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We propose a distributionally robust formulation of the traditional risk parity portfolio optimization problem. Distributional robustness is introduced by targeting the discrete probabilities attached to each observation used during…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
Auxiliary particle filters (APFs) are a class of sequential Monte Carlo (SMC) methods for Bayesian inference in state-space models. In their original derivation, APFs operate in an extended state space using an auxiliary variable to improve…
The accelerated proximal point algorithm (APPA), also known as "Catalyst", is a well-established reduction from convex optimization to approximate proximal point computation (i.e., regularized minimization). This reduction is conceptually…
In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the…
The use of reconfigurable intelligent surfaces (RIS) can improve wireless communication by modifying the wireless link to create virtual line-of-sight links, bypass blockages, suppress interference, and enhance localization. However,…
This paper addresses risk averse constrained optimization problems where the objective and constraint functions can only be computed by a blackbox subject to unknown uncertainties. To handle mixed aleatory/epistemic uncertainties, the…
RANSAC is a popular technique for estimating model parameters in the presence of outliers. The best speed is achieved when the minimum possible number of points is used to estimate hypotheses for the model. Many useful problems can be…
We study the robust matrix completion (RMC) problem subject to both sparse outliers and stochastic noise. A non-convex method termed Accelerated Robust Matrix Completion (ARMC) is proposed, which accelerates a prior non-convex approach by…
Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
Motivated by robust matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss function applied to the sum of two blocks of variables,…
We investigate a data-driven quasiconcave maximization problem where information about the objective function is limited to a finite sample of data points. We begin by defining an ambiguity set for admissible objective functions based on…
Physics-Informed Machine Learning (PIML) offers a powerful paradigm of integrating data with physical laws to address important scientific problems, such as parameter estimation, inferring hidden physics, equation discovery, and state…
We consider a generic empirical composition optimization problem, where there are empirical averages present both outside and inside nonlinear loss functions. Such a problem is of interest in various machine learning applications, and…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they…
In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem…
When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…