Related papers: Estimating Shape Parameters of Piecewise Linear-Qu…
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to…
We develop efficient algorithms for optimizing piecewise smooth (PWS) functions where the underlying partition of the domain into smooth pieces is \emph{unknown}. For PWS functions satisfying a quadratic growth (QG) condition, we propose a…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
To conduct regression analysis for data contaminated with outliers, many approaches have been proposed for simultaneous outlier detection and robust regression, so is the approach proposed in this manuscript. This new approach is called…
Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its…
This paper develops a unified nonconvex optimization framework for the design of group-sparse feedback controllers in infinite-horizon linear-quadratic (LQ) problems. We address two prominent extensions of the classical LQ problem: the…
A $\mathcal{H}_2$-guaranteed sparse-feedback linear-quadratic (LQ) optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where $\ell_0$-penalty is added into the $\mathcal{H}_2$ cost to…
We consider the problem of choosing between several models in least-squares regression with heteroscedastic data. We prove that any penalization procedure is suboptimal when the penalty is a function of the dimension of the model, at least…
In this paper, we study a variant of the quadratic penalty method for linearly constrained convex problems, which has already been widely used but actually lacks theoretical justification. Namely, the penalty parameter steadily increases…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
Huber's criterion can be used for robust joint estimation of regression and scale parameters in the linear model. Huber's (Huber, 1981) motivation for introducing the criterion stemmed from non-convexity of the joint maximum likelihood…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an L1 sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a…
The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they…
Feedback control problems involving autonomous polynomial systems are prevalent, yet there are limited algorithms and software for approximating their solution. This paper represents a step forward by considering the special case of the…
We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…
Partial least squares, as a dimension reduction method, has become increasingly important for its ability to deal with problems with a large number of variables. Since noisy variables may weaken the performance of the model, the sparse…