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We consider the problem of robust estimation involving filtering and smoothing for nonlinear state space models which are disturbed by heavy-tailed impulsive noises. To deal with heavy-tailed noises and improve the robustness of the…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…
We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…
Most existing methodologies of estimating low-rank matrices rely on Burer-Monteiro factorization, but these approaches can suffer from slow convergence, especially when dealing with solutions characterized by a large condition number,…
The continuation method is a popular approach in non-convex optimization and computer vision. The main idea is to start from a simple function that can be minimized efficiently, and gradually transform it to the more complicated original…
Motivated by the problem of tuning hyperparameters in machine learning, we present a new approach for gradually and adaptively optimizing an unknown function using estimated gradients. We validate the empirical performance of the proposed…
Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…
This paper presents a parametric solution to piecewise linear regression through the Adaptive Block Gradient Descent (ABGD) algorithm. The heart of the method is the parametrization of piecewise linear functions as the difference of…
In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…
Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
Most existing robust fitting methods are designed for classical models, such as lines, circles, and planes. In contrast, fewer methods have been developed to robustly handle non-classical models, such as spiral curves, procedural character…
In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
In the wake of the explosive growth in smartphones and cyberphysical systems, there has been an accelerating shift in how data is generated away from centralised data towards on-device generated data. In response, machine learning…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…