Related papers: Robust Learning of Trimmed Estimators via Manifold…
The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…
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…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
Automatically learning features, especially robust features, has attracted much attention in the machine learning community. In this paper, we propose a new method to learn non-linear robust features by taking advantage of the data manifold…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against label corruptions in…
Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…
Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…
Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…
This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite…
Sampling biases in training data are a major source of algorithmic biases in machine learning systems. Although there are many methods that attempt to mitigate such algorithmic biases during training, the most direct and obvious way is…
The mean squared error loss is widely used in many applications, including auto-encoders, multi-target regression, and matrix factorization, to name a few. Despite computational advantages due to its differentiability, it is not robust to…
Channel estimation poses significant challenges in millimeter-wave massive multiple-input multiple-output systems, especially when the base station has fewer radio-frequency chains than antennas. To address this challenge, one promising…
Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the…
Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…