von mise estimator
SeFEF: A Seizure Forecasting Evaluation Framework
Carmo, Ana Sofia, Rodrigues, Lourenço Abrunhosa, Peralta, Ana Rita, Fred, Ana, Bentes, Carla, da Silva, Hugo Plácido
The lack of standardization in seizure forecasting slows progress in the field and limits the clinical translation of forecasting models. In this work, we introduce a Python-based framework aimed at streamlining the development, assessment, and documentation of individualized seizure forecasting algorithms. The framework automates data labeling, cross-validation splitting, forecast post-processing, performance evaluation, and reporting. It supports various forecasting horizons and includes a model card that documents implementation details, training and evaluation settings, and performance metrics. Three different models were implemented as a proof-of-concept. The models leveraged features extracted from time series data and seizure periodicity. Model performance was assessed using time series cross-validation and key deterministic and probabilistic metrics. Implementation of the three models was successful, demonstrating the flexibility of the framework. The results also emphasize the importance of careful model interpretation due to variations in probability scaling, calibration, and subject-specific differences. Although formal usability metrics were not recorded, empirical observations suggest reduced development time and methodological consistency, minimizing unintentional variations that could affect the comparability of different approaches. As a proof-of-concept, this validation is inherently limited, relying on a single-user experiment without statistical analyses or replication across independent datasets. At this stage, our objective is to make the framework publicly available to foster community engagement, facilitate experimentation, and gather feedback. In the long term, we aim to contribute to the establishment of a consensus on a standardized methodology for the development and validation of seizure forecasting algorithms in people with epilepsy.
On sample complexity of conditional independence testing with Von Mises estimator with application to causal discovery
Jamshidi, Fateme, Ganassali, Luca, Kiyavash, Negar
Motivated by conditional independence testing, an essential step in constraint-based causal discovery algorithms, we study the nonparametric Von Mises estimator for the entropy of multivariate distributions built on a kernel density estimator. We establish an exponential concentration inequality for this estimator. We design a test for conditional independence (CI) based on our estimator, called VM-CI, which achieves optimal parametric rates under smoothness assumptions. Leveraging the exponential concentration, we prove a tight upper bound for the overall error of VM-CI. This, in turn, allows us to characterize the sample complexity of any constraint-based causal discovery algorithm that uses VM-CI for CI tests. To the best of our knowledge, this is the first sample complexity guarantee for causal discovery for continuous variables. Furthermore, we empirically show that VM-CI outperforms other popular CI tests in terms of either time or sample complexity (or both), which translates to a better performance in structure learning as well.