1,236 research outputs found
Factoring variations in natural images with deep Gaussian mixture models
Generative models can be seen as the swiss army knives of machine learning, as many problems can be written probabilistically in terms of the distribution of the data, including prediction, reconstruction, imputation and simulation. One of the most promising directions for unsupervised learning may lie in Deep Learning methods, given their success in supervised learning. However, one of the cur- rent problems with deep unsupervised learning methods, is that they often are harder to scale. As a result there are some easier, more scalable shallow meth- ods, such as the Gaussian Mixture Model and the Student-t Mixture Model, that remain surprisingly competitive. In this paper we propose a new scalable deep generative model for images, called the Deep Gaussian Mixture Model, that is a straightforward but powerful generalization of GMMs to multiple layers. The parametrization of a Deep GMM allows it to efficiently capture products of vari- ations in natural images. We propose a new EM-based algorithm that scales well to large datasets, and we show that both the Expectation and the Maximization steps can easily be distributed over multiple machines. In our density estimation experiments we show that deeper GMM architectures generalize better than more shallow ones, with results in the same ballpark as the state of the art
Generative Image Modeling Using Spatial LSTMs
Modeling the distribution of natural images is challenging, partly because of
strong statistical dependencies which can extend over hundreds of pixels.
Recurrent neural networks have been successful in capturing long-range
dependencies in a number of problems but only recently have found their way
into generative image models. We here introduce a recurrent image model based
on multi-dimensional long short-term memory units which are particularly suited
for image modeling due to their spatial structure. Our model scales to images
of arbitrary size and its likelihood is computationally tractable. We find that
it outperforms the state of the art in quantitative comparisons on several
image datasets and produces promising results when used for texture synthesis
and inpainting
A note on the evaluation of generative models
Probabilistic generative models can be used for compression, denoising,
inpainting, texture synthesis, semi-supervised learning, unsupervised feature
learning, and other tasks. Given this wide range of applications, it is not
surprising that a lot of heterogeneity exists in the way these models are
formulated, trained, and evaluated. As a consequence, direct comparison between
models is often difficult. This article reviews mostly known but often
underappreciated properties relating to the evaluation and interpretation of
generative models with a focus on image models. In particular, we show that
three of the currently most commonly used criteria---average log-likelihood,
Parzen window estimates, and visual fidelity of samples---are largely
independent of each other when the data is high-dimensional. Good performance
with respect to one criterion therefore need not imply good performance with
respect to the other criteria. Our results show that extrapolation from one
criterion to another is not warranted and generative models need to be
evaluated directly with respect to the application(s) they were intended for.
In addition, we provide examples demonstrating that Parzen window estimates
should generally be avoided
Deep Gaussian Mixture Models
Deep learning is a hierarchical inference method formed by subsequent
multiple layers of learning able to more efficiently describe complex
relationships. In this work, Deep Gaussian Mixture Models are introduced and
discussed. A Deep Gaussian Mixture model (DGMM) is a network of multiple layers
of latent variables, where, at each layer, the variables follow a mixture of
Gaussian distributions. Thus, the deep mixture model consists of a set of
nested mixtures of linear models, which globally provide a nonlinear model able
to describe the data in a very flexible way. In order to avoid
overparameterized solutions, dimension reduction by factor models can be
applied at each layer of the architecture thus resulting in deep mixtures of
factor analysers.Comment: 19 pages, 4 figure
- …