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Register a new userGreedy Bayesian Posterior Approximation with Deep Ensembles
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Aleksei Tiulpin
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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.
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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.
In this paper, we present a general framework for distilling expectations with respect to the Bayesian posterior distribution of a deep neural network classifier, extending prior work on the Bayesian Dark Knowledge framework. The proposed framework takes as input teacher and student model architectures and a general posterior expectation of interest. The distillation method performs an online compression of the selected posterior expectation using iteratively generated Monte Carlo samples. We focus on the posterior predictive distribution and expected entropy as distillation targets. We investigate several aspects of this framework including the impact of uncertainty and the choice of student model architecture. We study methods for student model architecture search from a speed-storage-accuracy perspective and evaluate down-stream tasks leveraging entropy distillation including uncertainty ranking and out-of-distribution detection.
In the low-data regime, it is difficult to train good supervised models from scratch. Instead practitioners turn to pre-trained models, leveraging transfer learning. Ensembling is an empirically and theoretically appealing way to construct powerful predictive models, but the predominant approach of training multiple deep networks with different random initialisations collides with the need for transfer via pre-trained weights. In this work, we study different ways of creating ensembles from pre-trained models. We show that the nature of pre-training itself is a performant source of diversity, and propose a practical algorithm that efficiently identifies a subset of pre-trained models for any downstream dataset. The approach is simple: Use nearest-neighbour accuracy to rank pre-trained models, fine-tune the best ones with a small hyperparameter sweep, and greedily construct an ensemble to minimise validation cross-entropy. When evaluated together with strong baselines on 19 different downstream tasks (the Visual Task Adaptation Benchmark), this achieves state-of-the-art performance at a much lower inference budget, even when selecting from over 2,000 pre-trained models. We also assess our ensembles on ImageNet variants and show improved robustness to distribution shift.
We introduce a new and rigorously-formulated PAC-Bayes few-shot meta-learning algorithm that implicitly learns a prior distribution of the model of interest. Our proposed method extends the PAC-Bayes framework from a single task setting to the few-shot learning setting to upper-bound generalisation errors on unseen tasks and samples. We also propose a generative-based approach to model the shared prior and the posterior of task-specific model parameters more expressively compared to the usual diagonal Gaussian assumption. We show that the models trained with our proposed meta-learning algorithm are well calibrated and accurate, with state-of-the-art calibration and classification results on few-shot classification (mini-ImageNet and tiered-ImageNet) and regression (multi-modal task-distribution regression) benchmarks.
Uncertainty quantification for deep neural networks has recently evolved through many techniques. In this work, we revisit Laplace approximation, a classical approach for posterior approximation that is computationally attractive. However, instead of computing the curvature matrix, we show that, under some regularity conditions, the Laplace approximation can be easily constructed using the gradient second moment. This quantity is already estimated by many exponential moving average variants of Adagrad such as Adam and RMSprop, but is traditionally discarded after training. We show that our method (L2M) does not require changes in models or optimization, can be implemented in a few lines of code to yield reasonable results, and it does not require any extra computational steps besides what is already being computed by optimizers, without introducing any new hyperparameter. We hope our method can open new research directions on using quantities already computed by optimizers for uncertainty estimation in deep neural networks.
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