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Network reconstruction is important to the understanding and control of collective dynamics in complex systems. Most real networks exhibit sparsely connected properties, and the connection parameter is a signal (0 or 1). Well-known…
Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted…
Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…
Consider the problem of reconstructing a multidimensional signal from an underdetermined set of measurements, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
Both classification and regression tasks are susceptible to the biased distribution of training data. However, existing approaches are focused on the class-imbalanced learning and cannot be applied to the problems of numerical regression…
We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a "pre-conditioned" response…
The arrival of AI techniques in computations, with the potential for hallucinations and non-robustness, has made trustworthiness of algorithms a focal point. However, trustworthiness of the many classical approaches are not well understood.…
The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from…
In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…
We propose a self-tuning $\sqrt{\mathrm {Lasso}}$ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic)…
We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
In this paper, we derive non-asymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using $K$-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly…
High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional…
In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
Variable selection in linear regression settings is a much discussed problem. Best subset selection (BSS) is often considered the intuitive 'gold standard', with its use being restricted only by its NP-hard nature. Alternatives such as the…