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.
 A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penalizing large weights, etc.), (4) a measure of the effective number of well-determined parameters in a model, (5) quantified estimates of the error bars on network parameters and on network output, and (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian "evidence" automatically embodies "Occam's razor," penalizing overflexible and overcomplex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalization ability and the Bayesian evidence is obtained. 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. 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. This paper presents an algorithm to estimate simultaneously both mean and variance of a non parametric regression problem. The key point is that we are able to estimate variance locally unlike standard Gaussian Process regression or SVMs. This means that our estimator adapts to the local noise. The problem is cast in the setting of maximum a posteriori estimation in exponential families. Unlike previous work, we obtain a convex optimization problem which can be solved via Newton's method. Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at the intersection of Bayesian modelling and deep learning offer a Bayesian interpretation of common deep learning techniques such as dropout. This grounding of dropout in approximate Bayesian inference suggests an extension of the theoretical results, offering insights into the use of dropout with RNN models. We apply this new variational inference based dropout technique in LSTM and GRU models, assessing it on language modelling and sentiment analysis tasks. The new approach outperforms existing techniques, and to the best of our knowledge improves on the single model state-of-the-art in language modelling with the Penn Treebank (73.4 test perplexity). This extends our arsenal of variational tools in deep learning. Pedestrians follow different trajectories to avoid obstacles and accommodate fellow pedestrians. Any autonomous vehicle navigating such a scene should be able to foresee the future positions of pedestrians and accordingly adjust its path to avoid collisions. This problem of trajectory prediction can be viewed as a sequence generation task, where we are interested in predicting the future trajectory of people based on their past positions. Following the recent success of Recurrent Neural Network (RNN) models for sequence prediction tasks, we propose an LSTM model which can learn general human movement and predict their future trajectories. This is in contrast to traditional approaches which use hand-crafted functions such as Social forces. We demonstrate the performance of our method on several public datasets. Our model outperforms state-of-the-art methods on some of these datasets. We also analyze the trajectories predicted by our model to demonstrate the motion behaviour learned by our model. Introduces a method that estimates the mean and the variance of the probability distribution of the target as a function of the input, given an assumed target error-distribution model. Through the activation of an auxiliary output unit, this method provides a measure of the uncertainty of the usual network output for each input pattern. The authors derive the cost function and weight-update equations for the example of a Gaussian target error distribution, and demonstrate the feasibility of the network on a synthetic problem where the true input-dependent noise level is known. > There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks.