Related papers: A robust method based on LOVO functions for solvin…
We consider the robust estimation of the parameters of multivariate Gaussian linear regression models. To this aim we consider robust version of the usual (Mahalanobis) least-square criterion, with or without Ridge regularization. We…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
In this paper, we address a data dependent modification of the moving least squares (MLS) problem. We propose a novel approach by replacing the traditional weight functions with new functions that assign smaller weights to nodes that are…
This paper proposes a framework for simultaneous dimensionality reduction and regression in the presence of outliers in data by applying low-rank and sparse matrix decomposition. For multivariate data corrupted with outliers, it is…
We consider the problem of robustly fitting a model to data that includes outliers by formulating a percentile optimization problem. This problem is non-smooth and non-convex, hence hard to solve. We derive properties that the minimizers of…
Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust…
Least Absolute Deviations (LAD) regression provides a robust alternative to ordinary least squares by minimizing the sum of absolute residuals. However, its widespread use has been limited by the computational cost of existing solvers,…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
Many scientific and engineering applications require fitting regression models that are nonlinear in the parameters. Advances in computer hardware and software in recent decades have made it easier to fit such models. Relative to fitting…
Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…
Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is…
We consider optimization problems on Riemannian manifolds with equality and inequality constraints, which we call Riemannian nonlinear optimization (RNLO) problems. Although they have numerous applications, the existing studies on them are…
This work addresses the outlier removal problem in large-scale global structure-from-motion. In such applications, global outlier removal is very useful to mitigate the deterioration caused by mismatches in the feature point matching step.…
The presence of outliers (anomalous values) in synthetic aperture radar (SAR) data and the misspecification in statistical image models may result in inaccurate inferences. To avoid such issues, the Rayleigh regression model based on a…
A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables…
We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We…
Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…
We propose methods for estimating correspondence between two point sets under the presence of outliers in both the source and target sets. The proposed algorithms expand upon the theory of the regression without correspondence problem to…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
This paper proposes a robust, shocks-adaptive portfolio in a large-dimensional assets universe where the number of assets could be comparable to or even larger than the sample size. It is well documented that portfolios based on…