Distributionally Robust Statistical Verification with Imprecise Neural Networks

A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches are constrained by the distributional assumptions about the sampling process. Instead, we pose a distributionally robust version of the statistical verification problem for black-box systems, where our performance guarantees hold over a large family of distributions. This paper proposes a novel approach based on a combination of active learning, uncertainty quantification, and neural network verification. A central piece of our approach is an ensemble technique called Imprecise Neural Networks, which provides the uncertainty to guide active learning. The active learning uses an exhaustive neural-network verification tool Sherlock to collect samples. An evaluation on multiple physical simulators in the openAI gym Mujoco environments with reinforcement-learned controllers demonstrates that our approach can provide useful and scalable guarantees for high-dimensional systems.

Take Me Home: Reversing Distribution Shifts using Reinforcement Learning

Deep neural networks have repeatedly been shown to be non-robust to the uncertainties of the real world. Even subtle adversarial attacks and naturally occurring distribution shifts wreak havoc on systems relying on deep neural networks. In response to this, current state-of-the-art techniques use data-augmentation to enrich the training distribution of the model and consequently improve robustness to natural distribution shifts. We propose an alternative approach that allows the system to recover from distribution shifts online. Specifically, our method applies a sequence of semantic-preserving transformations to bring the shifted data closer in distribution to the training set, as measured by the Wasserstein distance. We formulate the problem of sequence selection as an MDP, which we solve using reinforcement learning. To aid in our estimates of Wasserstein distance, we employ dimensionality reduction through orthonormal projection. We provide both theoretical and empirical evidence that orthonormal projection preserves characteristics of the data at the distributional level. Finally, we apply our distribution shift recovery approach to the ImageNet-C benchmark for distribution shifts, targeting shifts due to additive noise and image histogram modifications. We demonstrate an improvement in average accuracy up to 14.21% across a variety of state-of-the-art ImageNet classifiers.

Imprecise Bayesian Neural Networks

Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian neural networks (BNNs) allow for uncertainty in the predictions to be assessed, different sources of uncertainty are indistinguishable. We present imprecise Bayesian neural networks (IBNNs); they generalize and overcome some of the drawbacks of standard BNNs. These latter are trained using a single prior and likelihood distributions, whereas IBNNs are trained using credal prior and likelihood sets. They allow to distinguish between aleatoric and epistemic uncertainties, and to quantify them. In addition, IBNNs are robust in the sense of Bayesian sensitivity analysis, and are more robust than BNNs to distribution shift. They can also be used to compute sets of outcomes that enjoy PAC-like properties. We apply IBNNs to two case studies. One, to model blood glucose and insulin dynamics for artificial pancreas control, and two, for motion prediction in autonomous driving scenarios. We show that IBNNs performs better when compared to an ensemble of BNNs benchmark.

Electroanatomic Mapping to determine Scar Regions in patients with Atrial Fibrillation

Left atrial voltage maps are routinely acquired during electroanatomic mapping in patients undergoing catheter ablation for atrial fibrillation. For patients, who have prior catheter ablation when they are in sinus rhythm, the voltage map can be used to identify low voltage areas using a threshold of 0.2 - 0.45 mV. However, such a voltage threshold for maps acquired during atrial fibrillation has not been well established. A prerequisite for defining a voltage threshold is to maximize the topologically matched low voltage areas between the electroanatomic mapping acquired during atrial fibrillation and sinus rhythm. This paper demonstrates a new technique to improve the sensitivity and specificity of the matched low voltage areas. This is achieved by computing omni-directional bipolar voltages and applying Gaussian Process Regression based interpolation to derive the AF map. The proposed method is evaluated on a test cohort of 7 male patients, and a total of 46,589 data points were included in analysis. The low voltage areas in the posterior left atrium and pulmonary vein junction are determined using the standard method and the proposed method. Overall, the proposed method showed patient-specific sensitivity and specificity in matching low voltage areas of 75.70% and 65.55% for a geometric mean of 70.69%. On average, there was an improvement of 3.00% in the geometric mean, 7.88% improvement in sensitivity, 0.30% improvement in specificity compared to the standard method. The results show that the proposed method is an improvement in matching low voltage areas. This may help develop the voltage threshold to better identify low voltage areas in the left atrium for patients in atrial fibrillation.