• Corpus ID: 221112392

Reparametrization Invariance in non-parametric Causal Discovery

@article{Jrgensen2020ReparametrizationII,
  title={Reparametrization Invariance in non-parametric Causal Discovery},
  author={Martin J{\o}rgensen and S{\o}ren Hauberg},
  journal={arXiv: Machine Learning},
  year={2020}
}
Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to turn the causal query into a statistical query, when only observational data is available. But what if these statistical queries are sensitive to causal invariants? This study investigates one such invariant: the causal relationship between X and Y is invariant to the marginal distributions of X and Y. We propose an… 

Figures and Tables from this paper

Perfect Density Models Cannot Guarantee Anomaly Detection

TLDR
A closer look at the behavior of distribution densities through the lens of reparametrization is taken and it is shown that these quantities carry less meaningful information than previously thought, beyond estimation issues or the curse of dimensionality.

References

SHOWING 1-10 OF 19 REFERENCES

Inference of Cause and Effect with Unsupervised Inverse Regression

TLDR
This work addresses the problem of causal discovery in the two-variable case, given a sample from their joint distribution and proposes an implicit notion of independence, namely that pY|X cannot be estimated based on pX (lower case denotes density), however, it may be possible to estimate pY |X based on the density of the effect, pY.

A Linear Non-Gaussian Acyclic Model for Causal Discovery

TLDR
This work shows how to discover the complete causal structure of continuous-valued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have non-Gaussian distributions of non-zero variances.

Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks

TLDR
Empirical results on real-world data indicate that certain methods are indeed able to distinguish cause from effect using only purely observational data, although more benchmark data would be needed to obtain statistically significant conclusions.

Inferring deterministic causal relations

TLDR
This paper considers two variables that are related to each other by an invertible function, and shows that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference.

Probabilistic latent variable models for distinguishing between cause and effect

TLDR
A novel method for inferring whether X causes Y or vice versa from joint observations of X and Y is proposed, which considers the hypothetical effect variable to be a function of the hypothetical cause variable and an independent noise term.

Cause-Effect Inference by Comparing Regression Errors

TLDR
This work addresses the problem of inferring the causal relation between two variables by comparing the least-squares errors of the predictions in both possible causal directions and provides an easily applicable method that only requires a regression in both Possible causal directions.

Nonlinear causal discovery with additive noise models

TLDR
It is shown that the basic linear framework can be generalized to nonlinear models and, in this extended framework, nonlinearities in the data-generating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true data-Generating mechanisms to be identified.

Distinguishing causes from effects using nonlinear acyclic causal models

TLDR
This paper presents a two-step method, which is constrained nonlinear ICA followed by statistical independence tests, to distinguish the cause from the effect in the two-variable case, and successfully identify causes from effects.

Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models

TLDR
A novel probabilistic interpretation of principal component analysis (PCA) that is based on a Gaussian process latent variable model (GP-LVM), and related to popular spectral techniques such as kernel PCA and multidimensional scaling.

Measuring Statistical Dependence with Hilbert-Schmidt Norms

We propose an independence criterion based on the eigen-spectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm