Deep neural networks for image classification only learn to map in-distribution inputs to their corresponding ground truth labels in training without differentiating out-of-distribution samples from in-distribution ones. This results from the assumption that all samples are independent and identically distributed (IID) without distributional distinction. Therefore, a pretrained network learned from in-distribution samples treats out-of-distribution samples as in-distribution and makes high-confidence predictions on them in the test phase. To address this issue, we draw out-of-distribution samples from the vicinity distribution of training in-distribution samples for learning to reject the prediction on out-of-distribution inputs. A \textit{Cross-class Vicinity Distribution} is introduced by assuming that an out-of-distribution sample generated by mixing multiple in-distribution samples does not share the same classes of its constituents. We thus improve the discriminability of a pretrained network by finetuning it with out-of-distribution samples drawn from the cross-class vicinity distribution, where each out-of-distribution input corresponds to a complementary label. Experiments on various in-/out-of-distribution datasets show that the proposed method significantly outperforms the existing methods in improving the capacity of discriminating between in- and out-of-distribution samples.

Current machine learning methods provide unprecedented accuracy across a range of domains, from computer vision to natural language processing. However, in many important high-stakes applications, such as medical diagnosis or autonomous driving, rare mistakes can be extremely costly, and thus effective deployment of learned models requires not only high accuracy, but also a way to measure the certainty in a model's predictions. Reliable uncertainty quantification is especially important when faced with out-of-distribution inputs, as model accuracy tends to degrade heavily on inputs that differ significantly from those seen during training. In this blog post, we will discuss how we can get reliable uncertainty estimation with a strategy that does not simply rely on a learned model to extrapolate to out-of-distribution inputs, but instead asks: "given my training data, which labels would make sense for this input?". To illustrate how this can allow for more reasonable predictions on out-of-distribution data, consider the following example where we attempt to classify automobiles, where all the class 1 training examples are sedans and class 2 examples are large buses.

Xenofon Koutsoukos V anderbilt University Nashville, TN xenofon.koutsoukos@vanderbilt.edu Abstract --Cyber-physical systems (CPS) greatly benefit by using machine learning components that can handle the uncertainty and variability of the real-world. Typical components such as deep neural networks, however, introduce new types of hazards that may impact system safety. The system behavior depends on data that are available only during runtime and may be different than the data used for training. Out-of-distribution data may lead to a large error and compromise safety. The paper considers the problem of efficiently detecting out-of-distribution data in CPS control systems. Detection must be robust and limit the number of false alarms while being computational efficient for real-time monitoring. The proposed approach leverages inductive confor-mal prediction and anomaly detection for developing a method that has a well-calibrated false alarm rate. We use variational autoencoders and deep support vector data description to learn models that can be used efficiently compute the nonconformity of new inputs relative to the training set and enable real-time detection of out-of-distribution high-dimensional inputs. We demonstrate the method using an advanced emergency braking system and a self-driving end-to-end controller implemented in an open source simulator for self-driving cars. The simulation results show very small number of false positives and detection delay while the execution time is comparable to the execution time of the original machine learning components. I NTRODUCTION Learning-enabled components (LECs) such as neural networks are used in many classes of cyber-physical systems (CPS). Semi-autonomous and autonomous vehicles, in particular, are CPS examples where LECs can play a significant role for perception, planning, and control if they are complemented with methods for analyzing and ensuring safety [1], [2]. However, there are several characteristics of LECs that can complicate safety analysis. LECs encode knowledge in a form that is not transparent.

Recent work has shown that deep generative models assign higher likelihood to out-of-distribution inputs than to training data. We show that a factor underlying this phenomenon is a mismatch between the nature of the prior distribution and that of the data distribution, a problem found in widely used deep generative models such as VAEs and Glow. While a typical choice for a prior distribution is a standard Gaussian distribution, properties of distributions of real data sets may not be consistent with a unimodal prior distribution. This paper focuses on the relationship between the choice of a prior distribution and the likelihoods assigned to out-of-distribution inputs. We propose the use of a mixture distribution as a prior to make likelihoods assigned by deep generative models sensitive to out-of-distribution inputs. Furthermore, we explain the theoretical advantages of adopting a mixture distribution as the prior, and we present experimental results to support our claims. Finally, we demonstrate that a mixture prior lowers the out-of-distribution likelihood with respect to two pairs of real image data sets: Fashion-MNIST vs. MNIST and CIFAR10 vs. SVHN.

Deep learning provides a powerful tool for machine perception when the observations resemble the training data. However, real-world robotic systems must react intelligently to their observations even in unexpected circumstances. This requires a system to reason about its own uncertainty given unfamiliar, out-of-distribution observations. Approximate Bayesian approaches are commonly used to estimate uncertainty for neural network predictions, but can struggle with out-of-distribution observations. Generative models can in principle detect out-of-distribution observations as those with a low estimated density. However, the mere presence of an out-of-distribution input does not by itself indicate an unsafe situation. In this paper, we present a method for uncertainty-aware robotic perception that combines generative modeling and model uncertainty to cope with uncertainty stemming from out-of-distribution states. Our method estimates an uncertainty measure about the model's prediction, taking into account an explicit (generative) model of the observation distribution to handle out-of-distribution inputs. This is accomplished by probabilistically projecting observations onto the training distribution, such that out-of-distribution inputs map to uncertain in-distribution observations, which in turn produce uncertain task-related predictions, but only if task-relevant parts of the image change. We evaluate our method on an action-conditioned collision prediction task with both simulated and real data, and demonstrate that our method of projecting out-of-distribution observations improves the performance of four standard Bayesian and non-Bayesian neural network approaches, offering more favorable trade-offs between the proportion of time a robot can remain autonomous and the proportion of impending crashes successfully avoided.