Consistent Sparse Deep Learning: Theory and Computation

• URL: http://arxiv.org/abs/2102.13229v1
• Date: Thu, 25 Feb 2021 23:31:24 GMT
• Title: Consistent Sparse Deep Learning: Theory and Computation
• Authors: Yan Sun, Qifan Song, Faming Liang
• Abstract summary: We propose a frequentist-like method for learning sparse deep learning networks (DNNs) The proposed method can perform very well for large-scale network compression and high-dimensional nonlinear variable selection.
• Score: 11.24471623055182
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most $O(n/\log(n))$ connections and nice theoretical guarantees such as posterior consistency, variable selection consistency and asymptotically optimal generalization bounds. In particular, we establish posterior consistency for the sparse DNN with a mixture Gaussian prior, show that the structure of the sparse DNN can be consistently determined using a Laplace approximation-based marginal posterior inclusion probability approach, and use Bayesian evidence to elicit sparse DNNs learned by an optimization method such as stochastic gradient descent in multiple runs with different initializations. The proposed method is computationally more efficient than standard Bayesian methods for large-scale sparse DNNs. The numerical results indicate that the proposed method can perform very well for large-scale network compression and high-dimensional nonlinear variable selection, both advancing interpretable machine learning.

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)
• 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)
• 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)
• AskewSGD : An Annealed interval-constrained Optimisation method to train Quantized Neural Networks [12.229154524476405]
  We develop a new algorithm, Annealed Skewed SGD - AskewSGD - for training deep neural networks (DNNs) with quantized weights. Unlike algorithms with active sets and feasible directions, AskewSGD avoids projections or optimization under the entire feasible set. Experimental results show that the AskewSGD algorithm performs better than or on par with state of the art methods in classical benchmarks.
  arXiv  Detail & Related papers  (2022-11-07T18:13:44Z)
• Masked Bayesian Neural Networks : Computation and Optimality [1.3649494534428745]
  We propose a novel sparse Bayesian neural network (BNN) which searches a good deep neural network with an appropriate complexity. We employ the masking variables at each node which can turn off some nodes according to the posterior distribution to yield a nodewise sparse DNN. By analyzing several benchmark datasets, we illustrate that the proposed BNN performs well compared to other existing methods.
  arXiv  Detail & Related papers  (2022-06-02T02:59:55Z)
• Variational Sparse Coding with Learned Thresholding [6.737133300781134]
  We propose a new approach to variational sparse coding that allows us to learn sparse distributions by thresholding samples. We first evaluate and analyze our method by training a linear generator, showing that it has superior performance, statistical efficiency, and gradient estimation.
  arXiv  Detail & Related papers  (2022-05-07T14:49:50Z)
• 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)
• Scaling Structured Inference with Randomization [64.18063627155128]
  We propose a family of dynamic programming (RDP) randomized for scaling structured models to tens of thousands of latent states. Our method is widely applicable to classical DP-based inference. It is also compatible with automatic differentiation so can be integrated with neural networks seamlessly.
  arXiv  Detail & Related papers  (2021-12-07T11:26:41Z)
• Improving predictions of Bayesian neural nets via local linearization [79.21517734364093]
  We argue that the Gauss-Newton approximation should be understood as a local linearization of the underlying Bayesian neural network (BNN) Because we use this linearized model for posterior inference, we should also predict using this modified model instead of the original one. We refer to this modified predictive as "GLM predictive" and show that it effectively resolves common underfitting problems of the Laplace approximation.
  arXiv  Detail & Related papers  (2020-08-19T12:35:55Z)
• Fast Learning of Graph Neural Networks with Guaranteed Generalizability: One-hidden-layer Case [93.37576644429578]
  Graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice. We provide a theoretically-grounded generalizability analysis of GNNs with one hidden layer for both regression and binary classification problems.
  arXiv  Detail & Related papers  (2020-06-25T00:45:52Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)

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.