Gabriel de Albuquerque Gleizer

Shabnam Khodakaramzadeh, Soroosh Shafiee, Gabriel de Albuquerque Gleizer et al.

We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a first-order algorithm that solves this reformulation by leveraging a linear minimization oracle (LMO). We further develop semi-closed form solutions (up to a scalar) for three specific LMOs, corresponding to the Frobenius norm, Kullback-Leibler divergence, and Gelbrich (aka Wasserstein) distance. The analysis includes explicit quantification of these LMOs' regularity conditions, notably the Lipschitz constants of the dual function, which govern the algorithm's convergence performance. Numerical experiments confirm our method's effectiveness in high-dimensional settings, outperforming standard off-the-shelf optimization solvers.

Mohammad Amin Sheikhi, Gabriel de Albuquerque Gleizer, Peyman Mohajerin Esfahani et al.

We study the problem of fault isolation in linear systems with actuator and sensor faults within a data-driven framework. We propose a nullspace-based filter that uses solely fault-free input-output data collected under process and measurement noises. By reparameterizing the problem within a behavioral framework, we achieve a direct fault isolation filter design that is independent of any explicit system model. The underlying classification problem is approached from a geometric perspective, enabling a characterization of mutual fault discernibility in terms of fundamental system properties given a noise-free setting. In addition, the provided conditions can be evaluated using only the available data. Finally, a simulation study is conducted to demonstrate the effectiveness of the proposed method.