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High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and…

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

Consensus maximization is one of the most widely used robust fitting paradigms in computer vision, and the development of algorithms for consensus maximization is an active research topic. In this paper, we propose an efficient…

We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of…

The goal of this work is to accelerate the identification of an unknown ARX system from trajectory data through online input design. Specifically, we present an active learning algorithm that sequentially selects the input to excite the…

This paper proposes a unified framework for designing robustness in optimization under uncertainty using gauge sets, convex sets that generalize distance and capture how distributions may deviate from a nominal reference. Representing…

Cartoon-texture image decomposition is a fundamental yet challenging problem in image processing. A significant hurdle in achieving accurate decomposition is the pervasive presence of noise in the observed images, which severely impedes…

Supervised learning is an active research area, with numerous applications in diverse fields such as data analytics, computer vision, speech and audio processing, and image understanding. In most cases, the loss functions used in machine…

This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…

The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…

Support vector machines are widely used in machine learning classification tasks, but traditional SVM models suffer from sensitivity to outliers and instability in resampling, which limits their performance in practical applications. To…

We study high-probability convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. In the proposed scenario, the model is updated in an online fashion, as new information is observed, without storing any…

With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to…

This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient…

High-dimensional data are commonly seen in modern statistical applications, variable selection methods play indispensable roles in identifying the critical features for scientific discoveries. Traditional best subset selection methods are…

We consider the problem of demixing a sequence of source signals from the sum of noisy bilinear measurements. It is a generalized mathematical model for blind demixing with blind deconvolution, which is prevalent across the areas of…

Neural networks can be drastically shrunk in size by removing redundant parameters. While crucial for the deployment on resource-constraint hardware, oftentimes, compression comes with a severe drop in accuracy and lack of adversarial…

Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational…

Robust loss minimization is an important strategy for handling robust learning issue on noisy labels. Current approaches for designing robust losses involve the introduction of noise-robust factors, i.e., hyperparameters, to control the…