4,900 research outputs found
Incomplete graphical model inference via latent tree aggregation
Graphical network inference is used in many fields such as genomics or
ecology to infer the conditional independence structure between variables, from
measurements of gene expression or species abundances for instance. In many
practical cases, not all variables involved in the network have been observed,
and the samples are actually drawn from a distribution where some variables
have been marginalized out. This challenges the sparsity assumption commonly
made in graphical model inference, since marginalization yields locally dense
structures, even when the original network is sparse. We present a procedure
for inferring Gaussian graphical models when some variables are unobserved,
that accounts both for the influence of missing variables and the low density
of the original network. Our model is based on the aggregation of spanning
trees, and the estimation procedure on the Expectation-Maximization algorithm.
We treat the graph structure and the unobserved nodes as missing variables and
compute posterior probabilities of edge appearance. To provide a complete
methodology, we also propose several model selection criteria to estimate the
number of missing nodes. A simulation study and an illustration flow cytometry
data reveal that our method has favorable edge detection properties compared to
existing graph inference techniques. The methods are implemented in an R
package
Robust causal structure learning with some hidden variables
We introduce a new method to estimate the Markov equivalence class of a
directed acyclic graph (DAG) in the presence of hidden variables, in settings
where the underlying DAG among the observed variables is sparse, and there are
a few hidden variables that have a direct effect on many of the observed ones.
Building on the so-called low rank plus sparse framework, we suggest a
two-stage approach which first removes the effect of the hidden variables, and
then estimates the Markov equivalence class of the underlying DAG under the
assumption that there are no remaining hidden variables. This approach is
consistent in certain high-dimensional regimes and performs favourably when
compared to the state of the art, both in terms of graphical structure recovery
and total causal effect estimation
Causal Effect Inference with Deep Latent-Variable Models
Learning individual-level causal effects from observational data, such as
inferring the most effective medication for a specific patient, is a problem of
growing importance for policy makers. The most important aspect of inferring
causal effects from observational data is the handling of confounders, factors
that affect both an intervention and its outcome. A carefully designed
observational study attempts to measure all important confounders. However,
even if one does not have direct access to all confounders, there may exist
noisy and uncertain measurement of proxies for confounders. We build on recent
advances in latent variable modeling to simultaneously estimate the unknown
latent space summarizing the confounders and the causal effect. Our method is
based on Variational Autoencoders (VAE) which follow the causal structure of
inference with proxies. We show our method is significantly more robust than
existing methods, and matches the state-of-the-art on previous benchmarks
focused on individual treatment effects.Comment: Published as a conference paper at NIPS 201
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