174 research outputs found
Multi-consensus Decentralized Accelerated Gradient Descent
This paper considers the decentralized optimization problem, which has
applications in large scale machine learning, sensor networks, and control
theory. We propose a novel algorithm that can achieve near optimal
communication complexity, matching the known lower bound up to a logarithmic
factor of the condition number of the problem. Our theoretical results give
affirmative answers to the open problem on whether there exists an algorithm
that can achieve a communication complexity (nearly) matching the lower bound
depending on the global condition number instead of the local one. Moreover,
the proposed algorithm achieves the optimal computation complexity matching the
lower bound up to universal constants. Furthermore, to achieve a linear
convergence rate, our algorithm \emph{doesn't} require the individual functions
to be (strongly) convex. Our method relies on a novel combination of known
techniques including Nesterov's accelerated gradient descent, multi-consensus
and gradient-tracking. The analysis is new, and may be applied to other related
problems. Empirical studies demonstrate the effectiveness of our method for
machine learning applications
Dynamic Self-training Framework for Graph Convolutional Networks
Graph neural networks (GNN) such as GCN, GAT, MoNet have achieved
state-of-the-art results on semi-supervised learning on graphs. However, when
the number of labeled nodes is very small, the performances of GNNs downgrade
dramatically. Self-training has proved to be effective for resolving this
issue, however, the performance of self-trained GCN is still inferior to that
of G2G and DGI for many settings. Moreover, additional model complexity make it
more difficult to tune the hyper-parameters and do model selection. We argue
that the power of self-training is still not fully explored for the node
classification task. In this paper, we propose a unified end-to-end
self-training framework called \emph{Dynamic Self-traning}, which generalizes
and simplifies prior work. A simple instantiation of the framework based on GCN
is provided and empirical results show that our framework outperforms all
previous methods including GNNs, embedding based method and self-trained GCNs
by a noticeable margin. Moreover, compared with standard self-training,
hyper-parameter tuning for our framework is easier.Comment: 11page
One-dimensional Tensor Network Recovery
We study the recovery of the underlying graphs or permutations for tensors in
tensor ring or tensor train format. Our proposed algorithms compare the
matricization ranks after down-sampling, whose complexity is for
-th order tensors. We prove that our algorithms can almost surely recover
the correct graph or permutation when tensor entries can be observed without
noise. We further establish the robustness of our algorithms against
observational noise. The theoretical results are validated by numerical
experiments
- …