Coordination recognition and subtle pattern prediction of future trajectories play a significant role when modeling interactive behaviors of multiple agents. Due to the essential property of uncertainty in the future evolution, deterministic predictors are not sufficiently safe and robust. In order to tackle the task of probabilistic prediction for multiple, interactive entities, we propose a coordination and trajectory prediction system (CTPS), which has a hierarchical structure including a macro-level coordination recognition module and a micro-level subtle pattern prediction module which solves a probabilistic generation task. We illustrate two types of representation of the coordination variable: categorized and real-valued, and compare their effects and advantages based on empirical studies. We also bring the ideas of Bayesian deep learning into deep generative models to generate diversified prediction hypotheses. The proposed system is tested on multi-ple driving datasets in various traffic scenarios, which achieves better performance than baseline approaches in terms of a set of evaluation metrics. The results also show that using categorized coordination can better capture multi-modality and generate more diversified samples than the real-valued coordination, while the latter can generate prediction hypotheses with smaller errors with a sacrifice of sample diversity. Moreover, employing neural networks with weight uncertainty is able to generate samples with larger variance and diversity.
The parameters of deep neural networks in most deep learning literature are deterministic, which may not fully represent the model uncertainty. In recent years, more attention has been paid to avoid over-fitting or being over-confident on unseen cases by incorporating distributions over network parameters @cite_17 @cite_2 . In @cite_18 , a stochastic dynamical system was modeled by a Bayesian neural network (BNN) and used for model-based reinforcement learning. Moreover, in real-world applications such as autonomous driving, the surrounding environment is highly dynamic and full of uncertainty. @cite_8 suggested employing Bayesian deep learning to address safety issues. In this work, we treat the parameters in the proposed system as sampled instances from the learned distributions, which improves uncertainty modeling and increases the diversity of prediction hypotheses.
@cite_8 @cite_18 @cite_2 @cite_17
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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. 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. 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. 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. Deep convolutional neural networks (CNNs) have been shown to perform extremely well at a variety of tasks including subtasks of autonomous driving such as image segmentation and object classification. However, networks designed for these tasks typically require vast quantities of training data and long training periods to converge. We investigate the design rationale behind end-to-end driving network designs by proposing and comparing three small and computationally inexpensive deep end-to-end neural network models that generate driving control signals directly from input images. In contrast to prior work that segments the autonomous driving task, our models take on a novel approach to the autonomous driving problem by utilizing deep and thin Fully Convolutional Nets (FCNs) with recurrent neural nets and low parameter counts to tackle a complex end-to-end regression task predicting both steering and acceleration commands. In addition, we include layers optimized for classification to allow the networks to implicitly learn image semantics. We show that the resulting networks use 3x fewer parameters than the most recent comparable end-to-end driving network and 500x fewer parameters than the AlexNet variations and converge both faster and to lower losses while maintaining robustness against overfitting.