3.1 Objective function convergence

The ELBO (Evidence Lower BOund) is the objective function that the algorithm maximizes, possibly combined with penalization: ||(ELBO - \lambda * penalty||) The objective function's value should steadily increase and eventually plateau just below zero. Note that oscillations occur naturally due to inherent stochasticity. What to look for:

Good convergence: Steady upward trend that flattens into a plateau. The curve should stabilize before the end of iterations. The final 10-20% of iterations should show minimal change.
Not converged: Still increasing steeply at the end → increase number of iterations.
Unstable: Erratic oscillations are not dampened over time → decrease learning rate or adjust batch size.
Too high absolute value: Values in millions or more signify a major problem with the algorithm setup. Assess the features' trajectories below. (Values in low thousands, depending on lambda, are generally favorable.)

3.2 Feature convergence in components

These plots are crucial for assessment of whether the feature selector produced sensible results. Each plot shows how feature importance values (mu) evolve during optimization for one component. The algorithm assigns each feature to either the Spike (near zero) or Slab (non-zero) distribution. What to look for:

Good separation: Clear gap between features converging to ~0 and features with significant non-zero values.
Optimization process:

Problem indicators:

All features → 0: Over-regularization. Increase spike variance.
Features' ordering does not change over time: May indicate under-regularization.
Too many non-zero features: May indicate under-regularization. Carefully decrease spike variance and/or enforce stronger sparsity.
Oscillating values: Learning rate too high or batch size too small.
Set of important features changes multiple times over time (situation: while most features converge to 0, a few become nonzero. Then the nonzero features become 0 and others emerge. The set of important features significantly changes multiple times.): The algorithm cannot find any significant signal among noise. May indicate fundamental problem with the dataset.

3.3 Relative importances of components

The pie chart shows how the algorithm distributes probability mass across the components. (Alphas represent the mixing weights in the Gaussian mixture model that approximate the posterior distribution.) The alphas should correspond to the predictive potential of the components. What to look for:

(Un)balanced distribution: If you expect multiple solutions of comparable significance, alphas should be relatively balanced across components. If some components dominate, too many components may have been requested (i.e. the dataset supports fewer distinct solutions).