Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network

• URL: http://arxiv.org/abs/2210.04349v1
• Date: Sun, 9 Oct 2022 20:56:57 GMT
• Title: Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network
• Authors: Siqi Liang, Yan Sun, Faming Liang
• Abstract summary: We propose a new type of neural network for sufficient dimension reduction for large-scale data. The proposed neural network is trained using an adaptive gradient Markov chain Monte Carlo algorithm. We show that the proposed method compares favorably with the existing state-of-the-art sufficient dimension reduction methods.
• Score: 9.173528450234906
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient dimension reduction methods often lack the scalability necessary for dealing with large-scale data. We propose a new type of stochastic neural network under a rigorous probabilistic framework and show that it can be used for sufficient dimension reduction for large-scale data. The proposed stochastic neural network is trained using an adaptive stochastic gradient Markov chain Monte Carlo algorithm, whose convergence is rigorously studied in the paper as well. Through extensive experiments on real-world classification and regression problems, we show that the proposed method compares favorably with the existing state-of-the-art sufficient dimension reduction methods and is computationally more efficient for large-scale data.

Related papers

• Golden Ratio-Based Sufficient Dimension Reduction [6.184279198087624]
  We propose a neural network based sufficient dimension reduction method. It identifies the structural dimension effectively and estimates the central space well. It takes advantages of approximation capabilities of neural networks for functions in Barron classes and leads to reduced computation cost.
  arXiv  Detail & Related papers  (2024-10-25T04:15:15Z)
• Towards a Better Theoretical Understanding of Independent Subnetwork Training [56.24689348875711]
  We take a closer theoretical look at Independent Subnetwork Training (IST) IST is a recently proposed and highly effective technique for solving the aforementioned problems. We identify fundamental differences between IST and alternative approaches, such as distributed methods with compressed communication.
  arXiv  Detail & Related papers  (2023-06-28T18:14:22Z)
• MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variability [0.30693357740321775]
  We propose a machine learning method that do not rely on graph neural networks. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization.
  arXiv  Detail & Related papers  (2023-05-22T09:50:15Z)
• Information bottleneck theory of high-dimensional regression: relevancy, efficiency and optimality [6.700873164609009]
  Overfitting is a central challenge in machine learning, yet many large neural networks readily achieve zero training loss. We quantify overfitting via residual information, defined as the bits in fitted models that encode noise in training data.
  arXiv  Detail & Related papers  (2022-08-08T00:09:12Z)
• Distributed Dynamic Safe Screening Algorithms for Sparse Regularization [73.85961005970222]
  We propose a new distributed dynamic safe screening (DDSS) method for sparsity regularized models and apply it on shared-memory and distributed-memory architecture respectively. We prove that the proposed method achieves the linear convergence rate with lower overall complexity and can eliminate almost all the inactive features in a finite number of iterations almost surely.
  arXiv  Detail & Related papers  (2022-04-23T02:45:55Z)
• Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies [1.6457778420360534]
  A framework of outlier-resistant estimation is introduced to robustify arbitrarily loss function. A new technique is proposed to alleviate the requirement on starting point such that on regular datasets the number of data reestimations can be substantially reduced. The obtained estimators, though not necessarily globally or even globally, enjoymax optimality in both low dimensions.
  arXiv  Detail & Related papers  (2021-12-15T20:35:21Z)
• Deep Efficient Continuous Manifold Learning for Time Series Modeling [11.876985348588477]
  A symmetric positive definite matrix is being studied in computer vision, signal processing, and medical image analysis. In this paper, we propose a framework to exploit a diffeomorphism mapping between Riemannian manifold and a Cholesky space. For dynamic modeling of time-series data, we devise a continuous manifold learning method by systematically integrating a manifold ordinary differential equation and a gated recurrent neural network.
  arXiv  Detail & Related papers  (2021-12-03T01:38:38Z)
• Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classification [69.26747803963907]
  Rank-R Feedforward Neural Network (FNN) is a tensor-based nonlinear learning model that imposes Canonical/Polyadic decomposition on its parameters. First, it handles inputs as multilinear arrays, bypassing the need for vectorization, and can thus fully exploit the structural information along every data dimension. We establish the universal approximation and learnability properties of Rank-R FNN, and we validate its performance on real-world hyperspectral datasets.
  arXiv  Detail & Related papers  (2021-04-11T16:37:32Z)
• A Local Similarity-Preserving Framework for Nonlinear Dimensionality Reduction with Neural Networks [56.068488417457935]
  We propose a novel local nonlinear approach named Vec2vec for general purpose dimensionality reduction. To train the neural network, we build the neighborhood similarity graph of a matrix and define the context of data points. Experiments of data classification and clustering on eight real datasets show that Vec2vec is better than several classical dimensionality reduction methods in the statistical hypothesis test.
  arXiv  Detail & Related papers  (2021-03-10T23:10:47Z)
• Deep Dimension Reduction for Supervised Representation Learning [51.10448064423656]
  We propose a deep dimension reduction approach to learning representations with essential characteristics. The proposed approach is a nonparametric generalization of the sufficient dimension reduction method. We show that the estimated deep nonparametric representation is consistent in the sense that its excess risk converges to zero.
  arXiv  Detail & Related papers  (2020-06-10T14:47:43Z)
• Large-Scale Gradient-Free Deep Learning with Recursive Local Representation Alignment [84.57874289554839]
  Training deep neural networks on large-scale datasets requires significant hardware resources. Backpropagation, the workhorse for training these networks, is an inherently sequential process that is difficult to parallelize. We propose a neuro-biologically-plausible alternative to backprop that can be used to train deep networks.
  arXiv  Detail & Related papers  (2020-02-10T16:20:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.