Scattering convolutional hidden Markov trees

We here combine the rich, overcomplete signal representation afforded by the scattering transform together with a probabilistic graphical model which captures hierarchical dependencies between coefficients at different layers. The wavelet scattering network result in a high-dimensional representation which is translation invariant and stable to deformations whilst preserving informative content. Such properties are achieved by cascading wavelet transform convolutions with non-linear modulus and averaging operators. The network structure and its distributions are described using a Hidden Markov Tree. This yields a generative model for high-dimensional inference and offers a means to perform various inference tasks such as prediction. Our proposed scattering convolutional hidden Markov tree displays promising results on classification tasks of complex images in the challenging case where the number of training examples is extremely small.