We quantify the efficiency of temporal difference (TD) learning over the direct, or Monte Carlo (MC), estimator for policy evaluation in reinforcement learning, with an emphasis on estimation of quantities related to rare events. Policy evaluation is complicated in the rare event setting by the long timescale of the event and by the need for \emph{relative accuracy} in estimates of very small values. Specifically, we focus on least-squares TD (LSTD) prediction for finite state Markov chains, and show that LSTD can achieve relative accuracy far more efficiently than MC. We prove a central limit theorem for the LSTD estimator and upper bound the \emph{relative asymptotic variance} by simple quantities characterizing the connectivity of states relative to the transition probabilities between them. Using this bound, we show that, even when both the timescale of the rare event and the relative accuracy of the MC estimator are exponentially large in the number of states, LSTD maintains a fixed level of relative accuracy with a total number of observed transitions of the Markov chain that is only \emph{polynomially} large in the number of states.

Rare events are occurrences that take place with a significantly lower frequency than more common regular events. In manufacturing, predicting such events is particularly important, as they lead to unplanned downtime, shortening equipment lifespan, and high energy consumption. The occurrence of events is considered frequently-rare if observed in more than 10% of all instances, very-rare if it is 1-5%, moderately-rare if it is 5-10%, and extremely-rare if less than 1%. The rarity of events is inversely correlated with the maturity of a manufacturing industry. Typically, the rarity of events affects the multivariate data generated within a manufacturing process to be highly imbalanced, which leads to bias in predictive models. This paper evaluates the role of data enrichment techniques combined with supervised machine-learning techniques for rare event detection and prediction. To address the data scarcity, we use time series data augmentation and sampling methods to amplify the dataset with more multivariate features and data points while preserving the underlying time series patterns in the combined alterations. Imputation techniques are used in handling null values in datasets. Considering 15 learning models ranging from statistical learning to machine learning to deep learning methods, the best-performing model for the selected datasets is obtained and the efficacy of data enrichment is evaluated. Based on this evaluation, our results find that the enrichment procedure enhances up to 48% of F1 measure in rare failure event detection and prediction of supervised prediction models. We also conduct empirical and ablation experiments on the datasets to derive dataset-specific novel insights. Finally, we investigate the interpretability aspect of models for rare event prediction, considering multiple methods.

Rare events are infrequent incidents characterized by scarcity, often presenting computational challenges in data analysis. These events don't happen often, as the name suggests, but they significantly impact when they do. For example, in pulp-and-paper manufacturing, paper breakage that occurs 1%, can cost $10,000/hour. Predicting such elusive occurrences is important in cost management, operational efficiency, and energy conservation. In fact, these rare events are hidden pieces that, when discovered and understood, can lead to better decision-making and more efficient models.

Rare event prediction involves identifying and forecasting events with a low probability using machine learning and data analysis. Due to the imbalanced data distributions, where the frequency of common events vastly outweighs that of rare events, it requires using specialized methods within each step of the machine learning pipeline, i.e., from data processing to algorithms to evaluation protocols. Predicting the occurrences of rare events is important for real-world applications, such as Industry 4.0, and is an active research area in statistical and machine learning. This paper comprehensively reviews the current approaches for rare event prediction along four dimensions: rare event data, data processing, algorithmic approaches, and evaluation approaches. Specifically, we consider 73 datasets from different modalities (i.e., numerical, image, text, and audio), four major categories of data processing, five major algorithmic groupings, and two broader evaluation approaches. This paper aims to identify gaps in the current literature and highlight the challenges of predicting rare events. It also suggests potential research directions, which can help guide practitioners and researchers.

Satellite imagery is now widely used in the defense sector for monitoring locations of interest. Although the increasing amount of data enables pattern identification and therefore prediction, carrying this task manually is hardly feasible. We hereby propose a cased-based reasoning approach for automatic prediction of rare events on strategic sites. This method allows direct incorporation of expert knowledge, and is adapted to irregular time series and small-size datasets. Experiments are carried out on two use-cases using real satellite images: the prediction of submarines arrivals and departures from a naval base, and the forecasting of imminent rocket launches on two space bases. The proposed method significantly outperforms a random selection of reference cases on these challenging applications, showing its strong potential. Keywords: Predictive analysis · Case-based reasoning · Earth observation · Submarine activity · Space launch.