We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients (n p 1). In this regime, optimization algorithms can immensely benefit from approximate second order information. We propose an alternative way of constructing the curvature information by formulating...

This paper appeared in the proceedings of ICASSP'95 bases can approximate it with only a few non-zero coefficients. It then becomes necessary to adaptively se-ABSTRACT lect an appropriate "best basis" which provides the best We propose a Best Basis Algorithm for Signal Enhance-signal estimate by discarding (thresholding) the noisy ment in white gaussian noise. We base our search of coefficients...

let be a random sample from a normal distribution with unknown mean and known variance the usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. in many practical situations, is known in advance to lie in an interval, say for some in this case, the maximum likelihood estimator changes and d...

In their enlightening and stimulating paper Svitlana Tyekucheva and Francesca Chiaromonte propose an “augmented bootstrap” (AB) approach to estimate covariance structure in high-dimensional data. They show that the AB estimator performs well in a catalog of examples. Moreover, according to the authors no assumption of a sparsity rationale is made. This is in contrast to a competing and computat...

In the present study, a novel signal restoration method from noisy data samples is presented and is termed as “signal split (SSplit)” approach. The new method utilizes Stein unbiased risk estimate estimator to split the signal, the Lipschitz exponents to identify noise elements and a heuristic approach for the signal reconstruction. However, unlike many noise removal techniques, the present met...

Abstract: In this paper, we propose a fast image deconvolution algorithm that combines adaptive block thresholding and Vaguelet-Wavelet Decomposition. The approach consists in first denoising the observed image using a wavelet-domain Stein block thresholding, and then inverting the convolution operator in the Fourier domain. Our main theoretical result investigates the minimax rates over Besov ...

This paper develops a novel framework to compute a projected Generalized Stein Unbiased Risk Estimator (GSURE) for a wide class of sparsely regularized solutions of inverse problems. This class includes arbitrary convex data fidelities with both analysis and synthesis mixed l − l norms. The GSURE necessitates to compute the (weak) derivative of a solution w.r.t. the observations. However, as th...

We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients (n p 1). In this regime, optimization algorithms can immensely benefit from approximate second order information. We propose an alternative way of constructing the curvature information by formulating...

In regression problems with errors having an unknown density f , least squares or robust M -estimation is the usual alternative to maximum likelihood, with the loss of asymptotic efficiency as a consequence. The search for efficiency in the absence of knowledge of f (adaptive estimation) has motivated a large amount of work, see in particular (Stein, 1956; Stone, 1975; Bickel, 1982) and the rev...

In this paper we propose an estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Vasicek (1976). Consistency of estimator is proved, and comparisons are made with Vasicek’s estimator (1976), van Es’s estimator (1992), Ebrahimi et al.’s estimator (1994) and Correa’s estimator (1995). The results indicate that the proposed esti...