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Deep ensembles have recently gained popularity in the deep learning community for their conceptual simplicity and efficiency. However, maintaining functional diversity between ensemble members that are independently trained with gradient descent is challenging. This can lead to pathologies when adding more ensemble members, such as a saturation of the ensemble performance, which converges to the performance of a single model. Moreover, this does not only affect the quality of its predictions, but even more so the uncertainty estimates of the ensemble, and thus its performance on out-of-distribution data. We hypothesize that this limitation can be overcome by discouraging different ensemble members from collapsing to the same function. To this end, we introduce a kernelized repulsive term in the update rule of the deep ensembles. We show that this simple modification not only enforces and maintains diversity among the members but, even more importantly, transforms the maximum a posteriori inference into proper Bayesian inference. Namely, we show that the training dynamics of our proposed repulsive ensembles follow a Wasserstein gradient flow of the KL divergence with the true posterior. We study repulsive terms in weight and function space and empirically compare their performance to standard ensembles and Bayesian baselines on synthetic and real-world prediction tasks.
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Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta functions. The training of ensembles relies on non-convexity of the loss landscape and random initialization of their individual members, making the resulting posterior approximation uncontrolled. This paper proposes a novel and principled method to tackle this limitation, minimizing an $f$-divergence between the true posterior and a kernel density estimator in a function space. We analyze this objective from a combinatorial point of view, and show that it is submodular with respect to mixture components for any $f$. Subsequently, we consider the problem of greedy ensemble construction, and from the marginal gain of the total objective, we derive a novel diversity term for ensemble methods. The performance of our approach is demonstrated on computer vision out-of-distribution benchmarks in a range of architectures trained on multiple datasets. The source code of our method is publicly available at https://github.com/MIPT-Oulu/greedy_ensembles_training.
Deep learning models have demonstrated outstanding performance in several problems, but their training process tends to require immense amounts of computational and human resources for training and labeling, constraining the types of problems that can be tackled. Therefore, the design of effective training methods that require small labeled training sets is an important research direction that will allow a more effective use of resources.Among current approaches designed to address this issue, two are particularly interesting: data augmentation and active learning. Data augmentation achieves this goal by artificially generating new training points, while active learning relies on the selection of the most informative subset of unlabeled training samples to be labelled by an oracle. Although successful in practice, data augmentation can waste computational resources because it indiscriminately generates samples that are not guaranteed to be informative, and active learning selects a small subset of informative samples (from a large un-annotated set) that may be insufficient for the training process. In this paper, we propose a Bayesian generative active deep learning approach that combines active learning with data augmentation -- we provide theoretical and empirical evidence (MNIST, CIFAR-${10,100}$, and SVHN) that our approach has more efficient training and better classification results than data augmentation and active learning.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the models predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
Bayesian formulations of deep learning have been shown to have compelling theoretical properties and offer practical functional benefits, such as improved predictive uncertainty quantification and model selection. The Laplace approximation (LA) is a classic, and arguably the simplest family of approximations for the intractable posteriors of deep neural networks. Yet, despite its simplicity, the LA is not as popular as alternatives like variational Bayes or deep ensembles. This may be due to assumptions that the LA is expensive due to the involved Hessian computation, that it is difficult to implement, or that it yields inferior results. In this work we show that these are misconceptions: we (i) review the range of variants of the LA includin
Reinforcement learning (RL) has gained increasing interest since the demonstration it was able to reach human performance on video game benchmarks using deep Q-learning (DQN). The current consensus for training neural networks on such complex environments is to rely on gradient-based optimization. Although alternative Bayesian deep learning methods exist, most of them still rely on gradient-based optimization, and they typically do not scale on benchmarks such as the Atari game environment. Moreover none of these approaches allow performing the analytical inference for the weights and biases defining the neural network. In this paper, we present how we can adapt the temporal difference Q-learning framework to make it compatible with the tractable approximate Gaussian inference (TAGI), which allows learning the parameters of a neural network using a closed-form analytical method. Throughout the experiments with on- and off-policy reinforcement learning approaches, we demonstrate that TAGI can reach a performance comparable to backpropagation-trained networks while using fewer hyperparameters, and without relying on gradient-based optimization.
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