Related papers: Asymptotic Efficiency Analysis of the Recursive Le…
The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS…
Recently, the proposal of the least mean square (LMS) and recursive least squares (RLS) algorithm for graph signal processing (GSP) provides excellent solutions for processing signals defined on irregular structures such as sensor networks.…
Bearing-only Target Motion Analysis (TMA) is a promising technique for passive tracking in various applications as a bearing angle is easy to measure. Despite its advantages, bearing-only TMA is challenging due to the nonlinearity of the…
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are…
Radar sensors have become an important part of the perception sensor suite due to their long range and their ability to work in adverse weather conditions. However, several shortcomings such as large amounts of noise and extreme sparsity of…
In this paper, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is…
We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm, called DCD-RTLS,…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
We propose an efficient online dictionary learning algorithm for kernel-based sparse representations. In this framework, input signals are nonlinearly mapped to a high-dimensional feature space and represented sparsely using a virtual…
Recently, it was demonstrated in [CS2012,CS2013] that the robustness of the classical Non-Local Means (NLM) algorithm [BCM2005] can be improved by incorporating $\ell^p (0 < p \leq 2)$ regression into the NLM framework. This general…
Traditionally, batch least squares (BLS) and recursive least squares (RLS) are used for identification of a vector of parameters that form a linear model. In some situations, however, it is of interest to identify parameters in a matrix…
Large Language Models (LLMs) possess encompassing capabilities that can process diverse language-related tasks. However, finetuning on LLMs will diminish this general skills and continual finetuning will further cause severe degradation on…
Linear regression in $\ell_p$-norm is a canonical optimization problem that arises in several applications, including sparse recovery, semi-supervised learning, and signal processing. Generic convex optimization algorithms for solving…
Affine sum-of-ranks minimization (ASRM) generalizes the affine rank minimization (ARM) problem from matrices to tensors. Here, the interest lies in the ranks of a family $\mathcal{K}$ of different matricizations. Transferring our priorly…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…
Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…
Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…