Related papers: A Constrained Least-Squares Ghost Sample Points (C…
High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…
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…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…
Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
It is well known that in the presence of heteroscedasticity ordinary least squares estimator is not efficient. I propose a generalized automatic least squares estimator (GALS) that makes partial correction of heteroscedasticity based on a…
We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by…
Sparse Partial Least Squares (sPLS) is a common dimensionality reduction technique for data fusion, which projects data samples from two views by seeking linear combinations with a small number of variables with the maximum variance.…
A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow…
A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equivalent least-squares (LS) formulation and uses ReLU neural…
Multi-view mesh reconstruction remains a core challenge in computer graphics and vision, especially for recovering high-frequency geometry from sparse observations. Recent methods such as 3D Gaussian Splatting (3DGS) and Neural Radiance…
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA).…
In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…
Ghost imaging via sparsity constraint (GISC) can recover objects from the intensity fluctuation of light fields even when the sampling rate is far below the Nyquist sampling rate. In this paper, we develop an efficient algorithm called the…
The processing, storage and transmission of large-scale point clouds is an ongoing challenge in the computer vision community which hinders progress in the application of 3D models to real-world settings, such as autonomous driving, virtual…
We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular…
We present a scheme implementing an a posteriori refinement strategy in the context of a high-order meshless method for problems involving point singularities and fluid-solid interfaces. The generalized moving least squares (GMLS)…
We propose a First-Order System Least Squares (FOSLS) method based on deep-learning for numerically solving second-order elliptic PDEs. The method we propose is capable of dealing with either variational and non-variational problems, and…
Sampling is widely used in various point cloud tasks as it can effectively reduce resource consumption. Recently, some methods have proposed utilizing neural networks to optimize the sampling process for various task requirements.…
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional…