--Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal distribution, importance sampling allows for more sample-efficient estimation of rare events or tails of distributions. A common choice of proposal density is a Gaussian mixture model (GMM). However, estimating full-rank GMM covariance matrices in high dimensions is a challenging task due to numerical instabilities. In this work, we propose using mixtures of probabilistic principal component analyzers (MPPCA) as the parametric proposal density for importance sampling methods. MPPCA models are a type of low-rank mixture model that can be fit quickly using expectation-maximization, even in high-dimensional spaces.

Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows for more efficient estimation of rare events or tails of distributions. However, importance sampling can fail when the proposal distribution does not effectively cover the target distribution. In this work, we propose a method for more efficient sampling by updating the proposal distribution in the latent space of a normalizing flow. Normalizing flows learn an invertible mapping from a target distribution to a simpler latent distribution. The latent space can be more easily explored during the search for a proposal distribution, and samples from the proposal distribution are recovered in the space of the target distribution via the invertible mapping. We empirically validate our methodology on simulated robotics applications such as autonomous racing and aircraft ground collision avoidance.

Estimating the probability of failure is a critical step in developing safety-critical autonomous systems. Direct estimation methods such as Monte Carlo sampling are often impractical due to the rarity of failures in these systems. Existing importance sampling approaches do not scale to sequential decision-making systems with large state spaces and long horizons. We propose an adaptive importance sampling algorithm to address these limitations. Our method minimizes the forward Kullback-Leibler divergence between a state-dependent proposal distribution and a relaxed form of the optimal importance sampling distribution. Our method uses Markov score ascent methods to estimate this objective. We evaluate our approach on four sequential systems and show that it provides more accurate failure probability estimates than baseline Monte Carlo and importance sampling techniques. This work is open sourced.

Consider the setting of multiple random walks (RWs) on a graph executing a certain computational task. For instance, in decentralized learning via RWs, a model is updated at each iteration based on the local data of the visited node and then passed to a randomly chosen neighbor. RWs can fail due to node or link failures. The goal is to maintain a desired number of RWs to ensure failure resilience. Achieving this is challenging due to the lack of a central entity to track which RWs have failed to replace them with new ones by forking (duplicating) surviving ones. Without duplications, the number of RWs will eventually go to zero, causing a catastrophic failure of the system. We propose a decentralized algorithm called DECAFORK that can maintain the number of RWs in the graph around a desired value even in the presence of arbitrary RW failures. Nodes continuously estimate the number of surviving RWs by estimating their return time distribution and fork the RWs when failures are likely to happen. We present extensive numerical simulations that show the performance of DECAFORK regarding fast detection and reaction to failures. We further present theoretical guarantees on the performance of this algorithm.

Autonomous vehicles are advanced driving systems that are well known to be vulnerable to various adversarial attacks, compromising vehicle safety and posing a risk to other road users. Rather than actively training complex adversaries by interacting with the environment, there is a need to first intelligently find and reduce the search space to only those states where autonomous vehicles are found to be less confident. In this paper, we propose a black-box testing framework ReMAV that uses offline trajectories first to analyze the existing behavior of autonomous vehicles and determine appropriate thresholds to find the probability of failure events. To this end, we introduce a three-step methodology which i) uses offline state action pairs of any autonomous vehicle under test, ii) builds an abstract behavior representation using our designed reward modeling technique to analyze states with uncertain driving decisions, and iii) uses a disturbance model for minimal perturbation attacks where the driving decisions are less confident. Our reward modeling technique helps in creating a behavior representation that allows us to highlight regions of likely uncertain behavior even when the standard autonomous vehicle performs well. We perform our experiments in a high-fidelity urban driving environment using three different driving scenarios containing single- and multi-agent interactions. Our experiment shows an increase in 35, 23, 48, and 50% in the occurrences of vehicle collision, road object collision, pedestrian collision, and offroad steering events, respectively by the autonomous vehicle under test, demonstrating a significant increase in failure events. We compare ReMAV with two baselines and show that ReMAV demonstrates significantly better effectiveness in generating failure events compared to the baselines in all evaluation metrics.

Predictive Maintenance (PdM) methods aim to facilitate the scheduling of maintenance work before equipment failure. In this context, detecting early faults in automated teller machines (ATMs) has become increasingly important since these machines are susceptible to various types of unpredictable failures. ATMs track execution status by generating massive event-log data that collect system messages unrelated to the failure event. Predicting machine failure based on event logs poses additional challenges, mainly in extracting features that might represent sequences of events indicating impending failures. Accordingly, feature learning approaches are currently being used in PdM, where informative features are learned automatically from minimally processed sensor data. However, a gap remains to be seen on how these approaches can be exploited for deriving relevant features from event-log-based data. To fill this gap, we present a predictive model based on a convolutional kernel (MiniROCKET and HYDRA) to extract features from the original event-log data and a linear classifier to classify the sample based on the learned features. The proposed methodology is applied to a significant real-world collected dataset. Experimental results demonstrated how one of the proposed convolutional kernels (i.e. HYDRA) exhibited the best classification performance (accuracy of 0.759 and AUC of 0.693). In addition, statistical analysis revealed that the HYDRA and MiniROCKET models significantly overcome one of the established state-of-the-art approaches in time series classification (InceptionTime), and three non-temporal ML methods from the literature. The predictive model was integrated into a container-based decision support system to support operators in the timely maintenance of ATMs.

Artificial intelligence (AI) systems have become increasingly popular in many areas. Nevertheless, AI technologies are still in their developing stages, and many issues need to be addressed. Among those, the reliability of AI systems needs to be demonstrated so that the AI systems can be used with confidence by the general public. In this paper, we provide statistical perspectives on the reliability of AI systems. Different from other considerations, the reliability of AI systems focuses on the time dimension. That is, the system can perform its designed functionality for the intended period. We introduce a so-called SMART statistical framework for AI reliability research, which includes five components: Structure of the system, Metrics of reliability, Analysis of failure causes, Reliability assessment, and Test planning. We review traditional methods in reliability data analysis and software reliability, and discuss how those existing methods can be transformed for reliability modeling and assessment of AI systems. We also describe recent developments in modeling and analysis of AI reliability and outline statistical research challenges in this area, including out-of-distribution detection, the effect of the training set, adversarial attacks, model accuracy, and uncertainty quantification, and discuss how those topics can be related to AI reliability, with illustrative examples. Finally, we discuss data collection and test planning for AI reliability assessment and how to improve system designs for higher AI reliability. The paper closes with some concluding remarks.

If you think carefully, you'll realize that the world we live in today is dependent heavily on the functioning of machines and systems. Almost everything from a light switch to a smartphone, from an elevator to a car, is a machine or a system that controls a machine. However, any machine is subject to wear and tear. What happens to a life so dependent on machines, when that particular machine breaks down? This is precisely why there's a dire need for predictive maintenance with machine learning.