Related papers: Node-screening tests for L0-penalized least-square…
The problem of planar registration consists in finding the transformation that better aligns two point sets. In our setting, the search domain is the set of planar rigid transformations and the objective function is the sum of the distances…
We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular…
We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective…
We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on…
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…
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the…
Nowadays, Non-Linear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last years, and this resulted in the development of several open-source…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…
We propose a practical method for $L_0$ norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up…
We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can…
Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs.…
We design simple screening tests to automatically discard data samples in empirical risk minimization without losing optimization guarantees. We derive loss functions that produce dual objectives with a sparse solution. We also show how to…
Recently, cutting-plane methods such as GCP-CROWN have been explored to enhance neural network verifiers and made significant advances. However, GCP-CROWN currently relies on generic cutting planes (cuts) generated from external mixed…
We present a generic Branch-and-Bound procedure designed to solve L0-penalized optimization problems. Existing approaches primarily focus on quadratic losses and construct relaxations using "Big-M" constraints and/or L2-norm penalties. In…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…
An important problem in networked systems is detection and removal of suspected malicious nodes. A crucial consideration in such settings is the uncertainty endemic in detection, coupled with considerations of network connectivity, which…
Tight and efficient neural network bounding is crucial to the scaling of neural network verification systems. Many efficient bounding algorithms have been presented recently, but they are often too loose to verify more challenging…