One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations lie on a low
er-dimensional manifold of high probability. It has been more difficult, however, to exploit this insight to build explicit, tractable density models for high-dimensional data. In this paper, we introduce the deep density model (DDM), a new approach to density estimation. We exploit insights from deep learning to construct a bijective map to a representation space, under which the transformation of the distribution of the data is approximately factorized and has identical and known marginal densities. The simplicity of the latent distribution under the model allows us to feasibly explore it, and the invertibility of the map to characterize contraction of measure across it. This enables us to compute normalized densities for out-of-sample data. This combination of tractability and flexibility allows us to tackle a variety of probabilistic tasks on high-dimensional datasets, including: rapid computation of normalized densities at test-time without evaluating a partition function; generation of samples without MCMC; and characterization of the joint entropy of the data.
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with multivariat
e Gaussian priors. Its key properties are: 1) it has simple, generic code applicable to many models, 2) it has no free parameters, 3) it works well for a variety of Gaussian process based models. These properties make our method ideal for use while model building, removing the need to spend time deriving and tuning updates for more complex algorithms.
