Related papers: Robust Learning of Trimmed Estimators via Manifold…

We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…

Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…

We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…

In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one \emph{single} sample from each distribution. We study mean estimation and linear…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…

Learning models that are robust to distribution shifts is a key concern in the context of their real-life applicability. Invariant Risk Minimization (IRM) is a popular framework that aims to learn robust models from multiple environments.…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…

We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…

The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an…

Numerous problems in machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for…

This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…

We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…

The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…

Adversarial training has been actively studied in recent computer vision research to improve the robustness of models. However, due to the huge computational cost of generating adversarial samples, adversarial training methods are often…

We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…