The Variational Homoencoder: Learning to learn high capacity generative models from few examples

Hierarchical Bayesian methods can unify many related tasks (e.g. k-shot classification, conditional and unconditional generation) as inference within a single generative model. However, when this generative model is expressed as a powerful neural network such as a PixelCNN, we show that existing learning techniques typically fail to effectively use latent variables. To address this, we develop a modification of the Variational Autoencoder in which encoded observations are decoded to new elements from the same class. This technique, which we call a Variational Homoencoder (VHE), produces a hierarchical latent variable model which better utilises latent variables. We use the VHE framework to learn a hierarchical PixelCNN on the Omniglot dataset, which outperforms all existing models on test set likelihood and achieves strong performance on one-shot generation and classification tasks. We additionally validate the VHE on natural images from the YouTube Faces database. Finally, we develop extensions of the model that apply to richer dataset structures such as factorial and hierarchical categories.Comment: UAI 2018 oral presentatio

LANDSAT application of remote sensing to shoreline-form analysis

The author has identified the following significant results. LANDSAT imagery of the southern end of Assateague Island, Virginia, was enlarged to 1:80,000 and compared with high altitude (1:130,000) and low altitude (1:24,000) aerial photography in an attempt to quantify change in land area over a nine month period. Change in area and configuration was found with LANDSAT and low altitude photography. Change in configuration, but no change in area was found with high altitude photography. Due to tidal differences at time of image obtention and lack of baseline data, the accuracy of the LANDSAT measurements could not be determined. They were consistent with the measurements from the low altitude photography

Integrability and explicit solutions in some Bianchi cosmological dynamical systems

The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G_2 cosmologies. By using Darboux's theory in order to study ordinary differential equations in the complex projective plane CP^2 we solve the Bianchi V models totally. Moreover, we carry out a study of Bianchi VI models and first integrals are given in particular cases