Related papers: Approximate Least Squares
In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
Performance analysis of $l_0$ norm constrained Recursive least Squares (RLS) algorithm is attempted in this paper. Though the performance pretty attractive compared to its various alternatives, no thorough study of theoretical analysis has…
Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization…
In many application of noise cancellation, the changes in signal characteristics could be quite fast. This requires the utilization of adaptive algorithms, which converge rapidly. Least Mean Squares (LMS) adaptive filters have been used in…
In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…
This paper studies least-squares ReLU neural network method for solving the linear advection-reaction problem with discontinuous solution. The method is a discretization of an equivalent least-squares formulation in the set of neural…
Least-squares approximation is one of the most important methods for recovering an unknown function from data. While in many applications the data is fixed, in many others there is substantial freedom to choose where to sample. In this…
This paper argues that the method of least squares has significant unfulfilled potential in modern machine learning, far beyond merely being a tool for fitting linear models. To release its potential, we derive custom gradients that…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
We consider a setting in which it is desired to find an optimal complex vector $\mathbf{x}\in\mathbb{C}^N$ that satisfies $\mathcal{A}(\mathbf{x}) \approx \mathbf{b}$ in a least-squares sense, where $\mathbf{b} \in \mathbb{C}^M$ is a data…
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when…
This paper describes a new efficient conjugate subgradient algorithm which minimizes a convex function containing a least squares fidelity term and an absolute value regularization term. This method is successfully applied to the inversion…
We study the convergence rate of the proximal-gradient homotopy algorithm applied to norm-regularized linear least squares problems, for a general class of norms. The homotopy algorithm reduces the regularization parameter in a series of…
Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…
In this paper, we study the problem of multipath channel estimation for direct sequence spread spectrum signals. To resolve multipath components arriving within a short interval, we propose a new algorithm called the least-squares based…
In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required…
In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…