Beyond MSE: Rethinking the Evaluation Metric and Benchmarking for Irregular Time Series Forecasting

Existing research on irregular time-series forecasting has primarily focused on model design, while evaluation metrics remain insufficiently studied. Existing benchmarks typically use mean squared error (MSE) as the evaluation metric. We show that, in irregular forecasting, MSE is determined not only by the model prediction but also by the sample-specific timestamp sampling distributions, leading to a biased assessment of the models' continuous-time predictive performance. To address this issue, we propose the Continuous-time Squared Error (CSE), which employs importance weighting to eliminate the influence of the timestamp sampling distributions. We further theoretically prove that CSE's asymptotic estimation error with respect to continuous-time risk is no greater than that of MSE. Finally, we construct a systematic benchmark covering synthetic, semi-synthetic, and eight real-world datasets to validate the effectiveness of CSE and systematically evaluate models' continuous-time predictive performance. Experiments show that CSE can recover continuous-time risk more accurately than MSE, while relying solely on MSE may not fully reflect models' continuous-time predictive performance in real-world scenarios. Our code can be obtained at https://github.com/hnu-vis/ITS-Bench.

Beyond Accuracy: Measuring Logical Compliance of Predictive Models

Machine learning models are predominantly evaluated through predictive performance metrics such as ranking quality, prediction error, or classification accuracy. While these metrics effectively quantify how closely predictions match the ground truth, they do not assess whether model outputs respect predefined logical or domain-specific constraints. In high-stakes applications, including healthcare, finance, and autonomous systems, logical consistency can be as critical as predictive accuracy, yet no standard metric captures this dimension. We introduce the Rule Violation Score (RVS), a complementary evaluation metric that quantifies the extent to which a predictive model respects a given set of logical rules, independently of predictive accuracy. RVS treats hard rules (strict constraints) and soft rules (statistical regularities) differently, can be evaluated on any dataset and on any predictive model expressed over a relational vocabulary, and can be computed using SQL queries that are automatically generated for Horn rules. Beyond evaluating models, RVS can also evaluate the logical consistency of training datasets and help identify poorly defined rules. We evaluate RVS on three benchmarks covering knowledge graph link prediction and relational regression, including rule-based, embedding-based, and neuro-symbolic predictive models. Our results demonstrate that two models achieving comparable predictive accuracy can exhibit substantially different levels of logical compliance, revealing differences in model behavior that standard metrics fail to capture.