lanczosRTMB

Lanczos methods for RTMB

Uses

lanczosRTMB is designed to approximate properties of a hierarchical model implemented in RTMB without ever constructing or inverting the matrix of second derivatives (“Hessian matrix”). It can be used to approximate:

• Standard errors using a matrix-free delta method
• The log-determinant of the Hessian using stochastic trace estimation
• The log marginal likelihood using the Laplace approximation

Potential developments

There’s many avenues for further improvement. These include:

• Adding a quasi-Newton inner optimizer using Hq, i.e., a variant of conjugate gradient;
• Moving the FD logic for the obj$gr to tape;
• Exploring a conjugate gradient algorithm for an implicit solution to the gradient of the log-determinant;