An implementaton of probabilisitc principal components analysis which is a variant of vanilla PCA that can be used to
- compute factors where some of the data are missing
- interpolate data by using information from additional series
Often, you want to use PCA but your lovely matrix is smattered with NaNs everywhere.
If you don't have too many NaNs, you could try filling in the NaNs with means or some other interpolated value but if you have too many NaNs, your rudimentary interpolation is going to overwhelm the signal in the data with noise. (Think about the limiting case with all but one NaN).
A better way: suppose you had the latent factors representing the matrix. Construct a linear model for each series and then use the resulting model for interpolation. Intuitively, this will preserve the signal from the data as the interpolated values come from latent factors.
However, the problem is you never have these factors to begin with. The old chicken and egg problem. But no matter, fixed point algorithms via Probabilistic PCA to the rescue.
Install via pip:
pip install ppca
Load in the data which should be arranged as n_samples by features. As usual, you should make sure your data is stationary (take first differences if possible) and standardized.
from ppca import PPCA
ppca = PPCA(data)
Fit the model with parameter d specifying the number of components and verbose printing convergence output if required.
ppca.fit(d=100, verbose=True)
The model parameters and components will be attached to the ppca object.
variance_explained = ppca.var_exp
components = ppca.X
model_params = ppca.C
If you want the principal components, call transform.
component_mat = ppca.transform()
Post fitting the model, save the model if you want.
ppca.save('mypcamodel')
Load a model, post instantiating a PPCA object. This will make fitting/transforming much faster.
ppca.load('mypcamodel.npy')