Intermittent time series, characterised by the presence of a significant amount of zeros, constitute a large percentage of inventory items in supply chain. Probabilistic forecasts are needed to plan the inventory levels; the predictive distribution should cover non-negative values, have a mass in zero and a long upper tail. Intermittent time series are commonly forecast using local models, which are trained individually on each time series. In the last years global models, which are trained on a large collection of time series, have become popular for time series forecasting. Global models are often based on neural networks. However, they have not yet been exhaustively tested on intermittent time series. We carry out the first study comparing state-of-the-art local (iETS, TweedieGP) and global models (D-Linear, DeepAR, Transformers) on intermittent time series. For neural networks models we consider three different distribution heads suitable for intermittent time series: negative binomial, hurdle-shifted negative binomial and Tweedie. We use, for the first time, the last two distribution heads with neural networks. We perform experiments on five large datasets comprising more than 40'000 real-world time series. Among neural networks D-Linear provides best accuracy; it also consistently outperforms the local models. Moreover, it has also low computational requirements. Transformers-based architectures are instead much more computationally demanding and less accurate. Among the distribution heads, the Tweedie provides the best estimates of the highest quantiles, while the negative binomial offers overall the best performance.

Conformal prediction for time series presents two key challenges: (1) leveraging sequential correlations in features and non-conformity scores and (2) handling multi-dimensional outcomes. We propose a novel conformal prediction method to address these two key challenges by integrating Transformer and Normalizing Flow. Specifically, the Transformer encodes the historical context of time series, and normalizing flow learns the transformation from the base distribution to the distribution of non-conformity scores conditioned on the encoded historical context. This enables the construction of prediction regions by transforming samples from the base distribution using the learned conditional flow. We ensure the marginal coverage by defining the prediction regions as sets in the transformed space that correspond to a predefined probability mass in the base distribution. The model is trained end-to-end by Flow Matching, avoiding the need for computationally intensive numerical solutions of ordinary differential equations. We demonstrate that our proposed method achieves smaller prediction regions compared to the baselines while satisfying the desired coverage through comprehensive experiments using simulated and real-world time series datasets.

Unlike other single-point Artificial Intelligence (AI)-based prediction techniques, such as Long-Short Term Memory (LSTM), probabilistic forecasting techniques (e.g., DeepAR and Transformer) provide a range of possible outcomes and associated probabilities that enable decision makers to make more informed and robust decisions. At the same time, the architecture of Open RAN has emerged as a revolutionary approach for mobile networks, aiming at openness, interoperability and innovation in the ecosystem of RAN. In this paper, we propose the use of probabilistic forecasting techniques as a radio App (rApp) within the Open RAN architecture. We investigate and compare different probabilistic and single-point forecasting methods and algorithms to estimate the utilization and resource demands of Physical Resource Blocks (PRBs) of cellular base stations. Through our evaluations, we demonstrate the numerical advantages of probabilistic forecasting techniques over traditional single-point forecasting methods and show that they are capable of providing more accurate and reliable estimates. In particular, DeepAR clearly outperforms single-point forecasting techniques such as LSTM and Seasonal-Naive (SN) baselines and other probabilistic forecasting techniques such as Simple-Feed-Forward (SFF) and Transformer neural networks.

The transition to sustainable Open Radio Access Network (O-RAN) architectures brings new challenges for resource management, especially in predicting the utilization of Physical Resource Block (PRB)s. In this paper, we propose a novel approach to characterize the PRB load using probabilistic forecasting techniques. First, we provide background information on the O-RAN architecture and components and emphasize the importance of energy/power consumption models for sustainable implementations. The problem statement highlights the need for accurate PRB load prediction to optimize resource allocation and power efficiency. We then investigate probabilistic forecasting techniques, including Simple-Feed-Forward (SFF), DeepAR, and Transformers, and discuss their likelihood model assumptions. The simulation results show that DeepAR estimators predict the PRBs with less uncertainty and effectively capture the temporal dependencies in the dataset compared to SFF- and Transformer-based models, leading to power savings. Different percentile selections can also increase power savings, but at the cost of over-/under provisioning. At the same time, the performance of the Long-Short Term Memory (LSTM) is shown to be inferior to the probabilistic estimators with respect to all error metrics. Finally, we outline the importance of probabilistic, prediction-based characterization for sustainable O-RAN implementations and highlight avenues for future research.

The need for intelligent and efficient resource provisioning for the productive management of resources in real-world scenarios is growing with the evolution of telecommunications towards the 6G era. Technologies such as Open Radio Access Network (O-RAN) can help to build interoperable solutions for the management of complex systems. Probabilistic forecasting, in contrast to deterministic single-point estimators, can offer a different approach to resource allocation by quantifying the uncertainty of the generated predictions. This paper examines the cloud-native aspects of O-RAN together with the radio App (rApp) deployment options. The integration of probabilistic forecasting techniques as a rApp in O-RAN is also emphasized, along with case studies of real-world applications. Through a comparative analysis of forecasting models using the error metric, we show the advantages of Deep Autoregressive Recurrent network (DeepAR) over other deterministic probabilistic estimators. Furthermore, the simplicity of Simple-Feed-Forward (SFF) leads to a fast runtime but does not capture the temporal dependencies of the input data. Finally, we present some aspects related to the practical applicability of cloud-native O-RAN with probabilistic forecasting.

In learning-enabled autonomous systems, safety monitoring of learned components is crucial to ensure their outputs do not lead to system safety violations, given the operational context of the system. However, developing a safety monitor for practical deployment in real-world applications is challenging. This is due to limited access to internal workings and training data of the learned component. Furthermore, safety monitors should predict safety violations with low latency, while consuming a reasonable amount of computation. To address the challenges, we propose a safety monitoring method based on probabilistic time series forecasting. Given the learned component outputs and an operational context, we empirically investigate different Deep Learning (DL)-based probabilistic forecasting to predict the objective measure capturing the satisfaction or violation of a safety requirement (safety metric). We empirically evaluate safety metric and violation prediction accuracy, and inference latency and resource usage of four state-of-the-art models, with varying horizons, using an autonomous aviation case study. Our results suggest that probabilistic forecasting of safety metrics, given learned component outputs and scenarios, is effective for safety monitoring. Furthermore, for the autonomous aviation case study, Temporal Fusion Transformer (TFT) was the most accurate model for predicting imminent safety violations, with acceptable latency and resource consumption.

Azure Core workload insights have time-series data with different metric units. Faults or Anomalies are observed in these time-series data owing to faults observed with respect to metric name, resources region, dimensions, and its dimension value associated with the data. For Azure Core, an important task is to highlight faults or anomalies to the user on a dashboard that they can perceive easily. The number of anomalies reported should be highly significant and in a limited number, e.g., 5-20 anomalies reported per hour. The reported anomalies will have significant user perception and high reconstruction error in any time-series forecasting model. Hence, our task is to automatically identify 'high significant anomalies' and their associated information for user perception.

We present a randomized approximation scheme for the permanent of a matrix with nonnegative entries. Our scheme extends a recursive rejection sampling method of Huber and Law (SODA 2008) by replacing the upper bound for the permanent with a linear combination of the subproblem bounds at a moderately large depth of the recursion tree. This method, we call deep rejection sampling, is empirically shown to outperform the basic, depth-zero variant, as well as a related method by Kuck et al. (NeurIPS 2019). We analyze the expected running time of the scheme on random (0, 1)-matrices where each entry is independently 1 with probability p. Our bound is superior to a previous one for p less than 1/5, matching another bound that was known to hold when every row and column has density exactly p.

As the popularity of hierarchical point forecast reconciliation methods increases, there is a growing interest in probabilistic forecast reconciliation. Many studies have utilized machine learning or deep learning techniques to implement probabilistic forecasting reconciliation and have made notable progress. However, these methods treat the reconciliation step as a fixed and hard post-processing step, leading to a trade-off between accuracy and coherency. In this paper, we propose a new approach for probabilistic forecast reconciliation. Unlike existing approaches, our proposed approach fuses the prediction step and reconciliation step into a deep learning framework, making the reconciliation step more flexible and soft by introducing the Kullback-Leibler divergence regularization term into the loss function. The approach is evaluated using three hierarchical time series datasets, which shows the advantages of our approach over other probabilistic forecast reconciliation methods.