A Julia package for differential-geometric analyses of parameter inference problems.
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In essence, the functionality provided by InformationGeometry.jl revolves around analyzing the parameter space associated with mathematical models, given observed data. In particular, it employs novel methods to quantify and visualize the exact uncertainties in the best fit parameter configuration. That is, the confidence regions around the best fit parameters can be constructed without resorting to any approximations of their shape (e.g. as ellipsoids by assuming linear covariance between the parameters). Moreover, the utilized schemes are highly efficient since they do not require one to sample large domains of the parameter space either on a grid or stochastically in order to find said confidence regions, which constitutes a significant improvement over previously established methods.
For example, given two different parametrizations of the same linear relationship between observed x and y-data, one finds the following confidence regions and intervals:
y(x, θ) = θ[1] * x + θ[2] |
y(x, θ) = θ[1]^3 * x + exp(θ[1] + θ[2]) |
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In addition, this package also allows for computations of
- confidence bands around the prediction,
- profile likelihoods,
- multistart optimization with optimizers from the Optimization.jl ecosystem,
- the Fisher metric, geodesics,
- Riemann and Ricci curvature tensors
and more. With its unique features, the toolkit of InformationGeometry.jl offers valuable insights into complicated modeling problems from various areas of science and engineering. Examples detailing how to use this package can be found in the documentation.
The simple high-level interface of InformationGeometry.jl is conducive to automation of many repetitive aspects of the parameter inference process. Moreover, this prospectively also enables researchers without specialised programming or modelling backgrounds to orchestrate parameter inference with natural language.
A work-in-progress of agentic skill files for automating iterative model development via the InformationGeometry.jl package can be found at AgenticParameterInference.
A preprint discussing some of the mathematical ideas underlying the methods employed by InformationGeometry.jl can be found in 2211.03421.
If InformationGeometry.jl was helpful in your own work, please consider citing https://doi.org/10.48550/arXiv.2211.03421 and https://doi.org/10.5281/zenodo.5530660.