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It is common practice to collect observations of feature and response pairsfrom different environments. A natural question is how to identify featuresthat have consistent prediction power across environments. The invariant causalprediction framework proposes to approach this problem through invariance,assuming a linear model that is invariant under different environments. In thiswork, we make an attempt to shed light on this framework by connecting it tothe Gaussian multiple access channel problem. Specifically, we incorporateoptimal code constructions and decoding methods to provide lower bounds on theerror probability. We illustrate our findings by various simulation settings.

Lower Bounds on the Error Probability for Invariant Causal Prediction