minPCA

Installation

First, create a Python environment:

python -m venv venv_minpca
source venv_minpca/bin/activate  # On Windows use `venv_minpca\Scripts\activate`

The code is organized as a Python package, and can be installed using pip:

git clone https://github.com/anyafries/minPCA.git
cd minPCA
pip install . --extra-index-url https://download.pytorch.org/whl/cpu # only downloads lightweight torch
cd ..

To install it in editable mode (for modifying the code and seeing the changes immediately) and with developer dependencies (for testing and code formatting), use

pip install -e ".[dev]"

Example use

Load libraries and functions

import numpy as np
from minPCA.minpca import minPCA
from minPCA.utils import get_random_covs

Set-up

p = 20              # number of covariances
n_components = 5    # true rank of covariance
n_envs = 5          # number of environments
n = 5000            # number of observations to draw

# Generate covariance matrices
covs = get_random_covs(p=p, rank=5, nenvs=n_envs)

# Sample from them
Xs = [np.random.multivariate_normal(mean=np.zeros(p), cov=cov, size=n) 
      for cov in covs]

Solve minPCA

• function is one of 'minpca', 'maxrcs', 'maxregret'
• argument norm can be set to True or False for the normalized versions (default)
• to fit empirical losses, simply use the empirical covariances as input to fit().

minpca = minPCA(n_components=n_components, function='maxreconstruction')
minpca = minpca.fit(covs)

# errors/variance on the covariance matrices
print(f"Maximum (population) error: {minpca.maxerr():.3f}")
print(f"Minimum (population) variance: {minpca.minvar():.3f}")

# access the projection
components = minpca.components()
# reconstruct data with the projection
Xs_reconstructed = [Xs[i] @ components @ components.T for i in range(n_envs)]

# compute errors in finite sample
errs = [
      np.linalg.matrix_norm(Xs[i] - Xs_reconstructed[i], ord='fro')**2 / n 
      for i in range(n_envs)
]
print(f"Maximum (sample) error: {max(errs):.3f}")