Learning and Inference in Sparse Coding Models with Langevin Dynamics
This work addresses a bottleneck in probabilistic latent variable models for researchers in machine learning and neuroscience, offering an incremental improvement by applying existing stochastic methods to sparse coding.
The paper tackled the challenge of sampling posterior distributions in sparse coding models by using Langevin dynamics to harness natural stochasticity, resulting in an efficient method for inference and learning without digital accumulators, demonstrated on synthetic and natural image datasets with probabilistic correctness.
We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to be solved by harnessing natural sources of stochasticity inherent in electronic and neural systems. We demonstrate this idea for a sparse coding model by deriving a continuous-time equation for inferring its latent variables via Langevin dynamics. The model parameters are learned by simultaneously evolving according to another continuous-time equation, thus bypassing the need for digital accumulators or a global clock. Moreover we show that Langevin dynamics lead to an efficient procedure for sampling from the posterior distribution in the 'L0 sparse' regime, where latent variables are encouraged to be set to zero as opposed to having a small L1 norm. This allows the model to properly incorporate the notion of sparsity rather than having to resort to a relaxed version of sparsity to make optimization tractable. Simulations of the proposed dynamical system on both synthetic and natural image datasets demonstrate that the model is capable of probabilistically correct inference, enabling learning of the dictionary as well as parameters of the prior.