Reproduce “Empirical fixed point bifurcation analysis” on OpenResearch

About this paper

Gergo Bohner, Maneesh Sahani

Fixed Point Sparse Gaussian Process learns a noisy system’s discrete-time transition map while fitting fixed points and local stability. It uses sparse Gaussian Processes, derivative information, and automatic relevance determination to select supported points. In simulations, it recovered fixed-point patterns in one- and two-dimensional systems, but noise shifted transitions and hid nearby branches; the evidence is not from biological recordings.

Key insights

• Directly embedding fixed points and their local linearizations into a non-parametric GP model allows for robust, data-driven identification of critical dynamical features in stochastic systems.
• The FPSGP framework enables stochastic bifurcation analysis in empirical settings by relaxing the need for known, continuous, and noiseless underlying system equations.
• The approach balances the descriptive power of flexible non-parametric models with the interpretability derived from explicitly modeling fixed points and their stability, bridging a gap in current methodologies.

Summary by alphaXiv.