24,849 research outputs found
Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures
Probabilistic graphical models are a central tool in AI; however, they are
generally not as expressive as deep neural models, and inference is notoriously
hard and slow. In contrast, deep probabilistic models such as sum-product
networks (SPNs) capture joint distributions in a tractable fashion, but still
lack the expressive power of intractable models based on deep neural networks.
Therefore, we introduce conditional SPNs (CSPNs), conditional density
estimators for multivariate and potentially hybrid domains which allow
harnessing the expressive power of neural networks while still maintaining
tractability guarantees. One way to implement CSPNs is to use an existing SPN
structure and condition its parameters on the input, e.g., via a deep neural
network. This approach, however, might misrepresent the conditional
independence structure present in data. Consequently, we also develop a
structure-learning approach that derives both the structure and parameters of
CSPNs from data. Our experimental evidence demonstrates that CSPNs are
competitive with other probabilistic models and yield superior performance on
multilabel image classification compared to mean field and mixture density
networks. Furthermore, they can successfully be employed as building blocks for
structured probabilistic models, such as autoregressive image models.Comment: 13 pages, 6 figure
Deep Markov Random Field for Image Modeling
Markov Random Fields (MRFs), a formulation widely used in generative image
modeling, have long been plagued by the lack of expressive power. This issue is
primarily due to the fact that conventional MRFs formulations tend to use
simplistic factors to capture local patterns. In this paper, we move beyond
such limitations, and propose a novel MRF model that uses fully-connected
neurons to express the complex interactions among pixels. Through theoretical
analysis, we reveal an inherent connection between this model and recurrent
neural networks, and thereon derive an approximated feed-forward network that
couples multiple RNNs along opposite directions. This formulation combines the
expressive power of deep neural networks and the cyclic dependency structure of
MRF in a unified model, bringing the modeling capability to a new level. The
feed-forward approximation also allows it to be efficiently learned from data.
Experimental results on a variety of low-level vision tasks show notable
improvement over state-of-the-arts.Comment: Accepted at ECCV 201
Approximation in shift-invariant spaces with deep ReLU neural networks
We study the expressive power of deep ReLU neural networks for approximating
functions in dilated shift-invariant spaces, which are widely used in signal
processing, image processing, communications and so on. Approximation error
bounds are estimated with respect to the width and depth of neural networks.
The network construction is based on the bit extraction and data-fitting
capacity of deep neural networks. As applications of our main results, the
approximation rates of classical function spaces such as Sobolev spaces and
Besov spaces are obtained. We also give lower bounds of the approximation error for Sobolev spaces, which show that our
construction of neural network is asymptotically optimal up to a logarithmic
factor
- …