arXiv subjects

Kaidi Shao

Publications and source records attributed to Kaidi Shao.

5 recordsLinked to original sources

arXiv2025

TranCIT: Transient Causal Interaction Toolbox

Quantifying transient causal interactions from non-stationary neural signals is a fundamental challenge in neuroscience. Traditional methods are often inadequate for brief neural events, and advanced, event-specific techniques have lacked accessible implementations within the Python ecosystem. Here, we introduce trancit (Transient Causal Interaction Toolbox), an open-source Python package designed to bridge this gap. TranCIT implements a comprehensive analysis pipeline, including Granger Causality, Transfer Entropy, and the more robust Structural Causal Model-based Dynamic Causal Strength (DCS) and relative Dynamic Causal Strength (rDCS) for accurately detecting event-driven causal effects. We demonstrate TranCIT's utility by successfully capturing causality in high-synchrony regimes where traditional methods fail and by identifying the known transient information flow from hippocampal CA3 to CA1 during sharp-wave ripple events in real-world data. The package offers a user-friendly, validated solution for investigating the transient causal dynamics that govern complex systems.

cs.LG↗

arXiv2025

A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems

We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing methods, SDMD explicitly incorporates sampling time into its approximation, ensuring numerical stability and precision. By directly approximating the Koopman semigroup instead of the generator, SDMD avoids computationally expensive matrix exponential computations, which offers a more efficient and practical pathway for analyzing stochastic dynamics. The framework further integrates neural networks to automate basis selection, which reduces the reliance on manual intervention while maintaining computational efficiency. Rigorous theoretical guarantees, including convergence in the large data limit, zero-limit of sampling time, and large dictionary size, establish the method's reliability. Numerical experiments on canonical stochastic systems validate SDMD's effectiveness in approximating eigenvalues and eigenfunctions of the stochastic Koopman operator.

math.DS↗

arXiv2025

ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residuals

Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global linearization tool, current methods for approximating its spectral components often face theoretical limitations and depend on predefined dictionaries. Residual Dynamic Mode Decomposition (ResDMD) advanced the field by introducing the \emph{spectral residual} to assess Koopman operator approximation accuracy; however, its approach of only filtering precomputed spectra prevents the discovery of the operator's complete spectral information, a limitation known as the `spectral inclusion' problem. We introduce ResKoopNet (Residual-based Koopman-learning Network), a novel method that directly addresses this by explicitly minimizing the \emph{spectral residual} to compute Koopman eigenpairs. This enables the identification of a more precise and complete Koopman operator spectrum. Using neural networks, our approach provides theoretical guarantees while maintaining computational adaptability. Experiments on a variety of physical and biological systems show that ResKoopNet achieves more accurate spectral approximations than existing methods, particularly for high-dimensional systems and those with continuous spectra, which demonstrates its effectiveness as a tool for analyzing complex dynamical systems.

cs.LG↗

arXiv2022

Information Theoretic Measures of Causal Influences during Transient Neural Events

Transient phenomena play a key role in coordinating brain activity at multiple scales, however,their underlying mechanisms remain largely unknown. A key challenge for neural data science is thus to characterize the network interactions at play during these events. Using the formalism of Structural Causal Models and their graphical representation, we investigate the theoretical and empirical properties of Information Theory based causal strength measures in the context of recurring spontaneous transient events. After showing the limitations of Transfer Entropy and Dynamic Causal Strength in such a setting, we introduce a novel measure, relative Dynamic Causal Strength, and provide theoretical and empirical support for its benefits. These methods are applied to simulated and experimentally recorded neural time series, and provide results in agreement with our current understanding of the underlying brain circuits.

q-bio.NC↗

arXiv2022

Bayesian Information Criterion for Event-based Multi-trial Ensemble data

Transient recurring phenomena are ubiquitous in many scientific fields like neuroscience and meteorology. Time inhomogenous Vector Autoregressive Models (VAR) may be used to characterize peri-event system dynamics associated with such phenomena, and can be learned by exploiting multi-dimensional data gathering samples of the evolution of the system in multiple time windows comprising, each associated with one occurrence of the transient phenomenon, that we will call "trial". However, optimal VAR model order selection methods, commonly relying on the Akaike or Bayesian Information Criteria (AIC/BIC), are typically not designed for multi-trial data. Here we derive the BIC methods for multi-trial ensemble data which are gathered after the detection of the events. We show using simulated bivariate AR models that the multi-trial BIC is able to recover the real model order. We also demonstrate with simulated transient events and real data that the multi-trial BIC is able to estimate a sufficiently small model order for dynamic system modeling.

stat.ML↗