Stochastic Methods

The cca_zoo.stochastic module provides mini-batch CCA methods, for datasets too large to fit a full-batch gradient step in memory.

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StochasticCCAEY

StochasticCCAEY fits the same unconstrained Eckart-Young (EY) objective as cca_zoo.linear.CCAEY — see that page's Background section for the objective itself — by mini-batch momentum SGD instead of full-batch L-BFGS-B:

from cca_zoo.stochastic import StochasticCCAEY

model = StochasticCCAEY(
    latent_dimensions=2, learning_rate=0.01, batch_size=128, max_iter=200
)
model.fit([X1, X2])

When to use: the dataset doesn't fit comfortably in memory for a full-batch gradient step, or is naturally streamed/out-of-core. Otherwise, CCAEY is simpler to tune (no learning_rate or batch_size) and converges more predictably.

batch_size trades off gradient-estimate noise against per-step cost; learning_rate and the momentum term interact with it the same way they do for any mini-batch SGD method — too large a learning rate for a given batch size can diverge, too small converges slowly. random_state controls both the initial weights and the batch sampling order, so it must be fixed for reproducible fits.