Module distprop 

Distribution propagation through nonlinear functions.

Given a Gaussian input N(mu, sigma^2), propagate through a nonlinear function f to approximate the output distribution using moment matching.

Two approximation methods:

• Linearization (first-order Taylor): output ~ N(f(mu), f’(mu)^2 * sigma^2)
• Unscented transform: sigma-point propagation (more accurate for nonlinear f)

Based on: Petersen et al., “Distribution Propagation” – propagating distributions through computational graphs via moment matching.

When to use

Distribution propagation is useful when you have uncertain inputs and need to estimate the distribution of outputs without Monte Carlo sampling. Common in uncertainty quantification, Bayesian neural networks, and probabilistic programming.

Modules

activations

Common activation functions with derivatives for distribution propagation.

Structs

DifferentiableFunc

A nonlinear function with its derivative, for linearization-based propagation.

Gaussian

Gaussian distribution parameterized by mean and standard deviation.

Functions

propagate_elementwise

Propagate a multivariate diagonal Gaussian through an element-wise function.

propagate_linearized

Propagate a Gaussian through a nonlinear function using first-order linearization.

propagate_unscented

Propagate a Gaussian through any function using the unscented transform.