52,289 research outputs found
Modelling and Analysis Using GROOVE
In this paper we present case studies that describe how the graph transformation tool GROOVE has been used to model problems from a wide variety of domains. These case studies highlight the wide applicability of GROOVE in particular, and of graph transformation in general. They also give concrete templates for using GROOVE in practice. Furthermore, we use the case studies to analyse the main strong and weak points of GROOVE
Convex and Network Flow Optimization for Structured Sparsity
We consider a class of learning problems regularized by a structured
sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over
groups of variables. Whereas much effort has been put in developing fast
optimization techniques when the groups are disjoint or embedded in a
hierarchy, we address here the case of general overlapping groups. To this end,
we present two different strategies: On the one hand, we show that the proximal
operator associated with a sum of l_infinity-norms can be computed exactly in
polynomial time by solving a quadratic min-cost flow problem, allowing the use
of accelerated proximal gradient methods. On the other hand, we use proximal
splitting techniques, and address an equivalent formulation with
non-overlapping groups, but in higher dimension and with additional
constraints. We propose efficient and scalable algorithms exploiting these two
strategies, which are significantly faster than alternative approaches. We
illustrate these methods with several problems such as CUR matrix
factorization, multi-task learning of tree-structured dictionaries, background
subtraction in video sequences, image denoising with wavelets, and topographic
dictionary learning of natural image patches.Comment: to appear in the Journal of Machine Learning Research (JMLR
Learning Generalized Reactive Policies using Deep Neural Networks
We present a new approach to learning for planning, where knowledge acquired
while solving a given set of planning problems is used to plan faster in
related, but new problem instances. We show that a deep neural network can be
used to learn and represent a \emph{generalized reactive policy} (GRP) that
maps a problem instance and a state to an action, and that the learned GRPs
efficiently solve large classes of challenging problem instances. In contrast
to prior efforts in this direction, our approach significantly reduces the
dependence of learning on handcrafted domain knowledge or feature selection.
Instead, the GRP is trained from scratch using a set of successful execution
traces. We show that our approach can also be used to automatically learn a
heuristic function that can be used in directed search algorithms. We evaluate
our approach using an extensive suite of experiments on two challenging
planning problem domains and show that our approach facilitates learning
complex decision making policies and powerful heuristic functions with minimal
human input. Videos of our results are available at goo.gl/Hpy4e3
Graph Element Networks: adaptive, structured computation and memory
We explore the use of graph neural networks (GNNs) to model spatial processes
in which there is no a priori graphical structure. Similar to finite element
analysis, we assign nodes of a GNN to spatial locations and use a computational
process defined on the graph to model the relationship between an initial
function defined over a space and a resulting function in the same space. We
use GNNs as a computational substrate, and show that the locations of the nodes
in space as well as their connectivity can be optimized to focus on the most
complex parts of the space. Moreover, this representational strategy allows the
learned input-output relationship to generalize over the size of the underlying
space and run the same model at different levels of precision, trading
computation for accuracy. We demonstrate this method on a traditional PDE
problem, a physical prediction problem from robotics, and learning to predict
scene images from novel viewpoints.Comment: Accepted to ICML 201
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