8,248 research outputs found
A Deep and Tractable Density Estimator
The Neural Autoregressive Distribution Estimator (NADE) and its real-valued version RNADE are competitive density models of multidimensional data across a variety of domains. These models use a fixed, arbitrary ordering of the data dimen-sions. One can easily condition on variables at the beginning of the ordering, and marginalize out variables at the end of the ordering, however other inference tasks require approximate infer-ence. In this work we introduce an efficient pro-cedure to simultaneously train a NADE model for each possible ordering of the variables, by shar-ing parameters across all these models. We can thus use the most convenient model for each infer-ence task at hand, and ensembles of such models with different orderings are immediately available. Moreover, unlike the original NADE, our train-ing procedure scales to deep models. Empirically, ensembles of Deep NADE models obtain state of the art density estimation performance. 1
Hierarchical Implicit Models and Likelihood-Free Variational Inference
Implicit probabilistic models are a flexible class of models defined by a
simulation process for data. They form the basis for theories which encompass
our understanding of the physical world. Despite this fundamental nature, the
use of implicit models remains limited due to challenges in specifying complex
latent structure in them, and in performing inferences in such models with
large data sets. In this paper, we first introduce hierarchical implicit models
(HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian
modeling, thereby defining models via simulators of data with rich hidden
structure. Next, we develop likelihood-free variational inference (LFVI), a
scalable variational inference algorithm for HIMs. Key to LFVI is specifying a
variational family that is also implicit. This matches the model's flexibility
and allows for accurate approximation of the posterior. We demonstrate diverse
applications: a large-scale physical simulator for predator-prey populations in
ecology; a Bayesian generative adversarial network for discrete data; and a
deep implicit model for text generation.Comment: Appears in Neural Information Processing Systems, 201
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
Mining gold from implicit models to improve likelihood-free inference
Simulators often provide the best description of real-world phenomena.
However, they also lead to challenging inverse problems because the density
they implicitly define is often intractable. We present a new suite of
simulation-based inference techniques that go beyond the traditional
Approximate Bayesian Computation approach, which struggles in a
high-dimensional setting, and extend methods that use surrogate models based on
neural networks. We show that additional information, such as the joint
likelihood ratio and the joint score, can often be extracted from simulators
and used to augment the training data for these surrogate models. Finally, we
demonstrate that these new techniques are more sample efficient and provide
higher-fidelity inference than traditional methods.Comment: Code available at
https://github.com/johannbrehmer/simulator-mining-example . v2: Fixed typos.
v3: Expanded discussion, added Lotka-Volterra example. v4: Improved clarit
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