Deep learning provides a powerful tool for robotic perception in the open world. However, real-world robotic systems, especially mobile robots, must be able to react intelligently and safely even in unexpected circumstances. This requires a system that knows what it knows, and can estimate its own uncertainty for unfamiliar, out-of-distribution observations. Approximate Bayesian approaches are commonly used to estimate uncertainty for neural network predictions, but struggle with out-of-distribution observations. Generative models can in principle detect out-of-distribution observations as those with a low estimated density, but overly pessimistic as an uncertainty measure, since the mere presence of an out-of-distribution input does not by itself indicate an unsafe situation. Intuitively, we would like a perception system that can detect when task-salient parts of the image are unfamiliar or uncertain, while ignoring task-irrelevant features. In this paper, we present a method for uncertainty-aware robotic perception that combines generative modeling and model uncertainty. Our method estimates an uncertainty measure about the model’s prediction, taking into account an explicit generative model of the observation distribution to handle out-of-distribution inputs. We evaluate our method on an action-conditioned collision prediction task with both simulated and real data, and demonstrate that our approach improves on a variety of Bayesian neural network techniques.
Prior work has investigated improving the calibration of deep models. Bayesian neural networks based on variational inference have been widely applied to neural network training @cite_18 @cite_5 . Bootstrapping provides an effective alternative to variational Bayesian methods @cite_13 @cite_4 , and simple ensembles (without dataset resampling) typically perform just as well as full bootstrapping with deep neural networks @cite_13 @cite_4 . Indeed, in our experiments, ensembles provide the best uncertainty estimates compared to other Bayesian neural network methods, though our approach improves on all of them. However, while these methods estimate a posterior distribution over the model parameters, they do not explicitly reason about the data distribution itself.
@cite_5 @cite_18 @cite_13 @cite_4
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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. Bayesian treatments of learning in neural networks are typically based either on a local Gaussian approximation to a mode of the posterior weight distribution, or on Markov chain Monte Carlo simulations. A third approach, called ensemble learning, was introduced by Hinton and van Camp (1993). It aims to approximate the posterior distribution by minimizing the Kullback-Leibler divergence between the true posterior and a parametric approximating distribution. The original derivation of a deterministic algorithm relied on the use of a Gaussian approximating distribution with a diagonal covariance matrix and hence was unable to capture the posterior correlations between parameters. In this chapter we show how the ensemble learning approach can be extended to full-covariance Gaussian distributions while remaining computationally tractable. We also extend the framework to deal with hyperparameters, leading to a simple re-estimation procedure. One of the benefits of our approach is that it yields a strict lower bound on the marginal likelihood, in contrast to other approximate procedures. 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. 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.