Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman-Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.
We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for the locally optimal control algorithm presented here, with objective formed from the variance trace of the expected posterior distribution. We present results for linear flows near hyperbolic fixed points.
End-to-end learning has recently emerged as a promising technique to tackle the problem of autonomous driving. Existing works show that learning a navigation policy from raw sensor data may reduce the system's reliance on external sensing systems, (e.g. GPS), and/or outperform traditional methods based on state estimation and planning. However, existing end-to-end methods generally trade off performance for safety, hindering their diffusion to real-life applications. For example, when confronted with an input which is radically different from the training data, end-to-end autonomous driving systems are likely to fail, compromising the safety of the vehicle. To detect such failure cases, this work proposes a general framework for uncertainty estimation which enables a policy trained end-to-end to predict not only action commands, but also a confidence about its own predictions. In contrast to previous works, our framework can be applied to any existing neural network and task, without the need to change the network's architecture or loss, or to train the network. In order to do so, we generate confidence levels by forward propagation of input and model uncertainties using Bayesian inference. We test our framework on the task of steering angle regression for an autonomous car, and compare our approach to existing methods with both qualitative and quantitative results on a real dataset. Finally, we show an interesting by-product of our framework: robustness against adversarial attacks.
Autonomous vehicles (AV) are expected to navigate in complex traffic scenarios with multiple surrounding vehicles. The correlations between road users vary over time, the degree of which, in theory, could be infinitely large, and thus posing a great challenge in modeling and predicting the driving environment. In this research, we propose a method to reproduce such high-dimensional scenarios in a finitely tractable form by defining a stochastic vector field model in multi-vehicle interactions. We then apply non-parametric Bayesian learning to extract the underlying motion patterns from a large quantity of naturalistic traffic data. We use Gaussian process to model multi-vehicle motion, and Dirichlet process to assign each observation to a specific scenario. We implement the proposed method on NGSim highway and intersection data sets, in which complex multi-vehicle interactions are prevalent. The results show that the proposed method is capable of capturing motion patterns from both settings, without imposing heroic prior, hence can be applied for a wide array of traffic situations. The proposed modeling can enable simulation platforms and other testing methods designed for AV evaluation, to easily model and generate traffic scenarios emulating large scale driving data.
Variational inference for Bayesian deep neural networks (DNNs) requires specifying priors and approximate posterior distributions for neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dimensional weight space. We propose Bayesian MOdel Priors Extracted from Deterministic DNN (MOPED) method for stochastic variational inference to choose meaningful prior distributions over weight space using deterministic weights derived from the pretrained DNNs of equivalent architecture. We evaluate the proposed approach on multiple datasets and real-world application domains with a range of varying complex model architectures to demonstrate MOPED enables scalable variational inference for Bayesian DNNs. The proposed method achieves faster training convergence and provides reliable uncertainty quantification, without compromising on the accuracy provided by the deterministic DNNs. We also propose hybrid architectures to Bayesian DNNs where deterministic and variational layers are combined to balance computation complexity during prediction phase and while providing benefits of Bayesian inference. We will release the source code for this work.