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 SGD instead of full-batch L-BFGS-B, with the adaptive step of sklearn's SGDRegressor(learning_rate="adaptive"):

from cca_zoo.stochastic import StochasticCCAEY

model = StochasticCCAEY(n_components=2, 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.

learning_rate is relative: the step is learning_rate / L, where L is the largest variance along any direction of any view, so the default suits data at any scale without standardising. batch_size trades off gradient-estimate noise against per-step cost. A mini-batch step cannot converge at a fixed size: it hovers at a distance set by the batches' noise. So, as in sklearn, whenever the epoch loss fails to improve by tol for n_iter_no_change epochs the step is divided by 5, and the fit stops once the step is negligible. Too large a learning_rate for a small batch can still diverge; the error says so. random_state controls both the initial weights and the batch sampling order, so it must be fixed for reproducible fits.