Emulator-based Component Analysis (ECA)

This pytorch class implements Emulator-based component analysis (ECA) as described in J. Niskanen, A. Vladyka, J. Niemi, and C. J. Sahle, “Emulator-based decomposition for structural sensitivity of core-level spectra,” Royal Society Open Science, vol. 9, 2022, doi: 10.1098/rsos.220093.

Idea:

For a given trained predictor Emu: X -> Y (e.g., neural network)
We define N basis vectors V in X space, such that the covered variance for the prediction of the X, projected on V space, is maximized in respect to Y.
These vectors are calculated one by one, i.e. projections on the first vector cover most of the variance.

Being applied to spectroscopy: the model predictd spectrum from the structure. The goal of ECA is to find a subspace $V$ in structural space $X$ to cover the most of spectral variance.

Similar concept: see w:Projection pursuit regression

Glossary and functions:

V - space of ECA vectors

fit(x, y) calculation of the V basis

transform x -> t, t = x @ V.T - scores of X in V space (i.e. length of the projections of X on V space)

expand t -> x', x' = t @ V - projection of X data to V space

project x -> x', x' = expand(transform(x))

inverse y -> t', optimization search of the t-scores for the given Y

reconstruct y -> (t') -> x', via inverse

Requirements

pytorch (>2.0), tqdm

Usage

from eca import ECA

# define options
options = {
    'tol'   : 1E-5, 
    'epochs': 5000, 
    'lr'    : 1E-3, 
    'batch_size': 512,
    'seed' : 123
}
# assuming model is a torch-based (instance of nn.Module) neural network to predict X -> Y
eca = ECA(model) 
# run evaluation of the vectors
# data_x, data_y are torch.Tensor(torch.float32) tensors
v, y_var, x_var = eca.fit(data_x, data_y, n_comp=3, options=options, verbose=True)

To run inverse transformation (find an approximation in V-space for a given y):

# inverse transformation
options_inv = {
    'tol'   : 1E-4, 
    'epochs': 1000, 
    'lr'    : 5E-2, 
}
t = eca.inverse(y, options=options_inv, verbose=True)

antonvladyka/eca

Emulator-based Component Analysis (ECA)

Glossary and functions:

Requirements

Usage