Related papers: Golden Ratio-Based Sufficient Dimension Reduction

In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. We first construct a neural network-based orthogonal basis by some deep learning method and dimensionality…

In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated…

The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Parity functions are fundamental Boolean operations with critical applications across machine learning, cryptography, and error correction. Yet, learning high-dimensional parity functions poses significant challenges: in a general setting,…

Recently, neural tangent kernel (NTK) has been used to explain the dynamics of learning parameters of neural networks, at the large width limit. Quantitative analyses of NTK give rise to network widths that are often impractical and incur…

Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…

In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…

Recent research on deep neural networks (DNNs) has primarily focused on improving the model accuracy. Given a proper deep learning framework, it is generally possible to increase the depth or layer width to achieve a higher level of…

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…

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…

Deep neural networks (DNNs) usually contain massive parameters, but there is redundancy such that it is guessed that the DNNs could be trained in low-dimensional subspaces. In this paper, we propose a Dynamic Linear Dimensionality Reduction…

Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…

Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…

This paper presents a unified framework for sufficient dimension reduction (SDR) that generalizes several existing SDR techniques and offers new insights into the connection between inverse conditional moment independence and dimension…

We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

Pruning methods have shown to be effective at reducing the size of deep neural networks while keeping accuracy almost intact. Among the most effective methods are those that prune a network while training it with a sparsity prior loss and…