  We propose a semi-supervised approach to acoustic source localization in
reverberant environments based on deep generative modeling. Localization in
reverberant environments remains an open challenge. Even with large data
volumes, the number of labels available for supervised learning in reverberant
environments is usually small. We address this issue by performing
semi-supervised learning (SSL) with convolutional variational autoencoders
(VAEs) on reverberant speech signals recorded with microphone arrays. The VAE
is trained to generate the phase of relative transfer functions (RTFs) between
microphones, in parallel with a direction of arrival (DOA) classifier based on
RTF-phase. These models are trained using both labeled and unlabeled RTF-phase
sequences. In learning to perform these tasks, the VAE-SSL explicitly learns to
separate the physical causes of the RTF-phase (i.e., source location) from
distracting signal characteristics such as noise and speech activity. Relative
to existing semi-supervised localization methods in acoustics, VAE-SSL is
effectively an end-to-end processing approach which relies on minimal
preprocessing of RTF-phase features. As far as we are aware, our paper presents
the first approach to modeling the physics of acoustic propagation using deep
generative modeling. The VAE-SSL approach is compared with two signal
processing-based approaches, steered response power with phase transform
(SRP-PHAT) and MUltiple SIgnal Classification (MUSIC), as well as fully
supervised CNNs. We find that VAE-SSL can outperform the conventional
approaches and the CNN in label-limited scenarios. Further, the trained VAE-SSL
system can generate new RTF-phase samples, which shows the VAE-SSL approach
learns the physics of the acoustic environment. The generative modeling in
VAE-SSL thus provides a means of interpreting the learned representations.
