zoomgrid: zoomgrid: a package implementing the grid search algorithm...

In yukai-yang/zoomgrid: Grid Search Algorithm with a Zoom

Description

The package implements the grid search algorithm with a zoom.

Details

The grid search aims to help solving difficult optimization problem where there are many local optimizers inside the domain of the target function or the parameter space of the log-likelihood function. It offers suitable initial or starting value for the following optimization procedure provided that the global optimum exists in the neighbourhood of the initial or starting value. And therefore the grid search does not do optimization. But if the grid is fine enough, the result approximates the optimizer.

The grid search algorithm consists of two steps:

– firstly, it builds a grid with many points which discretize the domain of the target function;

– secondly, it evaluates the target function at these points in the grid and find the point which produces the smallest (minimization) or largest (maximization) function value.

A fine grid is needed in order for a satisfactory result (initial or starting value of the following optimization, or an approximation of the optimizer). For cases with multiple (high-dimensional) arguments, the grid may contain too many points to evaluate the target function within a reasonably short time period. Thus, a grid search algorithm with a zoom is implemented as an option in the package.

The grid search algorithm with a zoom does not require a very find grid, but a grid with a zoom-in mechanism. Based on the algorithm introduced above, the user of the package can choose to zoom in around the neighbourhoods the first n smallest (minimization) or largest (maximization) points obtained from the first round grid search. A much finer grid will be built in the neighbourhoods these points, and the grid search will continue.

The grid search with a zoom stops after k rounds and gives a final result. The result is equivalent to that from a grid search based on (one round) a very fine grid, if the true global optimum is in the neighbourhoods of the n points from the first round grid search. By doing so, the grid search algorithm with a zoom saves time tremendously in cases with high-dimenstional arguments.

Note that the user specifies n and k beforehand.

Parallel computation, which requires the parallel package, is implemented and is an option in the package.

Author and Maintainer

Yukai Yang

Department of Statistics, Uppsala University

[e-mail]

References

Yang, Yukai (2012, 1.5.4) "Modelling Nonlinear Vector Economic Time Series", PhD thesis, Aarhus University, Department of economics and business and CREATES.

functions in the package

build_grid build the grid for the following grid search algorithm.

grid_search_check check the time consumed by running the grid search algorithm with a zoom.

grid_search conduct the grid search algorithm with a zoom.

yukai-yang/zoomgrid documentation built on May 21, 2019, 2:31 a.m.