Model Order Selection with Variational Autoencoding

TL;DR

This paper introduces an unsupervised variational autoencoder approach for model order selection that outperforms classical methods, especially in low SNR or limited snapshot scenarios, by learning a covariance matrix approximation.

Contribution

It proposes a novel VAE-based method for model order selection that is unsupervised and effective with small datasets, outperforming classical techniques.

Findings

Outperforms classical model order selection methods.

Achieves comparable or better results than supervised approaches.

Effective in low SNR and limited snapshot conditions.

Abstract

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.