Deep Learning's recent successes have mostly relied on Convolutional
Networks, which exploit fundamental statistical properties of images, sounds
and video data: the local stationarity and multi-scale compositional structure,
that allows expressing long range interactions in terms of shorter, localized
interactions. However, there exist other important examples, such as text
documents or bioinformatic data, that may lack some or all of these strong
statistical regularities.
In this paper we consider the general question of how to construct deep
architectures with small learning complexity on general non-Euclidean domains,
which are typically unknown and need to be estimated from the data. In
particular, we develop an extension of Spectral Networks which incorporates a
Graph Estimation procedure, that we test on large-scale classification
problems, matching or improving over Dropout Networks with far less parameters
to estimate.

本文介绍了一种将谱网络与图估计过程相结合的方法，用于构建小学习复杂度和处理没有强规律的领域的深层神经网络，并在大规模分类问题中测试并达到更好的性能。

基于图结构数据的深度卷积网络

Deep Convolutional Networks on Graph-Structured Data

We study graph estimation and density estimation in high dimensions, using a
family of density estimators based on forest structured undirected graphical
models. For density estimation, we do not assume the true distribution
corresponds to a forest; rather, we form kernel density estimates of the
bivariate and univariate marginals, and apply Kruskal's algorithm to estimate
the optimal forest on held out data. We prove an oracle inequality on the
excess risk of the resulting estimator relative to the risk of the best forest.
For graph estimation, we consider the problem of estimating forests with
restricted tree sizes. We prove that finding a maximum weight spanning forest
with restricted tree size is NP-hard, and develop an approximation algorithm
for this problem. Viewing the tree size as a complexity parameter, we then
select a forest using data splitting, and prove bounds on excess risk and
structure selection consistency of the procedure. Experiments with simulated
data and microarray data indicate that the methods are a practical alternative
to Gaussian graphical models.

本文研究了高维图估计和密度估计问题，并使用基于森林结构无向图模型的一族密度估计器。对于图估计，研究了估计具有限制树大小的森林的问题，并开发了一种近似算法。