[AUD-025][Medium] Return EM likelihood matching returned parameters

[gabrielsantosphilips]

Audit finding

• ID: AUD-025
• Status: Verified defect
• Severity: Medium
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

On iteration exhaustion, ExpectationMaximization::Run() evaluates likelihood for currentParams, applies one final M-step, then returns the updated parameters with the old likelihood. A one-iteration call reports M(theta0) together with L(theta0).

Source:

numerical-toolbox-cpp/numerical/estimators/offline/ExpectationMaximization.hpp

Lines 98 to 126 in 2f47932

	EmParameters currentParams = initialParameters;
	float prevLogLikelihood = std::numeric_limits<float>::lowest();
	float logLikelihood = std::numeric_limits<float>::lowest();
	std::size_t iter = 0;
	bool converged = false;
	while (iter < maxIterations)
	{
	const auto smootherOutput = smoother_.Smooth(
	{ currentParams.F, currentParams.H, currentParams.Q, currentParams.R },
	observations, numSteps,
	currentParams.initialState, currentParams.initialCovariance);
	logLikelihood = smootherOutput.logLikelihood;
	++iter;
	if (math::Abs(logLikelihood - prevLogLikelihood) < convergenceTolerance)
	{
	converged = true;
	break;
	}
	prevLogLikelihood = logLikelihood;
	currentParams = MStep(smootherOutput, observations, numSteps);
	}
	return EmResult{ currentParams, iter, logLikelihood, converged };
	}

Acceptance criteria

• Returned likelihood is evaluated for the returned parameter set.
• Iteration count and convergence flag describe the same E/M sequence.
• Add a one-iteration parameter/likelihood consistency test.
• Add monotonic-likelihood checks with an independent reference sequence.