Related papers: Golden Ratio-Based Sufficient Dimension Reduction
We present an error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method. Our main contribution is a redesigned hybrid solver [Larios-C\'ardenas and Gibou, J. Comput. Phys. (May 2022),…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are…
We study the problem of approximating and estimating classification functions that have their decision boundary in the $RBV^2$ space. Functions of $RBV^2$ type arise naturally as solutions of regularized neural network learning problems and…
Deep learning models like Transformers and Convolutional Neural Networks (CNNs) have revolutionized various domains, but their parameter-intensive nature hampers deployment in resource-constrained settings. In this paper, we introduce a…
Recurrent Neural Networks (RNN) are widely used to solve a variety of problems and as the quantity of data and the amount of available compute have increased, so have model sizes. The number of parameters in recent state-of-the-art networks…
Deep Neural Networks (DNNs) are computationally and memory intensive, which makes their hardware implementation a challenging task especially for resource constrained devices such as IoT nodes. To address this challenge, this paper…
This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of…
Dimensional reduction~(DR) maps high-dimensional data into a lower dimensions latent space with minimized defined optimization objectives. The DR method usually falls into feature selection~(FS) and feature projection~(FP). FS focuses on…
As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…
In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…
The increasing complexity of modern deep neural network models and the expanding sizes of datasets necessitate the development of optimized and scalable training methods. In this white paper, we addressed the challenge of efficiently…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
Many recurrent neural network machine learning paradigms can be formulated using state-space representations. The classical notion of canonical state-space realization is adapted in this paper to accommodate semi-infinite inputs so that it…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
An image retrieval method based on convolution neural network and dimension reduction is proposed in this paper. Convolution neural network is used to extract high-level features of images, and to solve the problem that the extracted…
We present a subspace method based on neural networks for solving the partial differential equation in weak form with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…