Deep Neural Networks (DNNs) often rely on very large datasets for training. Given the large size of such datasets, it is conceivable that they contain certain samples that either do not contribute or negatively impact the DNN's performance. If there is a large number of such samples, subsampling the training dataset in a way that removes them could provide an effective solution to both improve performance and reduce training time. In this paper, we propose an approach called Active Dataset Subsampling (ADS), to identify favorable subsets within a dataset for training using ensemble based uncertainty estimation. When applied to three image classification benchmarks (CIFAR-10, CIFAR-100 and ImageNet) we find that there are low uncertainty subsets, which can be as large as 50 of the full dataset, that negatively impact performance. These subsets are identified and removed with ADS. We demonstrate that datasets obtained using ADS with a lightweight ResNet-18 ensemble remain effective when used to train deeper models like ResNet-101. Our results provide strong empirical evidence that using all the available data for training can hurt performance on large scale vision tasks.
Uncertainty estimation is a key component of ADS. Due to several important applications, such as active learning and adversarial sample detection, techniques to improve the uncertainty estimates of a DNN have recently gained significant momentum @cite_2 @cite_32 . These techniques may be broadly categorized into (i) Bayesian @cite_12 @cite_26 @cite_16 and (ii) non-Bayesian techniques @cite_29 @cite_8 . Bayesian techniques approximate a class of neural networks called Bayesian Neural Networks (BNNs) @cite_14 . When BNNs are trained, each weight in the network takes the form of a probability distribution in the parameter space. However, training a BNN involves marginalization over all possible assignments of weights, which is intractable for deep BNNs without approximations @cite_12 @cite_26 @cite_16 . Due to this, these approaches have traditionally been computationally more demanding and conceptually more complicated than non-Bayesian ones @cite_29 @cite_8 .
@cite_26 @cite_14 @cite_8 @cite_29 @cite_32 @cite_2 @cite_16 @cite_12
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Annotating the right data for training deep neural networks is an important challenge. Active learning using uncertainty estimates from Bayesian Neural Networks (BNNs) could provide an effective solution to this. Despite being theoretically principled, BNNs require approximations to be applied to large-scale problems, where both performance and uncertainty estimation are crucial. In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep BNN. We conduct a series of large-scale visual active learning experiments to evaluate DPEs on classification with the CIFAR-10, CIFAR-100 and ImageNet datasets, and semantic segmentation with the BDD100k dataset. Our models require significantly less training data to achieve competitive performances, and steadily improve upon strong active learning baselines as the annotation budget is increased. As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modelling uncertainty is one of the key features of Bayesian methods. Bayesian DNNs that use dropout-based variational distributions and scale to complex tasks have recently been proposed. We evaluate Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We compare these Bayesian DNNs ability to represent their uncertainty about their outputs through sampling during inference. We tested the calibration of these Bayesian fully connected and convolutional DNNs on two visual inference tasks (MNIST and CIFAR-10). By adding different levels of Gaussian noise to the test images, we assessed how these DNNs represented their uncertainty about regions of input space not covered by the training set. These Bayesian DNNs represented their own uncertainty more accurately than traditional DNNs with a softmax output. We find that sampling of weights, whether Gaussian or Bernoulli, led to more accurate representation of uncertainty compared to sampling of units. However, sampling units using either Gaussian or Bernoulli dropout led to increased convolutional neural network (CNN) classification accuracy. Based on these findings we use both Bernoulli dropout and Gaussian dropconnect concurrently, which approximates the use of a spike-and-slab variational distribution. We find that networks with spike-and-slab sampling combine the advantages of the other methods: they classify with high accuracy and robustly represent the uncertainty of their classifications for all tested architectures. As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modeling uncertainty is one of the key features of Bayesian methods. Using Bernoulli dropout with sampling at prediction time has recently been proposed as an efficient and well performing variational inference method for DNNs. However, sampling from other multiplicative noise based variational distributions has not been investigated in depth. We evaluated Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We tested the calibration of the probabilistic predictions of Bayesian convolutional neural networks (CNNs) on MNIST and CIFAR-10. Sampling at prediction time increased the calibration of the DNNs' probabalistic predictions. Sampling weights, whether Gaussian or Bernoulli, led to more robust representation of uncertainty compared to sampling of units. However, using either Gaussian or Bernoulli dropout led to increased test set classification accuracy. Based on these findings we used both Bernoulli dropout and Gaussian dropconnect concurrently, which we show approximates the use of a spike-and-slab variational distribution without increasing the number of learned parameters. We found that spike-and-slab sampling had higher test set performance than Gaussian dropconnect and more robustly represented its uncertainty compared to Bernoulli dropout. Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defined directly on stochastic processes, i.e. distributions over functions. We prove that the KL divergence between stochastic processes equals the supremum of marginal KL divergences over all finite sets of inputs. Based on this, we introduce a practical training objective which approximates the functional ELBO using finite measurement sets and the spectral Stein gradient estimator. With fBNNs, we can specify priors entailing rich structures, including Gaussian processes and implicit stochastic processes. Empirically, we find fBNNs extrapolate well using various structured priors, provide reliable uncertainty estimates, and scale to large datasets.