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We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the…
In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output…
Multivariate linear regression models often face the problem of heteroscedasticity caused by multiple explanatory variables. The weighted least squares estimation with univariate-dependent weights has limitations in constructing weight…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
This paper proposes a novel distributed reduced--rank scheme and an adaptive algorithm for distributed estimation in wireless sensor networks. The proposed distributed scheme is based on a transformation that performs dimensionality…
Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…
Recurrent neural networks are a powerful tool, but they are very sensitive to their hyper-parameter configuration. Moreover, training properly a recurrent neural network is a tough task, therefore selecting an appropriate configuration is…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…
This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
Low-rank representation learning has emerged as a powerful tool for recovering missing values in power load data due to its ability to exploit the inherent low-dimensional structures of spatiotemporal measurements. Among various techniques,…