Fixed-Mean Gaussian Processes for Post-hoc Bayesian Deep Learning

• URL: http://arxiv.org/abs/2412.04177v1
• Date: Thu, 05 Dec 2024 14:17:16 GMT
• Title: Fixed-Mean Gaussian Processes for Post-hoc Bayesian Deep Learning
• Authors: Luis A. Ortega, Simón Rodríguez-Santana, Daniel Hernández-Lobato,
• Abstract summary: We introduce a novel family of sparse variational Gaussian processes (GPs), where the posterior mean is fixed to any continuous function when using a universal kernel. Specifically, we fix the mean of this GP to the output of the pre-trained DNN, allowing our approach to effectively fit the GP's predictive variances to estimate the prediction uncertainty. Experimental results demonstrate that FMGP improves both uncertainty estimation and computational efficiency when compared to state-of-the-art methods.
• Score: 11.22428369342346
• License:
• Abstract: Recently, there has been an increasing interest in performing post-hoc uncertainty estimation about the predictions of pre-trained deep neural networks (DNNs). Given a pre-trained DNN via back-propagation, these methods enhance the original network by adding output confidence measures, such as error bars, without compromising its initial accuracy. In this context, we introduce a novel family of sparse variational Gaussian processes (GPs), where the posterior mean is fixed to any continuous function when using a universal kernel. Specifically, we fix the mean of this GP to the output of the pre-trained DNN, allowing our approach to effectively fit the GP's predictive variances to estimate the DNN prediction uncertainty. Our approach leverages variational inference (VI) for efficient stochastic optimization, with training costs that remain independent of the number of training points, scaling efficiently to large datasets such as ImageNet. The proposed method, called fixed mean GP (FMGP), is architecture-agnostic, relying solely on the pre-trained model's outputs to adjust the predictive variances. Experimental results demonstrate that FMGP improves both uncertainty estimation and computational efficiency when compared to state-of-the-art methods.

Related papers

• Tractable Function-Space Variational Inference in Bayesian Neural Networks [72.97620734290139]
  A popular approach for estimating the predictive uncertainty of neural networks is to define a prior distribution over the network parameters. We propose a scalable function-space variational inference method that allows incorporating prior information. We show that the proposed method leads to state-of-the-art uncertainty estimation and predictive performance on a range of prediction tasks.
  arXiv  Detail & Related papers  (2023-12-28T18:33:26Z)
• Leveraging Locality and Robustness to Achieve Massively Scalable Gaussian Process Regression [1.3518297878940662]
  We introduce a new perspective by exploring robustness properties and limiting behaviour of GP nearest-neighbour (GPnn) prediction. As the data-size n increases, accuracy of estimated parameters and GP model assumptions become increasingly irrelevant to GPnn predictive accuracy. We show that this source of inaccuracy can be corrected for, thereby achieving both well-calibrated uncertainty measures and accurate predictions at remarkably low computational cost.
  arXiv  Detail & Related papers  (2023-06-26T14:32:46Z)
• 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)
• Improved uncertainty quantification for neural networks with Bayesian last layer [0.0]
  Uncertainty quantification is an important task in machine learning. We present a reformulation of the log-marginal likelihood of a NN with BLL which allows for efficient training using backpropagation.
  arXiv  Detail & Related papers  (2023-02-21T20:23:56Z)
• Deep Neural Networks as Point Estimates for Deep Gaussian Processes [44.585609003513625]
  We propose a sparse variational approximation for DGPs for which the approximate posterior mean has the same mathematical structure as a Deep Neural Network (DNN) We make the forward pass through a DGP equivalent to a ReLU DNN by finding an interdomain transformation that represents the GP posterior mean as a sum of ReLU basis functions. Experiments demonstrate improved accuracy and faster training compared to current DGP methods, while retaining favourable predictive uncertainties.
  arXiv  Detail & Related papers  (2021-05-10T16:55:17Z)
• Sampling-free Variational Inference for Neural Networks with Multiplicative Activation Noise [51.080620762639434]
  We propose a more efficient parameterization of the posterior approximation for sampling-free variational inference. Our approach yields competitive results for standard regression problems and scales well to large-scale image classification tasks.
  arXiv  Detail & Related papers  (2021-03-15T16:16:18Z)
• Improving Uncertainty Calibration via Prior Augmented Data [56.88185136509654]
  Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. They are often overconfident in their predictions, which leads to inaccurate and miscalibrated probabilistic predictions. We propose a solution by seeking out regions of feature space where the model is unjustifiably overconfident, and conditionally raising the entropy of those predictions towards that of the prior distribution of the labels.
  arXiv  Detail & Related papers  (2021-02-22T07:02:37Z)
• 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)
• Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift [100.52588638477862]
  We develop an approximate Bayesian inference scheme based on posterior regularisation. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
  arXiv  Detail & Related papers  (2020-06-26T13:50:19Z)
• Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functions [121.10450359856242]
  Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Existing approaches for uncertainty quantification in RNNs are based predominantly on Bayesian methods. We develop a frequentist alternative that: (a) does not interfere with model training or compromise its accuracy, (b) applies to any RNN architecture, and (c) provides theoretical coverage guarantees on the estimated uncertainty intervals.
  arXiv  Detail & Related papers  (2020-06-20T22:45:32Z)

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.