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 itself is unsupervised and only requires a small representative dataset for calibration purposes after training of the VAE. Numerical simulations show that the proposed method clearly outperforms classical methods and even reaches or beats a supervised approach depending on the considered snapshots.

翻译：变分自编码器下的模型阶数选择 传统的模型阶数选择方法在低信噪比或快照数较少的情况下通常会失败。基于深度学习的方法是这种具有挑战性情况下的有希望的选择，因为它们通过在大型数据集上的训练来补偿可用观测信息的缺乏。本文提出了一种方法，利用变分自编码器(VAE)进行模型阶数的选择。其思想是在VAE解码器上学习一个参数化条件协方差矩阵以逼近真实信号协方差矩阵。该方法本身是无监督的，只需要在VAE训练之后使用少量的代表性数据集进行校准。数值模拟结果表明，所提出的方法明显优于传统方法，甚至能够根据考虑的快照数达到或超过监督方法。