Adaptive deep learning for nonlinear time series models

• URL: http://arxiv.org/abs/2207.02546v3
• Date: Fri, 3 May 2024 02:40:49 GMT
• Title: Adaptive deep learning for nonlinear time series models
• Authors: Daisuke Kurisu, Riku Fukami, Yuta Koike,
• Abstract summary: We develop a theory for adaptive nonparametric estimation of the mean function of a non-stationary and nonlinear time series model using deep neural networks (DNNs) We derive minimax lower bounds for estimating mean functions belonging to a wide class of nonlinear autoregressive (AR) models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we develop a general theory for adaptive nonparametric estimation of the mean function of a non-stationary and nonlinear time series model using deep neural networks (DNNs). We first consider two types of DNN estimators, non-penalized and sparse-penalized DNN estimators, and establish their generalization error bounds for general non-stationary time series. We then derive minimax lower bounds for estimating mean functions belonging to a wide class of nonlinear autoregressive (AR) models that include nonlinear generalized additive AR, single index, and threshold AR models. Building upon the results, we show that the sparse-penalized DNN estimator is adaptive and attains the minimax optimal rates up to a poly-logarithmic factor for many nonlinear AR models. Through numerical simulations, we demonstrate the usefulness of the DNN methods for estimating nonlinear AR models with intrinsic low-dimensional structures and discontinuous or rough mean functions, which is consistent with our theory.

Related papers

• 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)
• Efficient Interpretable Nonlinear Modeling for Multiple Time Series [5.448070998907116]
  This paper proposes an efficient nonlinear modeling approach for multiple time series. It incorporates nonlinear interactions among different time-series variables. Experimental results show that the proposed algorithm improves the identification of the support of the VAR coefficients in a parsimonious manner.
  arXiv  Detail & Related papers  (2023-09-29T11:42:59Z)
• Optimistic Estimate Uncovers the Potential of Nonlinear Models [3.0041514772139166]
  We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models. We estimate the optimistic sample sizes for matrix factorization models, deep models, and deep neural networks (DNNs) with fully-connected or convolutional architecture.
  arXiv  Detail & Related papers  (2023-07-18T01:37:57Z)
• A graph convolutional autoencoder approach to model order reduction for parametrized PDEs [0.8192907805418583]
  The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM) We develop a non-intrusive and data-driven nonlinear reduction approach, exploiting GNNs to encode the reduced manifold and enable fast evaluations of parametrized PDEs.
  arXiv  Detail & Related papers  (2023-05-15T12:01:22Z)
• 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)
• Deep Neural Network Based Accelerated Failure Time Models using Rank Loss [0.0]
  An accelerated failure time (AFT) model assumes a log-linear relationship between failure times and a set of covariates. Deep neural networks (DNNs) have received a focal attention over the past decades and have achieved remarkable success in a variety of fields. We propose to apply DNNs in fitting AFT models using a Gehan-type loss, combined with a sub-sampling technique.
  arXiv  Detail & Related papers  (2022-06-13T08:38:18Z)
• Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns [77.34726150561087]
  We introduce four complicated missing patterns, including missing and three fiber-like missing cases according to the mode-drivenn fibers. Despite nonity of the objective function in our model, we derive the optimal solutions by integrating alternating data-mputation method of multipliers.
  arXiv  Detail & Related papers  (2022-05-19T08:37:56Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• 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)
• Lower Bounds on the Generalization Error of Nonlinear Learning Models [2.1030878979833467]
  We study in this paper lower bounds for the generalization error of models derived from multi-layer neural networks, in the regime where the size of the layers is commensurate with the number of samples in the training data. We show that unbiased estimators have unacceptable performance for such nonlinear networks in this regime. We derive explicit generalization lower bounds for general biased estimators, in the cases of linear regression and of two-layered networks.
  arXiv  Detail & Related papers  (2021-03-26T20:37:54Z)
• LQF: Linear Quadratic Fine-Tuning [114.3840147070712]
  We present the first method for linearizing a pre-trained model that achieves comparable performance to non-linear fine-tuning. LQF consists of simple modifications to the architecture, loss function and optimization typically used for classification.
  arXiv  Detail & Related papers  (2020-12-21T06:40:20Z)

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.