Related papers: Efficient Non-oblivious Randomized Reduction for R…
Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we…
In this paper, we consider the problem of binary classification with a class of general deep convolutional neural networks, which includes fully-connected neural networks and fully convolutional neural networks as special cases. We…
In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…
We investigate the unconstrained global optimization of functions with low effective dimensionality, that are constant along certain (unknown) linear subspaces. Extending the technique of random subspace embeddings in [Wang et al., Bayesian…
We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated…
This work addresses the problem of regret minimization in non-stochastic multi-armed bandit problems, focusing on performance guarantees that hold with high probability. Such results are rather scarce in the literature since proving them…
We consider the problem of computationally-efficient prediction from high dimensional and highly correlated predictors in challenging settings where accurate variable selection is effectively impossible. Direct application of penalization…
In this paper, we consider non-convex stochastic bilevel optimization (SBO) problems that have many applications in machine learning. Although numerous studies have proposed stochastic algorithms for solving these problems, they are limited…
Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…
Unsupervised anomaly localization aims to identify anomalous regions that deviate from normal sample patterns. Most recent methods perform feature matching or reconstruction for the target sample with pre-trained deep neural networks.…
In this paper, we scale evolutionary algorithms to high-dimensional optimization problems that deceptively possess a low effective dimensionality (certain dimensions do not significantly affect the objective function). To this end, an…
We consider the estimation problem in high-dimensional semi-supervised learning. Our goal is to investigate when and how the unlabeled data can be exploited to improve the estimation of the regression parameters of linear model in light of…
Let X be a data matrix of rank \rho, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
Consider the following class of learning schemes: \begin{equation} \label{eq:main-problem1} \hat{\boldsymbol{\beta}} := \underset{\boldsymbol{\beta} \in \mathcal{C}}{\arg\min} \;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbol{\beta};…
An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
Gibbs-ERM learning is a natural idealized model of learning with stochastic optimization algorithms (such as Stochastic Gradient Langevin Dynamics and ---to some extent--- Stochastic Gradient Descent), while it also arises in other…