  Classical methods for model order selection often fail in scenarios with low
SNR or few snapshots. Deep learning-based methods are promising alternatives
for such challenging situations as they compensate lack of information in the
available observations with training on large datasets. This manuscript
proposes an approach that uses a variational autoencoder (VAE) for model order
selection. The idea is to learn a parameterized conditional covariance matrix
at the VAE decoder that approximates the true signal covariance matrix. The
method is unsupervised and only requires a small representative dataset for
calibration after training the VAE. Numerical simulations show that the
proposed method outperforms classical methods and even reaches or beats a
supervised approach depending on the considered snapshots.
