Preconditioner

Preconditioner(
    reference: Reference,
    Q: Callable[[Tensor, str], Tensor],
    Q_inv: Callable[[Tensor, str], Tensor],
    neglogdet_Q: Callable[[Tensor, str], Tensor],
    neglogdet_Q_inv: Callable[[Tensor, str], Tensor],
    dim: int,
)

A user-defined preconditioning function. Ideally, the pushforward of the reference density under the preconditioning function will be as similar as possible to the target density; this makes the subsequent construction of the DIRT approximation to the target density more efficient.

The mapping, which we denote using \(Q(\cdot)\), needs to be invertible. There are additional benefits if the mapping is lower or upper triangular (or both):

• If the mapping is lower triangular, one can evaluate the marginal densities of the corresponding DIRT object in the first \(k\) variables, and condition on the first \(k\) variables, where \(1 \leq k < d\).
• If the mapping is upper triangular, one can evaluate the marginal densities of the corresponding DIRT object in the last \(k\) variables, and condition on the final \(k\) variables, where \(1 \leq k < d\).

Parameters

reference : Reference

The density of the reference random variable.

Q : Callable[[Tensor, str], Tensor]

A function which takes an \(n \times k\) matrix containing samples from the reference domain and a string indicating whether these are samples of the first (subset='first') or last (subset='last') \(k\) variables, and returns an \(n \times k\) matrix containing samples from the approximation domain, after applying the mapping \(Q(\cdot)\) to each sample.

Q_inv : Callable[[Tensor, str], Tensor]

A function which takes an \(n \times k\) matrix containing samples from the approximation domain and a string indicating whether these are samples of the first (subset='first') or last (subset='last') \(k\) variables, and returns an \(n \times k\) matrix containing samples from the reference domain, after applying the mapping \(Q^{-1}(\cdot)\) to each sample.

neglogdet_Q : Callable[[Tensor, str], Tensor]

A function which takes an \(n \times k\) matrix containing samples from the reference domain and a string indicating whether these are samples of the first (subset='first') or last (subset='last') \(k\) variables, and returns an \(n\)-dimensional vector containing the negative log-determinant of \(Q(\cdot)\) evaluated at each sample.

neglogdet_Q_inv : Callable[[Tensor, str], Tensor]

A function which takes an \(n \times k\) matrix containing samples from the approximation domain and a string indicating whether these are samples of the first (subset='first') or last (subset='last') \(k\) variables, and returns an \(n\)-dimensional vector containing the negative log-determinant of \(Q^{-1}(\cdot)\) evaluated at each sample.

dim : int

The dimension, \(d\), of the target (and reference) random variable.