ANOVA_RFF: ANOVA-Boosting for Random Fourier Features

This algorithms aims to do sensitivity analysis for high-dimensional data, even for dependent input variables.

Included files

• test_anova_RFF.jl:
  Test file for testing the RFF-Boosting.

• anova_RFF.jl:
  Creates module anova_rff.

• algs_RFF.jl:
  Containes all algortihms used for the ANOVA-Boosting.

Notes on the implementation

The function

f = anova_RFF.RFF_model(X,y, "exp")

constructs a RFF model, where $X$ is the matrix of inputs and $y$ is the vector of outputs. The function

U = anova_RFF.ANOVA_boosting(f,q,N)

finds an ANOVA-truncated index set $U$. There are additional parameters to choose:

• dependence: true or false $\rightarrow$ there are two different possibilities implemented for the dependence of the input, see paper. The option true can also be applied to Independent Input
• anova_step: 'ascent' or 'descent' $\rightarrow$ either start with all all terms of order $1$ and increase the order iteratively to $q$ or start with all terms of order $q$ and delete nonimportant terms of highest order iteratively. See corresponding Dissertation for more information.
• epsilon: threshold parameter

Once you have found an index-set $U$, you can apply a RFF algorithm by e.g. anova_RFF.shrimp(X,y, U, N), which draws random Features according to the index set $U$. Implemented random feature algorithms to apply after sensitivity analysis are SHRIMP and HARFE.

All algorithms are implemented for the expoential basis $\mathrm e ^{\mathrm{i} \langle w, x \rangle}$, but you can add other functions: in the function make_A and in the module anova_rff.

References

This is the repository for the algorithms described in the paper

ANOVA-Boosting for Random Fourier Features
Daniel Potts, Laura Weidensager
ArXiv: 2404.03050

In the folder Dissertation you can find all numerical experiments for my Dissertation:
Figure 4.1: plots_kink.jl
Figure 6.8-6.11: interpretability.jl

Table 6.1: independent.jl
Table 6.2: numerik_dep.jl
Table 6.4: validate_trafo.jl, validate_RFF.jl