Conditional Independence Testing with Heteroskedastic Data and
Applications to Causal Discovery
- URL: http://arxiv.org/abs/2306.11498v1
- Date: Tue, 20 Jun 2023 12:36:38 GMT
- Title: Conditional Independence Testing with Heteroskedastic Data and
Applications to Causal Discovery
- Authors: Wiebke G\"unther, Urmi Ninad, jonas Wahl, Jakob Runge
- Abstract summary: Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields.
We present an adaptation of the partial correlation CI test that works well in the presence of heteroskedastic noise.
Numerical causal discovery experiments demonstrate that the adapted partial correlation CI test outperforms the standard test in the presence of heteroskedasticity.
- Score: 7.493779672689531
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Conditional independence (CI) testing is frequently used in data analysis and
machine learning for various scientific fields and it forms the basis of
constraint-based causal discovery. Oftentimes, CI testing relies on strong,
rather unrealistic assumptions. One of these assumptions is homoskedasticity,
in other words, a constant conditional variance is assumed. We frame
heteroskedasticity in a structural causal model framework and present an
adaptation of the partial correlation CI test that works well in the presence
of heteroskedastic noise, given that expert knowledge about the heteroskedastic
relationships is available. Further, we provide theoretical consistency results
for the proposed CI test which carry over to causal discovery under certain
assumptions. Numerical causal discovery experiments demonstrate that the
adapted partial correlation CI test outperforms the standard test in the
presence of heteroskedasticity and is on par for the homoskedastic case.
Finally, we discuss the general challenges and limits as to how expert
knowledge about heteroskedasticity can be accounted for in causal discovery.
Related papers
- Demystifying amortized causal discovery with transformers [21.058343547918053]
Supervised learning approaches for causal discovery from observational data often achieve competitive performance.
In this work, we investigate CSIvA, a transformer-based model promising to train on synthetic data and transfer to real data.
We bridge the gap with existing identifiability theory and show that constraints on the training data distribution implicitly define a prior on the test observations.
arXiv Detail & Related papers (2024-05-27T08:17:49Z) - Identifiable Latent Polynomial Causal Models Through the Lens of Change [85.67870425656368]
Causal representation learning aims to unveil latent high-level causal representations from observed low-level data.
One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability.
arXiv Detail & Related papers (2023-10-24T07:46:10Z) - Nonlinearity, Feedback and Uniform Consistency in Causal Structural
Learning [0.8158530638728501]
Causal Discovery aims to find automated search methods for learning causal structures from observational data.
This thesis focuses on two questions in causal discovery: (i) providing an alternative definition of k-Triangle Faithfulness that (i) is weaker than strong faithfulness when applied to the Gaussian family of distributions, and (ii) under the assumption that the modified version of Strong Faithfulness holds.
arXiv Detail & Related papers (2023-08-15T01:23:42Z) - Self-Compatibility: Evaluating Causal Discovery without Ground Truth [28.72650348646176]
We propose a novel method for falsifying the output of a causal discovery algorithm in the absence of ground truth.
Our key insight is that while statistical learning seeks stability across subsets of data points, causal learning should seek stability across subsets of variables.
We prove that detecting incompatibilities can falsify wrongly inferred causal relations due to violation of assumptions or errors from finite sample effects.
arXiv Detail & Related papers (2023-07-18T18:59:42Z) - Causal Discovery via Conditional Independence Testing with Proxy Variables [35.3493980628004]
The presence of unobserved variables, such as the latent confounder, can introduce bias in conditional independence testing.
We propose a novel hypothesis-testing procedure that can effectively examine the existence of the causal relationship over continuous variables.
arXiv Detail & Related papers (2023-05-09T09:08:39Z) - BaCaDI: Bayesian Causal Discovery with Unknown Interventions [118.93754590721173]
BaCaDI operates in the continuous space of latent probabilistic representations of both causal structures and interventions.
In experiments on synthetic causal discovery tasks and simulated gene-expression data, BaCaDI outperforms related methods in identifying causal structures and intervention targets.
arXiv Detail & Related papers (2022-06-03T16:25:48Z) - Nonparametric Conditional Local Independence Testing [69.31200003384122]
Conditional local independence is an independence relation among continuous time processes.
No nonparametric test of conditional local independence has been available.
We propose such a nonparametric test based on double machine learning.
arXiv Detail & Related papers (2022-03-25T10:31:02Z) - Typing assumptions improve identification in causal discovery [123.06886784834471]
Causal discovery from observational data is a challenging task to which an exact solution cannot always be identified.
We propose a new set of assumptions that constrain possible causal relationships based on the nature of the variables.
arXiv Detail & Related papers (2021-07-22T14:23:08Z) - Disentangling Observed Causal Effects from Latent Confounders using
Method of Moments [67.27068846108047]
We provide guarantees on identifiability and learnability under mild assumptions.
We develop efficient algorithms based on coupled tensor decomposition with linear constraints to obtain scalable and guaranteed solutions.
arXiv Detail & Related papers (2021-01-17T07:48:45Z) - Stable Prediction via Leveraging Seed Variable [73.9770220107874]
Previous machine learning methods might exploit subtly spurious correlations in training data induced by non-causal variables for prediction.
We propose a conditional independence test based algorithm to separate causal variables with a seed variable as priori, and adopt them for stable prediction.
Our algorithm outperforms state-of-the-art methods for stable prediction.
arXiv Detail & Related papers (2020-06-09T06:56:31Z) - High-dimensional and universally consistent k-sample tests [18.327837489069907]
k-sample testing problem involves determining whether $k$ groups of data points are each drawn from the same distribution.
Independence tests achieve universally consistent k-sample testing.
arXiv Detail & Related papers (2019-10-20T03:14:20Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.