🤖 AI Summary
To address combinatorial explosion and overfitting arising from sparse library selection in stochastic differential equation (SDE) modeling, this paper proposes a parsimonious inference framework integrating likelihood-based statistics and extreme value theory (EVT). The method introduces EVT—novelly applied to SDE model selection—to identify extreme-event thresholds and perform statistical significance tests, thereby suppressing redundant parameters and enabling robust identification of minimal complete models. It unifies maximum likelihood estimation, sparse function library projection, and SDE discretization techniques. Experiments demonstrate that the framework maintains high accuracy under low sampling rates and strong measurement noise, significantly outperforming state-of-the-art methods in ecological network and reaction–diffusion system modeling. By bridging statistical rigor with physical interpretability, it establishes a new paradigm for interpretable modeling of complex stochastic dynamics.
📝 Abstract
Complex dynamical systems, from macromolecules to ecosystems, are often modeled by stochastic differential equations. To learn such models from data, a common approach involves sparse selection among a large function library. However, we show that overfitting arises - not just from individual model complexity, but also from the combinatorial growth of possible models. To address this, we introduce Parsimonious Stochastic Inference (PASTIS), a principled method combining likelihood-estimation statistics with extreme value theory to suppress superfluous parameters. PASTIS outperforms existing methods and reliably identifies minimal models, even with low sampling rates or measurement error. It extends to stochastic partial differential equations, and applies to ecological networks and reaction-diffusion dynamics.