Related papers: A simplified L-curve method as error estimator
The Sorted L-One Estimator (SLOPE) is a popular regularization method in regression, which induces clustering of the estimated coefficients. That is, the estimator can have coefficients of identical magnitude. In this paper, we derive an…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…
The computation of 2-D optical flow by means of regularized pel-recursive algorithms raises a host of issues, which include the treatment of outliers, motion discontinuities and occlusion among other problems. We propose a new approach…
Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…
A new parameterization and algorithm are proposed for seeking the primary relative maximum of the likelihood function in the three-parameter lognormal distribution. The parameterization yields the dimension reduction of the three-parameter…
Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…
We provide an axiomatic characterization of the Logarithmic Least Squares Method (sometimes called row geometric mean), used for deriving a preference vector from a pairwise comparison matrix. This procedure is shown to be the only one…
The `Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a…
Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that…
We present an algorithm to fair a given planar curve by a log-aesthetic curve (LAC). We show how a general LAC segment can be uniquely characterized by seven parameters and present a method of parametric approximation based on this fact.…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
In the field of data mining, how to deal with high-dimensional data is an inevitable problem. Unsupervised feature selection has attracted more and more attention because it does not rely on labels. The performance of spectral-based…
We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and…
Least absolute deviation regression is applied using a fixed number of points for all values of the index to estimate the index and scale parameter of the stable distribution using regression methods based on the empirical characteristic…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
We derive sharp performance bounds for least squares regression with $L_1$ regularization from parameter estimation accuracy and feature selection quality perspectives. The main result proved for $L_1$ regularization extends a similar…
We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…
The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most…