8 research outputs found
Identifiability of causal graphs under nonadditive conditionally parametric causal models
Causal discovery from observational data is a very challenging, often
impossible, task. However, estimating the causal structure is possible under
certain assumptions on the data-generating process. Many commonly used methods
rely on the additivity of the noise in the structural equation models.
Additivity implies that the variance or the tail of the effect, given the
causes, is invariant; the cause only affects the mean. In many applications, it
is desirable to model the tail or other characteristics of the random variable
since they can provide different information about the causal structure.
However, models for causal inference in such cases have received only very
little attention.
It has been shown that the causal graph is identifiable under different
models, such as linear non-Gaussian, post-nonlinear, or quadratic variance
functional models. We introduce a new class of models called the Conditional
Parametric Causal Models (CPCM), where the cause affects the effect in some of
the characteristics of interest.We use the concept of sufficient statistics to
show the identifiability of the CPCM models, focusing mostly on the exponential
family of conditional distributions.We also propose an algorithm for estimating
the causal structure from a random sample under CPCM. Its empirical properties
are studied for various data sets, including an application on the expenditure
behavior of residents of the Philippines
Bivariate Causal Discovery for Categorical Data via Classification with Optimal Label Permutation
Causal discovery for quantitative data has been extensively studied but less
is known for categorical data. We propose a novel causal model for categorical
data based on a new classification model, termed classification with optimal
label permutation (COLP). By design, COLP is a parsimonious classifier, which
gives rise to a provably identifiable causal model. A simple learning algorithm
via comparing likelihood functions of causal and anti-causal models suffices to
learn the causal direction. Through experiments with synthetic and real data,
we demonstrate the favorable performance of the proposed COLP-based causal
model compared to state-of-the-art methods. We also make available an
accompanying R package COLP, which contains the proposed causal discovery
algorithm and a benchmark dataset of categorical cause-effect pairs
Causal Representation Learning Made Identifiable by Grouping of Observational Variables
A topic of great current interest is Causal Representation Learning (CRL),
whose goal is to learn a causal model for hidden features in a data-driven
manner. Unfortunately, CRL is severely ill-posed since it is a combination of
the two notoriously ill-posed problems of representation learning and causal
discovery. Yet, finding practical identifiability conditions that guarantee a
unique solution is crucial for its practical applicability. Most approaches so
far have been based on assumptions on the latent causal mechanisms, such as
temporal causality, or existence of supervision or interventions; these can be
too restrictive in actual applications. Here, we show identifiability based on
novel, weak constraints, which requires no temporal structure, intervention,
nor weak supervision. The approach is based assuming the observational mixing
exhibits a suitable grouping of the observational variables. We also propose a
novel self-supervised estimation framework consistent with the model, prove its
statistical consistency, and experimentally show its superior CRL performances
compared to the state-of-the-art baselines. We further demonstrate its
robustness against latent confounders and causal cycles