Related papers: Piecewise-Linear Approximation for Feature Subset …
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
We consider the problem of learning to choose from a given set of objects, where each object is represented by a feature vector. Traditional approaches in choice modelling are mainly based on learning a latent, real-valued utility function,…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
Feature selection is frequently used as a pre-processing step to machine learning. It is a process of choosing a subset of original features so that the feature space is optimally reduced according to a certain evaluation criterion. The…
In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the overapproximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes" the dynamical characteristics of the…
For regulatory and interpretability reasons, logistic regression is still widely used. To improve prediction accuracy and interpretability, a preprocessing step quantizing both continuous and categorical data is usually performed:…
Selecting the most relevant or informative features is a key issue in actual machine learning problems. Since an exhaustive search is not feasible even for a moderate number of features, an intelligent search strategy must be employed for…
We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate…
This paper focuses on optimal unimodal transformation of the score outputs of a univariate learning model under linear loss functions. We demonstrate that the optimal mapping between score values and the target region is a rectangular…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
This paper presents a parametric solution to piecewise linear regression through the Adaptive Block Gradient Descent (ABGD) algorithm. The heart of the method is the parametrization of piecewise linear functions as the difference of…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
Feature selection can select important features to address dimensional curses. Subspace learning, a widely used dimensionality reduction method, can project the original data into a low-dimensional space. However, the low-dimensional…
Sequence segmentation is a well-studied problem, where given a sequence of elements, an integer K, and some measure of homogeneity, the task is to split the sequence into K contiguous segments that are maximally homogeneous. A classic…
The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…