Related papers: Convex Techniques for Model Selection

We propose a generalization of the method of cyclic projections, which uses the lengths of projection steps carried out in the past to learn about the geometry of the problem and decides on this basis which projections to carry out in the…

Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these…

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…

We consider stochastic convex optimization with a strongly convex (but not necessarily smooth) objective. We give an algorithm which performs only gradient updates with optimal rate of convergence.

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions,…

Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate…

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…

In this article, we describe the regression test process to test and verify the changes made on software. A developed technique use the automation test based on decision tree and test selection process in order to reduce the testing cost is…

We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of…

This review presents modern gradient-free methods to solve convex optimization problems. By gradient-free methods, we mean those that use only (noisy) realizations of the objective value. We are motivated by various applications where…

We propose a general convex optimization problem for computing regularized geodesic distances. We show that under mild conditions on the regularizer the problem is well posed. We propose three different regularizers and provide analytical…

We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal…

Vehicle models have a long history of research and as of today are able to model the involved physics in a reasonable manner. However, each new vehicle has its new characteristics or parameters. The identification of these is the main task…

Two new approaches for checking the dimension of the basis functions when using penalized regression smoothers are presented. The first approach is a test for adequacy of the basis dimension based on an estimate of the residual variance…

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty.…

For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…