Related papers: orthoDr: Semiparametric Dimension Reduction via Or…
Distributionally robust optimization (DRO) has become a powerful framework for estimation under uncertainty, offering strong out-of-sample performance and principled regularization. In this paper, we propose a DRO-based method for linear…
Joint diagonalization of a set of positive (semi)-definite matrices has a wide range of analytical applications, such as estimation of common principal components, estimation of multiple variance components, and blind signal separation.…
Deep reinforcement learning (RL) agents commonly rely on high-dimensional neural representations, despite growing evidence that task-relevant value and policy structure may be intrinsically low-dimensional. In this work, we present a simple…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
Orthogonal Fractional Factorial Designs and in particular Orthogonal Arrays are frequently used in many fields of application, including medicine, engineering and agriculture. In this paper we present a methodology and an algorithm to find…
In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…
The starting point of this paper is that a spectral method is essentially a combination of an orthonormal basis of the underlying Hilbert space with Galerkin conditions. The choice of an orthonormal basis depends on a number of desirable…
With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…
Due to the demand for tackling the problem of streaming data with high dimensional covariates, we propose an online sparse sliced inverse regression (OSSIR) method for online sufficient dimension reduction. The existing online sufficient…
The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
Scientific applications produce vast amounts of data, posing grand challenges in the underlying data management and analytic tasks. Progressive compression is a promising way to address this problem, as it allows for on-demand data…
This paper investigates structure-preserving $H_2$-optimal model order reduction (MOR) for linear systems with quadratic outputs. Within a Petrov-Galerkin projection framework, the $H_2$-optimal MOR problem is first formulated as an…
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
An adaptation of Response Surface Methodology (RSM) when the covariate is of high or infinite dimensional is proposed, providing a tool for black-box optimization in this context. We combine dimension reduction techniques with classical…
In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear…
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…
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…