Related papers: Learning Trees of $\ell_0$-Minimization Problems
Overparameterization and overfitting are common concerns when designing and training deep neural networks, that are often counteracted by pruning and regularization strategies. However, these strategies remain secondary to most learning…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a…
The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which…
Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is…
We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
We demonstrate that challenging shortest path problems can be solved via direct spline regression from a neural network, trained in an unsupervised manner (i.e. without requiring ground truth optimal paths for training). To achieve this, we…
We study learning problems in which the underlying class is a bounded subset of $L_p$ and the target $Y$ belongs to $L_p$. Previously, minimax sample complexity estimates were known under such boundedness assumptions only when $p=\infty$.…
We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
Classification algorithms face difficulties when one or more classes have limited training data. We are particularly interested in classification trees, due to their interpretability and flexibility. When data are limited in one or more of…
This paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, called Learning from Ordered Answer Sets,…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…
We present a new approach to solve the sparse approximation or best subset selection problem, namely find a $k$-sparse vector ${\bf x}\in\mathbb{R}^d$ that minimizes the $\ell_2$ residual $\lVert A{\bf x}-{\bf y} \rVert_2$. We consider a…
The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS…
The $\ell^0$ minimization of compressed sensing is often relaxed to $\ell^1$, which yields easy computation using the shrinkage mapping known as soft thresholding, and can be shown to recover the original solution under certain hypotheses.…
In the recent years, branch-and-cut algorithms have been the target of data-driven approaches designed to enhance the decision making in different phases of the algorithm such as branching, or the choice of cutting planes (cuts). In…
In this paper we revisit one of the classical problems of compressed sensing. Namely, we consider linear under-determined systems with sparse solutions. A substantial success in mathematical characterization of an $\ell_1$ optimization…
A multi-objective optimization problem is $C^r$ weakly simplicial if there exists a $C^r$ surjection from a simplex onto the Pareto set/front such that the image of each subsimplex is the Pareto set/front of a subproblem, where $0\leq r\leq…