Related papers: A class of optimization problems motivated by rank…
Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…
A common data analysis task is the reduced-rank regression problem: $$\min_{\textrm{rank-}k \ X} \|AX-B\|,$$ where $A \in \mathbb{R}^{n \times c}$ and $B \in \mathbb{R}^{n \times d}$ are given large matrices and $\|\cdot\|$ is some norm.…
Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for…
This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative…
We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order…
The era of Big Data has spawned unprecedented interests in developing hashing algorithms for efficient storage and fast nearest neighbor search. Most existing work learn hash functions that are numeric quantizations of feature values in…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…
This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…
There is a growing interest in using robust control theory to analyze and design optimization and machine learning algorithms. This paper studies a class of nonconvex optimization problems whose cost functions satisfy the so-called…
Regression-via-Classification (RvC) is the process of converting a regression problem to a classification one. Current approaches for RvC use ad-hoc discretization strategies and are suboptimal. We propose a neural regression tree model for…
Methods for learning from data depend on various types of tuning parameters, such as penalization strength or step size. Since performance can depend strongly on these parameters, it is important to compare classes of estimators-by…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space $\mathcal{X}$ and the goal is to order all…
The two-sided matrix regression model $Y = A^*X B^* +E$ aims at predicting $Y$ by taking into account both linear links between column features of $X$, via the unknown matrix $B^*$, and also among the row features of $X$, via the matrix…
We consider the problem of learning support vector machines robust to uncertainty. It has been established in the literature that typical loss functions, including the hinge loss, are sensible to data perturbations and outliers, thus…
We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In…
The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…
Adequate evaluation of an information retrieval system to estimate future performance is a crucial task. Area under the ROC curve (AUC) is widely used to evaluate the generalization of a retrieval system. However, the objective function…