ECM

class ECM(breakpointers, pruners, optimizer)

Bases: BaseEstimator

An estimator that implements the Expectation-Conditional Maximization (ECM) algorithm.

This class encapsulates the logic for the ECM algorithm, a variant of the classic Expectation-Maximization (EM) algorithm. It constructs and executes a Pipeline consisting of an expectation step (ExpectationStep) and a conditional maximization step (MaximizationStep).

The key feature of this ECM implementation is that the maximization (M-step) is partitioned into separate, smaller optimization problems—one for each component in the mixture. For each component, all of its optimizable (non-fixed) parameters are estimated simultaneously by maximizing the Q-function. This component-wise update simplifies the optimization process.

The overall fitting process can be customized with stopping criteria, component pruning strategies, and a numerical optimizer.

Parameters:

• breakpointers (Sequence[Breakpointer]) – A sequence of strategies that define the stopping conditions for the iterative process.

• pruners (Sequence[Pruner]) – A sequence of strategies for removing (pruning) components from the mixture model during fitting.

• optimizer (Optimizer) – A numerical optimizer instance used in the maximization step to find the optimal parameters.

Variables:

• breakpointers (list[Breakpointer]) – The list of objects that determine when the fitting process should terminate.

• pruners (list[Pruner]) – The list of objects that may remove components from the mixture during the fitting process.

• optimizer (Optimizer) – The numerical optimizer used for parameter estimation.

• logger (IterationsHistory | None) – An object that collects information about each iteration. This attribute is only available after the fit() method has been called. Accessing it beforehand will raise an AttributeError.

Methods

fit(X, mixture[, once_in_iterations])

Fits the mixture model to the data using the ECM algorithm.