Nonlinear Spike-And-Slab Sparse Coding for Interpretable Image Encoding

摘要: Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) varying pixel intensities. Traditionally, are modelled sparse linear superposition of dictionary elements, where the probabilistic view this problem that coefficients follow Laplace or Cauchy prior distribution. We propose novel instead uses spike-and-slab nonlinear combination components. With prior, our can easily represent exact zeros for e.g. absence an component, such edge, distribution over non-zero nonlinearity (the max rule), idea target occlusions; elements correspond occlude each other. There major consequences assumptions made by both (non)linear approaches, thus goal paper isolate highlight differences between them. Parameter optimization analytically computationally intractable in model, contribution we design Gibbs sampler efficient inference which apply higher dimensional data using latent variable preselection. Results on artificial occlusion-rich with controlled forms structure show extract set closely match generating process, refer interpretable Furthermore, sparseness solution follows ground-truth number components/edges images. The did not learn any level sparsity. This suggests adaptively well-approximate characterize meaningful generation process.