A least distance estimator for a multivariate regression model using deep neural networks

• URL: http://arxiv.org/abs/2401.03123v1
• Date: Sat, 6 Jan 2024 04:36:00 GMT
• Title: A least distance estimator for a multivariate regression model using deep neural networks
• Authors: Jungmin Shin, Seung Jun Shin, Sungwan Bang
• Abstract summary: (A)GDNN-LD estimator enjoys variable selection and model estimation simultaneously, by applying the (adaptive) group Lasso penalty to weight parameters in the DNN structure. For the computation, we propose a quadratic smoothing approximation method to facilitate optimizing the non-smooth objective function based on the least distance loss.
• Score: 1.8876415010297893
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and nonlinear conditional mean functions can be easily modeled, and a multivariate regression model can be realized by simply adding extra nodes at the output layer. The proposed method is more efficient in capturing the dependency structure among responses than the least squares loss, and robust to outliers. In addition, we consider $L_1$-type penalization for variable selection, crucial in analyzing high-dimensional data. Namely, we propose what we call (A)GDNN-LD estimator that enjoys variable selection and model estimation simultaneously, by applying the (adaptive) group Lasso penalty to weight parameters in the DNN structure. For the computation, we propose a quadratic smoothing approximation method to facilitate optimizing the non-smooth objective function based on the least distance loss. The simulation studies and a real data analysis demonstrate the promising performance of the proposed method.

Related papers

• Solving Inverse Problems with Model Mismatch using Untrained Neural Networks within Model-based Architectures [14.551812310439004]
  We introduce an untrained forward model residual block within the model-based architecture to match the data consistency in the measurement domain for each instance. Our approach offers a unified solution that is less parameter-sensitive, requires no additional data, and enables simultaneous fitting of the forward model and reconstruction in a single pass.
  arXiv  Detail & Related papers  (2024-03-07T19:02:13Z)
• The Convex Landscape of Neural Networks: Characterizing Global Optima and Stationary Points via Lasso Models [75.33431791218302]
  Deep Neural Network Network (DNN) models are used for programming purposes. In this paper we examine the use of convex neural recovery models. We show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program. We also show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program.
  arXiv  Detail & Related papers  (2023-12-19T23:04:56Z)
• Reducing the Need for Backpropagation and Discovering Better Optima With Explicit Optimizations of Neural Networks [4.807347156077897]
  We propose a computationally efficient alternative for optimizing neural networks. We derive an explicit solution to a simple feed-forward language model. We show that explicit solutions perform near-optimality in experiments.
  arXiv  Detail & Related papers  (2023-11-13T17:38:07Z)
• A multiobjective continuation method to compute the regularization path of deep neural networks [1.3654846342364308]
  Sparsity is a highly feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models, and robustness. We present an algorithm that allows for the entire sparse front for the above-mentioned objectives in a very efficient manner for high-dimensional gradients with millions of parameters. We demonstrate that knowledge of the regularization path allows for a well-generalizing network parametrization.
  arXiv  Detail & Related papers  (2023-08-23T10:08:52Z)
• Sparse-Input Neural Network using Group Concave Regularization [10.103025766129006]
  Simultaneous feature selection and non-linear function estimation are challenging in neural networks. We propose a framework of sparse-input neural networks using group concave regularization for feature selection in both low-dimensional and high-dimensional settings.
  arXiv  Detail & Related papers  (2023-07-01T13:47:09Z)
• Variational Linearized Laplace Approximation for Bayesian Deep Learning [11.22428369342346]
  We propose a new method for approximating Linearized Laplace Approximation (LLA) using a variational sparse Gaussian Process (GP) Our method is based on the dual RKHS formulation of GPs and retains, as the predictive mean, the output of the original DNN. It allows for efficient optimization, which results in sub-linear training time in the size of the training dataset.
  arXiv  Detail & Related papers  (2023-02-24T10:32:30Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Neural Stochastic Dual Dynamic Programming [99.80617899593526]
  We introduce a trainable neural model that learns to map problem instances to a piece-wise linear value function. $nu$-SDDP can significantly reduce problem solving cost without sacrificing solution quality.
  arXiv  Detail & Related papers  (2021-12-01T22:55:23Z)
• Meta-Solver for Neural Ordinary Differential Equations [77.8918415523446]
  We investigate how the variability in solvers' space can improve neural ODEs performance. We show that the right choice of solver parameterization can significantly affect neural ODEs models in terms of robustness to adversarial attacks.
  arXiv  Detail & Related papers  (2021-03-15T17:26:34Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)
• 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)

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.