Out-of-distribution (OOD) detection has recently received much attention from the machine learning community because it is important for deploying machine learning models in real-world applications. In this paper we propose an uncertainty quantification approach by modeling data distributions in feature spaces. We further incorporate an efficient ensemble mechanism, namely batch-ensemble, to construct the batch-ensemble stochastic neural networks (BE-SNNs) and overcome the feature collapse problem. We compare the performance of the proposed BE-SNNs with the other state-of-the-art approaches and show that BE-SNNs yield superior performance on several OOD detection benchmarks, such as the Two-Moons dataset, the FashionMNIST vs MNIST dataset, Fashion-MNIST vs NotMNIST dataset, and the CIFAR10 vs SVHN dataset.

The particle flow Gaussian particle filter (PFGPF) uses an invertible particle flow to generate a proposal density. It approximates the predictive and posterior distributions as Gaussian densities. In this paper, we use a bank of PFGPF filters to construct a Particle flow Gaussian sum particle filter (PFGSPF), which approximates the prediction and posterior as Gaussian mixture model. This approximation is useful in complex estimation problems where a single Gaussian approximation is inadequate. We compare the performance of this proposed filter with the PFGPF and others in challenging numerical simulations.