Related papers: Piecewise linear regularized solution paths
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
In many real-world applications, the Pareto Set (PS) of a continuous multiobjective optimization problem can be a piecewise continuous manifold. A decision maker may want to find a solution set that approximates a small part of the PS and…
Penalized least squares estimation is a popular technique in high-dimensional statistics. It includes such methods as the LASSO, the group LASSO, and the nuclear norm penalized least squares. The existing theory of these methods is not…
The surge of explainable artificial intelligence methods seeks to enhance transparency and explainability in machine learning models. At the same time, there is a growing demand for explaining decisions taken through complex algorithms used…
We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original…
We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates. Classical functional logistic regression models rely on linear assumptions and fixed…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
We present an exploration of the rich theoretical connections between several classes of regularized models, network flows, and recent results in submodular function theory. This work unifies key aspects of these problems under a common…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
In this paper we analyze a budgeted learning setting, in which the learner can only choose and observe a small subset of the attributes of each training example. We develop efficient algorithms for ridge and lasso linear regression, which…
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the…
We provide a geometric approach to the lasso. We study the tangency of the level sets of the least square objective function with the polyhedral boundary sets $B(t)$ of the parameters in $\mathbb R^p$ with the $\ell_1$ norm equal to $t$.…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization…
We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei…
The graphical Lasso (GLASSO) is a widely used algorithm for learning high-dimensional undirected Gaussian graphical models (GGM). Given i.i.d. observations from a multivariate normal distribution, GLASSO estimates the precision matrix by…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…