Progress towards advanced systems for assisted and autonomous driving is leveraging recent advances in recognition and segmentation methods. Yet, we are still facing challenges in bringing reliable driving to inner cities, as those are composed of highly dynamic scenes observed from a moving platform at considerable speeds. Anticipation becomes a key element in order to react timely and prevent accidents. In this paper we argue that it is necessary to predict at least 1 second and we thus propose a new model that jointly predicts ego motion and people trajectories over such large time horizons. We pay particular attention to modeling the uncertainty of our estimates arising from the non-deterministic nature of natural traffic scenes. Our experimental results show that it is indeed possible to predict people trajectories at the desired time horizons and that our uncertainty estimates are informative of the prediction error. We also show that both sequence modeling of trajectories as well as our novel method of long term odometry prediction are essential for best performance.
Modeling Uncertainty in Deep Learning. Popular deep learning architectures do not model uncertainty. They assume uniform constant observation noise (aleatoric uncertainty). Heteroscedastic regression methods @cite_20 @cite_19 estimate aleatoric uncertanity by predicting the parameters of a assumed observation noise distribution (also in @cite_15 ). Bayesian neural networks @cite_4 @cite_26 offer a probabilistic view of deep learning and provide model (epistemic) uncertainty estimates. However, inference of model posterior in such networks is difficult. Variational Inference is a popular method. Gal et. al. in @cite_29 showed that dropout training in deep neural networks approximates Bayesian inference in deep Gaussian processes. Extending these results it was shown in @cite_28 that dropout training can be cast as approximate Bernoulli variational inference in Bayesian neural networks. These results were extended to RNNs in @cite_27 . The developed Bayesian RNNs showed superior performance to standard RNNs with dropout in various tasks. More recently, @cite_17 presents a Bayesian deep learning framework jointly estimating aleatoric uncertainty together with epistemic uncertainty. The resulting framework gives new state-of-the-art results on segmentation and depth regression benchmarks.
@cite_26 @cite_4 @cite_28 @cite_29 @cite_19 @cite_27 @cite_15 @cite_20 @cite_17
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Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs - extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and nonlinearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning. Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning. 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. 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.