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This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
Many Markov Chain Monte Carlo (MCMC) methods leverage gradient information of the potential function of target distribution to explore sample space efficiently. However, computing gradients can often be computationally expensive for large…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…
LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important…
Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS…
We consider the problem of detecting change-points in univariate time series by fitting a continuous piecewise linear signal using the residual sum of squares. Values of the inferred signal at slope breaks are restricted to a finite set of…
Since its inception, Benders Decomposition (BD) has been successfully applied to a wide range of large-scale mixed-integer (linear) problems. The key element of BD is the derivation of Benders cuts, which are often not unique. In this…
Downlink beamforming is an essential technology for wireless cellular networks; however, the design of beamforming vectors that maximize the weighted sum rate (WSR) is an NP-hard problem and iterative algorithms are typically applied to…
Five simple soft sensor methodologies with two update conditions were compared on two experimentally-obtained datasets and one simulated dataset. The soft sensors investigated were moving window partial least squares regression (and a…
We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of…
The democratization of machine learning systems has made the process of fine-tuning accessible to practitioners, leading to a wide range of open-source models fine-tuned on specialized tasks and datasets. Recent work has proposed to merge…
Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…
We developed a least squares fitter used for extracting expected physics parameters from the correlated experimental data in high energy physics. This fitter considers the correlations among the observables and handles the nonlinearity…
Shepard method is a fast algorithm that has been classically used to interpolate scattered data in several dimensions. This is an important and well-known technique in numerical analysis founded in the main idea that data that is far away…
The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate…
In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making…
There has been much recent progress in forecasting the next observation of a linear dynamical system (LDS), which is known as the improper learning, as well as in the estimation of its system matrices, which is known as the proper learning…