We present a deep learning framework for probabilistic pixel-wise semantic segmentation, which we term Bayesian SegNet. Semantic segmentation is an important tool for visual scene understanding and a meaningful measure of uncertainty is essential for decision making. Our contribution is a practical system which is able to predict pixel-wise class labels with a measure of model uncertainty. We achieve this by Monte Carlo sampling with dropout at test time to generate a posterior distribution of pixel class labels. In addition, we show that modelling uncertainty improves segmentation performance by 2-3 across a number of state of the art architectures such as SegNet, FCN and Dilation Network, with no additional parametrisation. We also observe a significant improvement in performance for smaller datasets where modelling uncertainty is more effective. We benchmark Bayesian SegNet on the indoor SUN Scene Understanding and outdoor CamVid driving scenes datasets.
Neural networks which model uncertainty are known as Bayesian neural networks @cite_29 @cite_9 . They offer a probabilistic interpretation of deep learning models by inferring distributions over the networks’ weights. They are often computationally very expensive, increasing the number of model parameters without increasing model capacity significantly. Performing inference in Bayesian neural networks is a difficult task, and approximations to the model posterior are often used, such as variational inference @cite_28 .
@cite_28 @cite_9 @cite_29
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Bayesian probability theory provides a unifying framework for data modelling. In this framework the overall aims are to find models that are well-matched to the data, and to use these models to make optimal predictions. Neural network learning is interpreted as an inference of the most probable parameters for the model, given the training data. The search in model space (i.e., the space of architectures, noise models, preprocessings, regularizers and weight decay constants) can then also be treated as an inference problem, in which we infer the relative probability of alternative models, given the data. This review describes practical techniques based on Gaussian approximations for implementation of these powerful methods for controlling, comparing and using adaptive networks. 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. Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally efficient. With wide recognition of potential advantages, why is it that variational Bayes has seen very limited practical use for BNNs in real applications? We argue that variational inference in neural networks is fragile: successful implementations require careful initialization and tuning of prior variances, as well as controlling the variance of Monte Carlo gradient estimates. We fix VB and turn it into a robust inference tool for Bayesian neural networks. We achieve this with two innovations: first, we introduce a novel deterministic method to approximate moments in neural networks, eliminating gradient variance; second, we introduce a hierarchical prior for parameters and a novel empirical Bayes procedure for automatically selecting prior variances. Combining these two innovations, the resulting method is highly efficient and robust. On the application of heteroscedastic regression we demonstrate strong predictive performance over alternative approaches. Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs overfit quickly. We present an efficient Bayesian CNN, offering better robustness to over-fitting on small data than traditional approaches. This is by placing a probability distribution over the CNN's kernels. We approximate our model's intractable posterior with Bernoulli variational distributions, requiring no additional model parameters. On the theoretical side, we cast dropout network training as approximate inference in Bayesian neural networks. This allows us to implement our model using existing tools in deep learning with no increase in time complexity, while highlighting a negative result in the field. We show a considerable improvement in classification accuracy compared to standard techniques and improve on published state-of-the-art results for CIFAR-10.