2,955 research outputs found
Large-Scale Differentiable Causal Discovery of Factor Graphs
A common theme in causal inference is learning causal relationships between
observed variables, also known as causal discovery. This is usually a daunting
task, given the large number of candidate causal graphs and the combinatorial
nature of the search space. Perhaps for this reason, most research has so far
focused on relatively small causal graphs, with up to hundreds of nodes.
However, recent advances in fields like biology enable generating experimental
data sets with thousands of interventions followed by rich profiling of
thousands of variables, raising the opportunity and urgent need for large
causal graph models. Here, we introduce the notion of factor directed acyclic
graphs (f-DAGs) as a way to restrict the search space to non-linear low-rank
causal interaction models. Combining this novel structural assumption with
recent advances that bridge the gap between causal discovery and continuous
optimization, we achieve causal discovery on thousands of variables.
Additionally, as a model for the impact of statistical noise on this estimation
procedure, we study a model of edge perturbations of the f-DAG skeleton based
on random graphs and quantify the effect of such perturbations on the f-DAG
rank. This theoretical analysis suggests that the set of candidate f-DAGs is
much smaller than the whole DAG space and thus may be more suitable as a search
space in the high-dimensional regime where the underlying skeleton is hard to
assess. We propose Differentiable Causal Discovery of Factor Graphs (DCD-FG), a
scalable implementation of -DAG constrained causal discovery for
high-dimensional interventional data. DCD-FG uses a Gaussian non-linear
low-rank structural equation model and shows significant improvements compared
to state-of-the-art methods in both simulations as well as a recent large-scale
single-cell RNA sequencing data set with hundreds of genetic interventions.Comment: 33 pages, 12 figure
Causal Discovery with Continuous Additive Noise Models
We consider the problem of learning causal directed acyclic graphs from an
observational joint distribution. One can use these graphs to predict the
outcome of interventional experiments, from which data are often not available.
We show that if the observational distribution follows a structural equation
model with an additive noise structure, the directed acyclic graph becomes
identifiable from the distribution under mild conditions. This constitutes an
interesting alternative to traditional methods that assume faithfulness and
identify only the Markov equivalence class of the graph, thus leaving some
edges undirected. We provide practical algorithms for finitely many samples,
RESIT (Regression with Subsequent Independence Test) and two methods based on
an independence score. We prove that RESIT is correct in the population setting
and provide an empirical evaluation
Structural Agnostic Modeling: Adversarial Learning of Causal Graphs
A new causal discovery method, Structural Agnostic Modeling (SAM), is
presented in this paper. Leveraging both conditional independencies and
distributional asymmetries in the data, SAM aims at recovering full causal
models from continuous observational data along a multivariate non-parametric
setting. The approach is based on a game between players estimating each
variable distribution conditionally to the others as a neural net, and an
adversary aimed at discriminating the overall joint conditional distribution,
and that of the original data. An original learning criterion combining
distribution estimation, sparsity and acyclicity constraints is used to enforce
the end-to-end optimization of the graph structure and parameters through
stochastic gradient descent. Besides the theoretical analysis of the approach
in the large sample limit, SAM is extensively experimentally validated on
synthetic and real data
Finding Exogenous Variables in Data with Many More Variables than Observations
Many statistical methods have been proposed to estimate causal models in
classical situations with fewer variables than observations (p<n, p: the number
of variables and n: the number of observations). However, modern datasets
including gene expression data need high-dimensional causal modeling in
challenging situations with orders of magnitude more variables than
observations (p>>n). In this paper, we propose a method to find exogenous
variables in a linear non-Gaussian causal model, which requires much smaller
sample sizes than conventional methods and works even when p>>n. The key idea
is to identify which variables are exogenous based on non-Gaussianity instead
of estimating the entire structure of the model. Exogenous variables work as
triggers that activate a causal chain in the model, and their identification
leads to more efficient experimental designs and better understanding of the
causal mechanism. We present experiments with artificial data and real-world
gene expression data to evaluate the method.Comment: A revised version of this was published in Proc. ICANN201
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