Probabilistic inference serves as a popular model for neural processing. It is still unclear, however, how approximate probabilistic inference can be accurate and scalable to very high-dimensional continuous latent spaces. Especially as typical posteriors for sensory data can be expected to exhibit complex latent dependencies including multiple modes.

Probabilistic inference serves as a popular model for neural processing. It is still unclear, however, how approximate probabilistic inference can be accurate and scalable to very high-dimensional continuous latent spaces. Especially as typical posteriors for sensory data can be expected to exhibit complex latent dependencies including multiple modes. Here, we study an approach that can efficiently be scaled while maintaining a richly structured posterior approximation under these conditions. As example model we use spike-and-slab sparse coding for V1 processing, and combine latent subspace selection with Gibbs sampling (selectand-sample).

Probabilistic inference serves as a popular model for neural processing. It is still unclear, however, how approximate probabilistic inference can be accurate and scalable to very high-dimensional continuous latent spaces. Especially as typical posteriors for sensory data can be expected to exhibit complex latent dependencies including multiple modes. Here, we study an approach that can efficiently be scaled while maintaining a richly structured posterior approximation under these conditions. As example model we use spike-and-slab sparse coding for V1 processing, and combine latent subspace selection with Gibbs sampling (select-and-sample). Unlike factored variational approaches, the method can maintain large numbers of posterior modes and complex latent dependencies. Unlike pure sampling, the method is scalable to very high-dimensional latent spaces. Among all sparse coding approaches with non-trivial posterior approximations (MAP or ICA-like models), we report the largest-scale results. In applications we firstly verify the approach by showing competitiveness in standard denoising benchmarks. Secondly, we use its scalability to, for the first time, study highly-overcomplete settings for V1 encoding using sophisticated posterior representations. More generally, our study shows that very accurate probabilistic inference for multi-modal posteriors with complex dependencies is tractable, functionally desirable and consistent with models for neural inference.

We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the application of a more flexible `spike-and-slab' distribution which models the absence or presence of a source's contribution independently of its strength if it contributes. We investigate two approaches to optimize the parameters of spike-and-slab sparse coding: a novel truncated EM approach and, for comparison, an approach based on standard factored variational distributions. The truncated approach can be regarded as a variational approach with truncated posteriors as variational distributions. In applications to source separation we find that both approaches improve the state-of-the-art in a number of standard benchmarks, which argues for the use of `spike-and-slab' priors for the corresponding data domains. Furthermore, we find that the truncated EM approach improves on the standard factored approach in source separation tasks$-$which hints to biases introduced by assuming posterior independence in the factored variational approach. Likewise, on a standard benchmark for image denoising, we find that the truncated EM approach improves on the factored variational approach. While the performance of the factored approach saturates with increasing numbers of hidden dimensions, the performance of the truncated approach improves the state-of-the-art for higher noise levels.