An Efficient Approach to Regression Problems with Tensor Neural Networks

• URL: http://arxiv.org/abs/2406.09694v2
• Date: Fri, 13 Sep 2024 02:46:51 GMT
• Title: An Efficient Approach to Regression Problems with Tensor Neural Networks
• Authors: Yongxin Li, Yifan Wang, Zhongshuo Lin, Hehu Xie,
• Abstract summary: This paper introduces a tensor neural network (TNN) to address nonparametric regression problems. The TNN demonstrates superior performance compared to conventional Feed-Forward Networks (FFN) and Radial Basis Function Networks (RBN) A significant innovation in our approach is the integration of statistical regression and numerical integration within the TNN framework.
• Score: 5.345144592056051
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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, high-dimensional functions. The TNN demonstrates superior performance compared to conventional Feed-Forward Networks (FFN) and Radial Basis Function Networks (RBN) in terms of both approximation accuracy and generalization capacity, even with a comparable number of parameters. A significant innovation in our approach is the integration of statistical regression and numerical integration within the TNN framework. This allows for efficient computation of high-dimensional integrals associated with the regression function and provides detailed insights into the underlying data structure. Furthermore, we employ gradient and Laplacian analysis on the regression outputs to identify key dimensions influencing the predictions, thereby guiding the design of subsequent experiments. These advancements make TNN a powerful tool for applications requiring precise high-dimensional data analysis and predictive modeling.

Related papers

• A Functional Extension of Semi-Structured Networks [2.482050942288848]
  Semi-structured networks (SSNs) merge structures familiar from additive models with deep neural networks. Inspired by large-scale datasets, this paper explores extending SSNs to functional data. We propose a functional SSN method that retains the advantageous properties of classical functional regression approaches while also improving scalability.
  arXiv  Detail & Related papers  (2024-10-07T18:50:18Z)
• On the Convergence Analysis of Over-Parameterized Variational Autoencoders: A Neural Tangent Kernel Perspective [7.580900499231056]
  Variational Auto-Encoders (VAEs) have emerged as powerful probabilistic models for generative tasks. This paper provides a mathematical proof of VAE under mild assumptions. We also establish a novel connection between the optimization problem faced by over-Eized SNNs and the Kernel Ridge (KRR) problem.
  arXiv  Detail & Related papers  (2024-09-09T06:10:31Z)
• Nonlinear functional regression by functional deep neural network with kernel embedding [20.306390874610635]
  We propose a functional deep neural network with an efficient and fully data-dependent dimension reduction method. The architecture of our functional net consists of a kernel embedding step, a projection step, and a deep ReLU neural network for the prediction. The utilization of smooth kernel embedding enables our functional net to be discretization invariant, efficient, and robust to noisy observations.
  arXiv  Detail & Related papers  (2024-01-05T16:43:39Z)
• End-to-End Meta-Bayesian Optimisation with Transformer Neural Processes [52.818579746354665]
  This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data.
  arXiv  Detail & Related papers  (2023-05-25T10:58:46Z)
• Learning Low Dimensional State Spaces with Overparameterized Recurrent Neural Nets [57.06026574261203]
  We provide theoretical evidence for learning low-dimensional state spaces, which can also model long-term memory. Experiments corroborate our theory, demonstrating extrapolation via learning low-dimensional state spaces with both linear and non-linear RNNs.
  arXiv  Detail & Related papers  (2022-10-25T14:45:15Z)
• Orthogonal Stochastic Configuration Networks with Adaptive Construction Parameter for Data Analytics [6.940097162264939]
  randomness makes SCNs more likely to generate approximate linear correlative nodes that are redundant and low quality. In light of a fundamental principle in machine learning, that is, a model with fewer parameters holds improved generalization. This paper proposes orthogonal SCN, termed OSCN, to filtrate out the low-quality hidden nodes for network structure reduction.
  arXiv  Detail & Related papers  (2022-05-26T07:07:26Z)
• Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks [64.23331120621118]
  We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs) INNs are a class of implicit learning models that use implicit equations as layers. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs.
  arXiv  Detail & Related papers  (2022-04-01T03:31:27Z)
• 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)
• Modeling from Features: a Mean-field Framework for Over-parameterized Deep Neural Networks [54.27962244835622]
  This paper proposes a new mean-field framework for over- parameterized deep neural networks (DNNs) In this framework, a DNN is represented by probability measures and functions over its features in the continuous limit. We illustrate the framework via the standard DNN and the Residual Network (Res-Net) architectures.
  arXiv  Detail & Related papers  (2020-07-03T01:37:16Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• A deep learning framework for solution and discovery in solid mechanics [1.4699455652461721]
  We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and elasticity relations into PINN, and explore in detail the application to linear elasticity.
  arXiv  Detail & Related papers  (2020-02-14T08:24:53Z)

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.