Causal Learning via Manifold Regularization
Authors: Steven M. Hill, Chris J. Oates, Duncan A. Blythe, Sach Mukherjee
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present empirical results on three different biological data sets (including examples where causal effects can be verified by experimental intervention), that together demonstrate the efficacy and general nature of the approach as well as its simplicity from a user s point of view. Keywords: causal learning, manifold regularization, semi-supervised learning, interventional data, causal graphs |
| Researcher Affiliation | Academia | Steven M. Hill EMAIL MRC Biostatistics Unit University of Cambridge Cambridge, CB2 0SR, UK Chris J. Oates EMAIL School of Mathematics, Statistics and Physics Newcastle University Newcastle-upon-Tyne, NE1 7RU, UK Duncan A. Blythe EMAIL Sach Mukherjee EMAIL German Center for Neurodegenerative Diseases 53127 Bonn, Germany |
| Pseudocode | No | The paper describes methods and mathematical formulations but does not include any explicitly labeled pseudocode or algorithm blocks. For instance, in Section 2.5.2, it refers to an equation from a cited work: "Given training labels y L, label estimates ˆy U = sign(ˆf U) are obtained by minimizing the objective function described above, as explained in Equation 8 in Belkin et al. (2006)." This is a description, not pseudocode. |
| Open Source Code | Yes | All computational analysis was performed in R (R Core Team, 2018). Source code for MRCL and scripts to generate the empirical results presented in Section 3 are available at https://github.com/Steven-M-Hill/MRCL. |
| Open Datasets | Yes | D1: Yeast knockout data. Here, we used a data set due to Kemmeren et al. (2014), previously considered for causal learning in Peters et al. (2016); Meinshausen et al. (2016). D2: Kinase intervention data from human cancer cell lines. These data, due to Hill et al. (2017), involve a small number of interventions on human cells, with corresponding protein measurements over time. D3: Protein data from cancer patient samples. These data arise from The Cancer Genome Atlas (TCGA) and are presented in Akbani et al. (2014). There are no interventional data, but the data pertain to relatively well-understood biological processes allowing inferences to be checked against causal scientific knowledge. ... retrieved from The Cancer Proteome Atlas (TCPA) data portal (Li et al., 2013, https://tcpaportal.org; data release version 4.0; Pan-Can 19 Level 4 data). |
| Dataset Splits | Yes | D1: Yeast Gene Expression: "We treated a fraction ρ of the entries in A(C) as the available labels Φ. ... The data set D comprised expression measurements for the genes in C for nobs train = 76 observational data samples (those samples not used to calculate the robust z-scores), plus nint train interventional data samples... We considered ntrain = 200, 500 and 1000 (corresponding to nint train = 124, 424 and 924 respectively, sampled at random)." D2: Protein Time-Course Data: "The intervention regime not included was a kinase inhibitor targeting the protein m TOR. This intervention was entirely held out and used to provide the test labels. As background knowledge Φc we took as training labels causal effects under the other interventions." D3: Human Cancer Data: "We formed a data set D consisting of measurements for the p = 35 proteins for three different sample sizes: (i) ntrain = 200, (ii) ntrain = 500 or (iii) all ntrain = 820 patient samples. For (i) and (ii) patient samples were selected at random. We then used a random fraction ρ of the reference graph as background knowledge, testing output on the (unseen) remainder." |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running the experiments. It only mentions that computational analysis was performed in R. |
| Software Dependencies | No | The paper states: "All computational analysis was performed in R (R Core Team, 2018)." While it mentions R and provides a citation for it, it does not specify versions for any other key libraries, packages, or frameworks used beyond the base R system. |
| Experiment Setup | Yes | 2.4.3. Implementation of the DE: "In practice, for all examples below, the data were standardized, then truncated to [−3, 3]2, following which a bivariate histogram with bins of fixed width 0.2 was used. The dimension of the resulting feature matrix was then reduced (to 100) using PCA." 2.5.2. Implementation of the Classifier: "The scale σ1 was set to the average distance to the nearest 50 points in the feature space (in practice estimated via a subsample). The two penalty parameters in (4) were set to small positive values (λ1 = λ2 = 0.001; we found results were broadly insensitive to this choice). Following common practice we worked with the normalized graph Laplacian L := D−1/2 in place of L (see Remark 3 of Belkin et al., 2006)." |