Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant attention: end-to-end training methods can now minimize the downstream task cost rather than the predictive error. However, despite their effectiveness, these decision-focused learning (DFL) approaches often rely on repeated solving of the underlying combinatorial optimization problem during training, making them computationally expensive and difficult to scale. We reframe the learning problem as a cost-sensitive multi-output regression problem: multi-output due to the combinatorial problem having multiple uncertain parameters, and cost-sensitive due to the downstream task cost being the real target. Our technical contribution is the formalization of multiple loss function components that follow from this reframing: cost-insensitive normalization, decision-aware asymmetric penalization of over- and underpredictions, and instance-based costs that mimic the true downstream task-based loss locally. These components require zero or one solve per training data instance, while requiring no further solves during training. Experiments show that the combination of loss components achieves comparable downstream task quality to the state of the art, while being significantly more efficient, enabling scaling to problem sizes that have not been tackled before with DFL.

In this appendix, we first introduce the datasets and evaluation metrics used in the experiments in Section A. Then, we provide extra experimental results in Section B. In Section C, we present details of network design, training scheme, and hyper-parameter tuning. We conduct experiments on 11 popular time series datasets: (1) Electricity Transformer Temperature [42] (ETTh(1,2),ETTm1) 3consists of 2 year electric power data collected from two separated counties of China. Each data point includes an "oil temperature" value and 6 power load features. The data is aggregated into 5-minutes windows, resulting in 12 points per hour and 288 points per day. A.1 Electricity Transformer Temperature (ETT) For data pre-processing, we perform zero-mean normalization, i.e., X We use Mean Absolute Errors (MAE) [17] and Mean Squared Errors (MSE) [26] for model comparison.

Intraoperative monitoring and prediction of vital signs are critical for ensuring patient safety and improving surgical outcomes. Despite recent advances in deep learning models for medical time-series forecasting, several challenges persist, including the lack of standardized benchmarks, incomplete data, and limited cross-center validation. To address these challenges, we introduce VitalBench, a novel benchmark specifically designed for intraoperative vital sign prediction. VitalBench includes data from over 4,000 surgeries across two independent medical centers, offering three evaluation tracks: complete data, incomplete data, and cross-center generalization. This framework reflects the real-world complexities of clinical practice, minimizing reliance on extensive preprocessing and incorporating masked loss techniques for robust and unbiased model evaluation. By providing a standardized and unified platform for model development and comparison, VitalBench enables researchers to focus on architectural innovation while ensuring consistency in data handling. This work lays the foundation for advancing predictive models for intraoperative vital sign forecasting, ensuring that these models are not only accurate but also robust and adaptable across diverse clinical environments. Our code and data are available at https://github.com/XiudingCai/VitalBench.

We introduce Toto, a time series forecasting foundation model with 151 million parameters. Toto uses a modern decoder-only architecture coupled with architectural innovations designed to account for specific challenges found in multivariate observability time series data. Toto's pre-training corpus is a mixture of observability data, open datasets, and synthetic data, and is 4-10$\times$ larger than those of leading time series foundation models. Additionally, we introduce BOOM, a large-scale benchmark consisting of 350 million observations across 2,807 real-world time series. For both Toto and BOOM, we source observability data exclusively from Datadog's own telemetry and internal observability metrics. Extensive evaluations demonstrate that Toto achieves state-of-the-art performance on both BOOM and on established general purpose time series forecasting benchmarks. Toto's model weights, inference code, and evaluation scripts, as well as BOOM's data and evaluation code, are all available as open source under the Apache 2.0 License available at https://huggingface.co/Datadog/Toto-Open-Base-1.0 and https://github.com/DataDog/toto.

Earthquakes, as natural phenomena, have continuously caused damage and loss of human life historically. Earthquake prediction is an essential aspect of any society's plans and can increase public preparedness and reduce damage to a great extent. Nevertheless, due to the stochastic character of earthquakes and the challenge of achieving an efficient and dependable model for earthquake prediction, efforts have been insufficient thus far, and new methods are required to solve this problem. Aware of these issues, this paper proposes a novel prediction method based on attention mechanism (AM), convolution neural network (CNN), and bi-directional long short-term memory (BiLSTM) models, which can predict the number and maximum magnitude of earthquakes in each area of mainland China-based on the earthquake catalog of the region. This model takes advantage of LSTM and CNN with an attention mechanism to better focus on effective earthquake characteristics and produce more accurate predictions. Firstly, the zero-order hold technique is applied as pre-processing on earthquake data, making the model's input data more proper. Secondly, to effectively use spatial information and reduce dimensions of input data, the CNN is used to capture the spatial dependencies between earthquake data. Thirdly, the Bi-LSTM layer is employed to capture the temporal dependencies. Fourthly, the AM layer is introduced to highlight its important features to achieve better prediction performance. The results show that the proposed method has better performance and generalize ability than other prediction methods.

Abstract--Extreme events frequently occur in real-world time series and often carry significant practical implications. In domains such as climate and healthcare, these events, such as floods, heatwaves, or acute medical episodes, can lead to serious consequences. Accurate forecasting of such events is therefore of substantial importance. Most existing time series forecasting models are optimized for overall performance within the prediction window, but often struggle to accurately predict extreme events, such as high temperatures or heart rate spikes. The main challenges are data imbalance and the neglect of valuable information contained in intermediate events that precede extreme events. In this paper, we propose xTime, a novel framework for extreme event forecasting in time series. In addition, we introduce a mixture of experts (MoE) mechanism that dynamically selects and fuses outputs from expert models across different rarity levels, which further improves the forecasting performance for extreme events. Experiments on multiple datasets show that xTime achieves consistent improvements, with forecasting accuracy on extreme events improving from 3% to 78%. Time series forecasting plays a fundamental role across a broad spectrum of critical applications, such as stock market analysis, weather and climate modeling, and electricity demand prediction.