Learning Structured Gaussians to Approximate Deep Ensembles

• URL: http://arxiv.org/abs/2203.15485v1
• Date: Tue, 29 Mar 2022 12:34:43 GMT
• Title: Learning Structured Gaussians to Approximate Deep Ensembles
• Authors: Ivor J.A. Simpson, Sara Vicente, Neill D.F. Campbell
• Abstract summary: This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approxorimator for dense image prediction tasks. We capture the uncertainty and structured correlations in the predictions explicitly in a formal distribution, rather than implicitly through sampling alone. We demonstrate the merits of our approach on monocular depth estimation and show that the advantages of our approach are obtained with comparable quantitative performance.
• Score: 10.055143995729415
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approximator for the output of probabilistic ensemble models used for dense image prediction tasks. This is achieved through a convolutional neural network that predicts the mean and covariance of the distribution, where the inverse covariance is parameterised by a sparsely structured Cholesky matrix. Similarly to distillation approaches, our single network is trained to maximise the probability of samples from pre-trained probabilistic models, in this work we use a fixed ensemble of networks. Once trained, our compact representation can be used to efficiently draw spatially correlated samples from the approximated output distribution. Importantly, this approach captures the uncertainty and structured correlations in the predictions explicitly in a formal distribution, rather than implicitly through sampling alone. This allows direct introspection of the model, enabling visualisation of the learned structure. Moreover, this formulation provides two further benefits: estimation of a sample probability, and the introduction of arbitrary spatial conditioning at test time. We demonstrate the merits of our approach on monocular depth estimation and show that the advantages of our approach are obtained with comparable quantitative performance.

Related papers

• Uncertainty Quantification via Stable Distribution Propagation [60.065272548502]
  We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity.
  arXiv  Detail & Related papers  (2024-02-13T09:40:19Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Implicit Variational Inference for High-Dimensional Posteriors [7.924706533725115]
  In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler.
  arXiv  Detail & Related papers  (2023-10-10T14:06:56Z)
• Continuous and Distribution-free Probabilistic Wind Power Forecasting: A Conditional Normalizing Flow Approach [1.684864188596015]
  We present a data-driven approach for probabilistic wind power forecasting based on conditional normalizing flow (CNF) In contrast with the existing, this approach is distribution-free (as for non-parametric and quantile-based approaches) and can directly yield continuous probability densities.
  arXiv  Detail & Related papers  (2022-06-06T08:48:58Z)
• Wrapped Distributions on homogeneous Riemannian manifolds [58.720142291102135]
  Control over distributions' properties, such as parameters, symmetry and modality yield a family of flexible distributions. We empirically validate our approach by utilizing our proposed distributions within a variational autoencoder and a latent space network model.
  arXiv  Detail & Related papers  (2022-04-20T21:25:21Z)
• Aggregating distribution forecasts from deep ensembles [0.0]
  We study the question of how to aggregate distribution forecasts based on neural network-based approaches. We show that combining forecast distributions can substantially improve the predictive performance. We propose a general quantile aggregation framework for deep ensembles that shows superior performance compared to a linear combination of the forecast densities.
  arXiv  Detail & Related papers  (2022-04-05T15:42:51Z)
• Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
  We take a two-step approach by first modeling the probability distribution and then sampling from that model. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
  arXiv  Detail & Related papers  (2021-10-20T12:25:22Z)
• A likelihood approach to nonparametric estimation of a singular distribution using deep generative models [4.329951775163721]
  We investigate a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. We prove that a novel and effective solution exists by perturbing the data with an instance noise. We also characterize the class of distributions that can be efficiently estimated via deep generative models.
  arXiv  Detail & Related papers  (2021-05-09T23:13:58Z)
• Calibrated Adversarial Refinement for Stochastic Semantic Segmentation [5.849736173068868]
  We present a strategy for learning a calibrated predictive distribution over semantic maps, where the probability associated with each prediction reflects its ground truth correctness likelihood. We demonstrate the versatility and robustness of the approach by achieving state-of-the-art results on the multigrader LIDC dataset and on a modified Cityscapes dataset with injected ambiguities. We show that the core design can be adapted to other tasks requiring learning a calibrated predictive distribution by experimenting on a toy regression dataset.
  arXiv  Detail & Related papers  (2020-06-23T16:39:59Z)
• Spatially Adaptive Inference with Stochastic Feature Sampling and Interpolation [72.40827239394565]
  We propose to compute features only at sparsely sampled locations. We then densely reconstruct the feature map with an efficient procedure. The presented network is experimentally shown to save substantial computation while maintaining accuracy over a variety of computer vision tasks.
  arXiv  Detail & Related papers  (2020-03-19T15:36:31Z)
• Bayesian Deep Learning and a Probabilistic Perspective of Generalization [56.69671152009899]
  We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization. We also propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction.
  arXiv  Detail & Related papers  (2020-02-20T15:13:27Z)

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.