180,424 research outputs found
backShift: Learning causal cyclic graphs from unknown shift interventions
We propose a simple method to learn linear causal cyclic models in the
presence of latent variables. The method relies on equilibrium data of the
model recorded under a specific kind of interventions ("shift interventions").
The location and strength of these interventions do not have to be known and
can be estimated from the data. Our method, called backShift, only uses second
moments of the data and performs simple joint matrix diagonalization, applied
to differences between covariance matrices. We give a sufficient and necessary
condition for identifiability of the system, which is fulfilled almost surely
under some quite general assumptions if and only if there are at least three
distinct experimental settings, one of which can be pure observational data. We
demonstrate the performance on some simulated data and applications in flow
cytometry and financial time series. The code is made available as R-package
backShift
Learning nonparametric latent causal graphs with unknown interventions
We establish conditions under which latent causal graphs are
nonparametrically identifiable and can be reconstructed from unknown
interventions in the latent space. Our primary focus is the identification of
the latent structure in measurement models without parametric assumptions such
as linearity or Gaussianity. Moreover, we do not assume the number of hidden
variables is known, and we show that at most one unknown intervention per
hidden variable is needed. This extends a recent line of work on learning
causal representations from observations and interventions. The proofs are
constructive and introduce two new graphical concepts -- imaginary subsets and
isolated edges -- that may be useful in their own right. As a matter of
independent interest, the proofs also involve a novel characterization of the
limits of edge orientations within the equivalence class of DAGs induced by
unknown interventions. These are the first results to characterize the
conditions under which causal representations are identifiable without making
any parametric assumptions in a general setting with unknown interventions and
without faithfulness.Comment: To appear at NeurIPS 202
Unsupervised learning of human motion
An unsupervised learning algorithm that can obtain a probabilistic model of an object composed of a collection of parts (a moving human body in our examples) automatically from unlabeled training data is presented. The training data include both useful "foreground" features as well as features that arise from irrelevant background clutter - the correspondence between parts and detected features is unknown. The joint probability density function of the parts is represented by a mixture of decomposable triangulated graphs which allow for fast detection. To learn the model structure as well as model parameters, an EM-like algorithm is developed where the labeling of the data (part assignments) is treated as hidden variables. The unsupervised learning technique is not limited to decomposable triangulated graphs. The efficiency and effectiveness of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled image sequences, and testing the learned models on a variety of sequences
Domain Adaptation on Graphs by Learning Graph Topologies: Theoretical Analysis and an Algorithm
Traditional machine learning algorithms assume that the training and test
data have the same distribution, while this assumption does not necessarily
hold in real applications. Domain adaptation methods take into account the
deviations in the data distribution. In this work, we study the problem of
domain adaptation on graphs. We consider a source graph and a target graph
constructed with samples drawn from data manifolds. We study the problem of
estimating the unknown class labels on the target graph using the label
information on the source graph and the similarity between the two graphs. We
particularly focus on a setting where the target label function is learnt such
that its spectrum is similar to that of the source label function. We first
propose a theoretical analysis of domain adaptation on graphs and present
performance bounds that characterize the target classification error in terms
of the properties of the graphs and the data manifolds. We show that the
classification performance improves as the topologies of the graphs get more
balanced, i.e., as the numbers of neighbors of different graph nodes become
more proportionate, and weak edges with small weights are avoided. Our results
also suggest that graph edges between too distant data samples should be
avoided for good generalization performance. We then propose a graph domain
adaptation algorithm inspired by our theoretical findings, which estimates the
label functions while learning the source and target graph topologies at the
same time. The joint graph learning and label estimation problem is formulated
through an objective function relying on our performance bounds, which is
minimized with an alternating optimization scheme. Experiments on synthetic and
real data sets suggest that the proposed method outperforms baseline
approaches
Learning the Network of Graphs for Graph Neural Networks
Graph neural networks (GNNs) have achieved great success in many scenarios
with graph-structured data. However, in many real applications, there are three
issues when applying GNNs: graphs are unknown, nodes have noisy features, and
graphs contain noisy connections. Aiming at solving these problems, we propose
a new graph neural network named as GL-GNN. Our model includes multiple
sub-modules, each sub-module selects important data features and learn the
corresponding key relation graph of data samples when graphs are unknown.
GL-GNN further obtains the network of graphs by learning the network of
sub-modules. The learned graphs are further fused using an aggregation method
over the network of graphs. Our model solves the first issue by simultaneously
learning multiple relation graphs of data samples as well as a relation network
of graphs, and solves the second and the third issue by selecting important
data features as well as important data sample relations. We compare our method
with 14 baseline methods on seven datasets when the graph is unknown and 11
baseline methods on two datasets when the graph is known. The results show that
our method achieves better accuracies than the baseline methods and is capable
of selecting important features and graph edges from the dataset. Our code will
be publicly available at \url{https://github.com/Looomo/GL-GNN}
- …