tobias-liaudat
commented
3 years ago To do:
- [x] Build spatial_dictionary for the hybrid graph+polynomial spatial constraints (as in MCCD).
- [x] Handling the batch dependent training with proper indexing. Done in commit
- [x] Add L1 loss fo alpha to the global loss. We need to enforce the new spatial constraints and we do it by enforcing the sparsity of the alpha matrix on the spatial_dictionary. commit
- [x] Add custom predict function. commit
Now the new prediction function is completely differentiable (not needed right now but could be useful for a side-project, if we want to incorporate knowledge on the galaxy images). It is based on a two-step interpolation:
- Polynomial part: the interpolation is done using the natural position polynomial framework (as done in the polynomial-only flavour of the model)
- Graph-constraint part: the interpolation is done using a RBF kernel interpolation (thin_plate) as was done in the original MCCD algorithm. The unique difference is that now we are not using the k nearest neighbours for the interpolation but we are using all the stars. This step is based on the tensorflow_addons tfa.image. interpolate_spline function.
Right now the L1 norm is only applied to the alpha_graph matrix as the alpha_poly matrix is already naturally sparse due to the identity initialisation and the way the poly_dic is built.
What is still needed to be done:
- [ ] Investigate an "optimal" optimisation strategy.
- [x] How should we choose the
l1_rateparameter for the L1 regularisation loss.
I should go to a full matrix factorisation of the style NP = S A instead of NP=S Pi (where Pi are not learned but calculated from the position as polynomials.
For this I need to handle properly the indexes in the training as each observation corresponds to a column in A.