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This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We consider convex relaxations for recovering low-rank tensors based on constrained minimization over a ball induced by the tensor nuclear norm, recently introduced in \cite{tensor_tSVD}. We build on a recent line of results that considered…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
In this paper, we consider comparison-based adaptive stochastic algorithms for solving numerical optimisation problems. We consider a specific subclass of algorithms that we call comparison-based step-size adaptive randomized search…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to $\mu$-strongly convex…
The Distributed Adaptive Signal Fusion (DASF) framework is a meta-algorithm for computing data-driven spatial filters in a distributed sensing platform with limited bandwidth and computational resources, such as a wireless sensor network.…
In this article, the state estimation problems with unknown process noise and measurement noise covariances for both linear and nonlinear systems are considered. By formulating the joint estimation of system state and noise parameters into…
For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…
This paper studies the convergence conditions and properties of the distributed adaptive signal fusion (DASF) algorithm, the framework itself having been introduced in a `Part I' companion paper. The DASF algorithm can be used to solve…
We present a general-purpose data compression algorithm, Regularized L21 Semi-NonNegative Matrix Factorization (L21 SNF). L21 SNF provides robust, parts-based compression applicable to mixed-sign data for which high fidelity, individualdata…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…
We present a new approach for Neural Optimal Transport (NOT) training procedure, capable of accurately and efficiently estimating optimal transportation plan via specific regularization on dual Kantorovich potentials. The main bottleneck of…
Building upon the mean p-power error (MPE) criterion, the normalized subband p-norm (NSPN) algorithm demonstrates superior robustness in $\alpha$-stable noise environments ($1 < \alpha \leq 2$) through effective utilization of low-order…
In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [5], we formulate it as an $l_1$-norm penalized maximum…
A distributed adaptive algorithm for estimation of sparse unknown parameters in the presence of nonGaussian noise is proposed in this paper based on normalized least mean fourth (NLMF) criterion. At the first step, local adaptive NLMF…
In real-time applications the characteristics and properties of a signal vary inconsistently. So, to maintain the integrity of such signals there is a need for effective adaptive filters. The conventional Least Mean Squared(LMS) algorithm…
Feature selection by maximizing high-order mutual information between the selected feature vector and a target variable is the gold standard in terms of selecting the best subset of relevant features that maximizes the performance of…
In this paper, we propose an ensemble learning algorithm called \textit{under-bagging $k$-nearest neighbors} (\textit{under-bagging $k$-NN}) for imbalanced classification problems. On the theoretical side, by developing a new learning…