Non-linear Causal Inference using Gaussianity Measures
Authors: Daniel Hernández-Lobato, Pablo Morales-Mombiela, David Lopez-Paz, Alberto Suárez
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The effectiveness of a method to discriminate between causes and effects based on this type of asymmetry is illustrated in a variety of experiments using different measures of Gaussianity. The proposed method is shown to be competitive with state-of-the-art techniques for causal inference. ... Section 6 contains a detailed description of the implementation. In section 6 we present the results of an empirical assessment of the proposed method in both synthetic and real-world cause-effect pairs. |
| Researcher Affiliation | Collaboration | Daniel Hern andez-Lobato EMAIL Universidad Aut onoma de Madrid Calle Francisco Tom as y Valiente 11, Madrid 28049, Spain Pablo Morales-Mombiela EMAIL Quantitative Risk Research Calle Faraday 7, Madrid 28049, Spain David Lopez-Paz EMAIL Facebook AI Research 6 rue Menars, Paris 75002, France Alberto Su arez EMAIL Universidad Aut onoma de Madrid Calle Francisco Tom as y Valiente 11, Madrid 28049, Spain |
| Pseudocode | Yes | Algorithm 1: Causal Inference Based on the Gaussianity of the Residuals (GR-AN) Data: Paired samples x and y from the random variables X and Y. Result: An estimated causal direction alongside with a confidence level. 1 Standardize x and y to have zero mean and unit variance; 2 Transform x to compute x ; // This guarantees that x is distributed as y. 3 ˆA x y Fit Model( x, y) ; // This also finds the hyper-parameters τ and γ. 4 z x y Obtain Residuals( x, y, ˆA x y) ; // First PCA component in feature space. 5 ˆAy x Fit Model(y, x) ; // Fit the model in the other direction 6 zy x Obtain Residuals(y, x, ˆAy x) ; // First PCA component in feature space. 7 G x Energy(z x y)/N Energy(zy x)/N ; // Get the Gaussianization level. 8 Swap x and y and repeat lines 2-7 of the algorithm to compute G y. 9 if |G x| > |G y| then 10 if G x > 0 then 11 Output: X Y with confidence |G x| 12 else 13 Output: Y X with confidence |G x| 14 end 15 else 16 if G y > 0 then 17 Output: Y X with confidence |G y| 18 else 19 Output: X Y with confidence |G y| 20 end 21 end |
| Open Source Code | Yes | To guarantee the exact reproducibility of the different experiments described in this paper, the source-code for all methods and data sets is available in the public repository https://bitbucket.org/dhernand/gr_causal_inference. |
| Open Datasets | Yes | A second batch of experiments is performed on the cause-effect pairs from the Cha Learn challenge2. This challenge contains 8073 cause-effect data pairs with a labeled causal direction. From these pairs, we consider a subset for our experiments. ... See https://www.codalab.org/competitions/1381 for more information. ... Finally, we also have evaluated the different methods in a subset of 82 cause-effect pairs extracted from the T ubingen cause-effect pairs3. ... See http://webdav.tuebingen.mpg.de/cause-effect/ for more details. |
| Dataset Splits | Yes | The method chosen to guarantee this is a grid search guided by a 10-fold cross-validation procedure, which requires computing the squared prediction error over unseen data. ... In these experiments we sample at random 500 instances from each cause-effect pair. |
| Hardware Specification | No | The paper does not provide specific hardware details for running the experiments. It only generally acknowledges 'the use of the facilities of Centro de Computacin Cientfica (CCC) at Universidad Aut onoma de Madrid'. |
| Software Dependencies | No | The paper mentions various software components and methods used (e.g., Gaussian processes, HSIC test, LINGAM, ICA, kernel density estimators) but does not provide specific version numbers for any of them. For instance, 'In LINGAM, we use the parameters recommended by the implementation provided by the authors.' implies an implementation but no version is given. |
| Experiment Setup | Yes | The method chosen to guarantee this is a grid search guided by a 10-fold cross-validation procedure, which requires computing the squared prediction error over unseen data. In this section we detail how to evaluate these errors. ... The ridge regression regularization parameter τ and the kernel bandwidth γ. ... 10 potential values are considered for both τ and γ. ... The number of neighbors in the entropy estimator of GR-ENT is set to 10, a value that we have observed to give a good trade-off between bias and variance. |