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Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…

One well established method of interactive image segmentation is the random walker algorithm. Considerable research on this family of segmentation methods has been continuously conducted in recent years with numerous applications. These…

We investigate unbiased high-dimensional mean estimators in differential privacy. We consider differentially private mechanisms whose expected output equals the mean of the input dataset, for every dataset drawn from a fixed bounded…

The performance of penalized likelihood approaches depends profoundly on the selection of the tuning parameter; however, there is no commonly agreed-upon criterion for choosing the tuning parameter. Moreover, penalized likelihood estimation…

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

Tissue segmentation is the mainstay of pathological examination, whereas the manual delineation is unduly burdensome. To assist this time-consuming and subjective manual step, researchers have devised methods to automatically segment…

In this paper, the traditional model based variational method and learning based algorithms are naturally integrated to address mixed noise removal problem. To be different from single type noise (e.g. Gaussian) removal, it is a challenge…

We propose a novel $\ell_1+\ell_2$-penalty, which we refer to as the Generalized Elastic Net, for regression problems where the feature vectors are indexed by vertices of a given graph and the true signal is believed to be smooth or…

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an at- tractive method for…

Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…

We consider the problem of detecting the presence of a spatially correlated multichannel signal corrupted by additive Gaussian noise (i.i.d across sensors). No prior knowledge is assumed about the system parameters such as the noise…

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…

We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show…

Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…

Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…

Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…

We develop a new approach for estimating the risk of an arbitrary estimator of the mean vector in the classical normal means problem. The key idea is to generate two auxiliary data vectors, by adding carefully constructed normal noise…

An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…

Large dimensional least-squares and regularised least-squares problems are expensive to solve. There exist many approximate techniques, some deterministic (like conjugate gradient), some stochastic (like stochastic gradient descent). Among…

Randomized smoothing is a recent technique that achieves state-of-art performance in training certifiably robust deep neural networks. While the smoothing family of distributions is often connected to the choice of the norm used for…