API Reference

Deep Inverse Rosenblatt Transport

An object used to generate an approximate coupling between random variables using a composition of squared inverse Rosenblatt transports, constructed using functional tensor trains.

DIRT	Deep (squared) inverse Rosenblatt transport.
DIRTOptions	Options for configuring the construction of a DIRT object.

Target Functions

Functions to approximate.

TargetFunc	The negative logarithm of a density function to be approximated.
RareEventFunc	A function for rare event estimation problems.

Preconditioners

Initial guesses for the mapping between the reference random variable and the target random variable.

Preconditioner	The base class for preconditioning mappings.
IdentityMapping	An identity mapping.
UniformMapping	A mapping between the reference density and a uniform density.
GaussianMapping	A mapping between two Gaussian densities.

Reference Densities

Product-form reference densities used as part of DIRT construction.

GaussianReference	The standard \(d\)-dimensional Gaussian density, \(\mathcal{N}(\boldsymbol{0}_{d}, \boldsymbol{I}_{d})\).
UniformReference	The standard \(d\)-dimensional uniform density, \(\mathcal{U}([0, 1]^{d})\).

Domain Mappings

Mappings between the approximation domain and the basis functions used as part of the functional tensor trains.

BoundedDomain

Mapping from a bounded domain to \([-1, 1]\).

Functional Tensor Trains

Objects used to construct functional tensor train approximations.

FTT	A functional tensor train, defined on \([-1, 1]^{d}\).
EFTT	An extended functional tensor train, defined on \([-1, 1]^{d}\).
EFTTOptions	Options for configuring the construction of an EFTT object.
ApproxBases	An object that contains a polynomial basis in each dimension,
TT	A tensor train factorisation.
TTOptions	Options for configuring the construction of a TT object.

Basis Functions

Basis functions used for functional tensor train approximations.

Lagrange1	Piecewise linear polynomials.
LagrangeP	Higher-order piecewise Lagrange polynomials.
Chebyshev1st	Chebyshev polynomials of the first kind.
Chebyshev2nd	Chebyshev polynomials of the second kind.
Fourier	Fourier polynomials.
Legendre	Legendre polynomials.

Bridges

Objects used to generate the intermediate densities approximated during DIRT construction.

SingleLayer	Constructs the DIRT using a single layer.
Tempering	Likelihood tempering.
SigmoidSmoothing	Uses a sigmoid function in place of an indicator function.

Debiasing

Functions used to remove the bias associated with the use of an approximation to the target density function.

run_importance_sampling	Computes the importance weights associated with a set of samples.
run_independence_sampler	Runs an independence Metropolis-Hastings sampler.
run_irt_pcn	Runs a pCN sampler using the DIRT mapping.
run_cirt_pcn	Runs a pCN sampler using a conditional of the DIRT mapping.
ImportanceSamplingResult	An object containing the results of importance sampling.
MCMCResult	An object containing a constructed Markov chain.