expressed genes in a time-course microarray experiment, to rank them and to estimate their expression profiles. Each gene expression profile is modeled as an expansion… (More)

- Marianna Pensky, Brani Vidakovic
- 1998

2 Wavelet-based regression analysis is widely used mostly for equally-spaced designs. For such designs wavelets are superior to other traditional orthonormal bases because of their versatility and ability to parsimoniously describe irregular functions. If the regression design is random, an automatic solution is not available. Given the observations (X i ;… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t A truly functional Bayesian method for detecting temporally… (More)

- Marianna Pensky, Theofanis Sapatinas
- 2009

We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation.… (More)