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Causal Identification under Markov equivalence: Calculus, Algorithm, and Completeness

Neural Information Processing Systems

A plethora of methods was developed for solving this problem, including the celebrated do-calculus [Pearl, 1995]. In practice, these results are not always applicable since they require a fully specified causal diagram as input, which is usually not available.





f3ada80d5c4ee70142b17b8192b2958e-Supplemental.pdf

Neural Information Processing Systems

First, a random patch of the image is selected and resized to224 224 with a random horizontal flip, followed byacolor distortion, consisting ofarandom sequence ofbrightness, contrast, saturation, hue adjustments, and anoptional grayscale conversion. FinallyGaussian blur and solarization are appliedtothepatches. Optimization We use theLARS optimizer [70] with a cosine decay learning rate schedule [71], without restarts, over1000epochs, with awarm-up period of10epochs. Wesetthebase learning rate to 0.2, scaled linearly [72] with the batch size (LearningRate = 0.2 BatchSize/256). Forthetargetnetwork,the exponential moving average parameterτ starts fromτbase = 0.996and is increased to one during training.