A Generative Process for Sampling Contractive Auto-Encoders
This addresses the challenge of efficient sampling and invariance learning in unsupervised representation learning for machine learning practitioners, though it is incremental as it builds on existing contractive auto-encoder methods.
The paper tackles the problem of generating samples consistent with the local manifold structure learned by contractive auto-encoders, proposing a stochastic process that experimentally converges quickly and mixes well between modes compared to Restricted Boltzmann Machines and Deep Belief Networks, and also improves classification error by learning invariances.
The contractive auto-encoder learns a representation of the input data that captures the local manifold structure around each data point, through the leading singular vectors of the Jacobian of the transformation from input to representation. The corresponding singular values specify how much local variation is plausible in directions associated with the corresponding singular vectors, while remaining in a high-density region of the input space. This paper proposes a procedure for generating samples that are consistent with the local structure captured by a contractive auto-encoder. The associated stochastic process defines a distribution from which one can sample, and which experimentally appears to converge quickly and mix well between modes, compared to Restricted Boltzmann Machines and Deep Belief Networks. The intuitions behind this procedure can also be used to train the second layer of contraction that pools lower-level features and learns to be invariant to the local directions of variation discovered in the first layer. We show that this can help learn and represent invariances present in the data and improve classification error.