Confounder Identification


- The
-MixIID problem handles a discrete mixture in which we are allowed to sample a single variables multiple times without re-sampling . Alternatively, we can think of this as multiple i.i.d. samples of the within-source (constant ) distribution. This is sometimes called the -coin problem because it corresponds to selecting a random biased coin and flipping it multiple times (and then repeating this process with another randomly selected coin). - The
-MixProd problem handles a discrete mixture with random variables that are independent from one another within each source (when conditioned on ). Graphically, this can be modeled as a single vertex with edges to vertices with no edges within . - The
-MixBND problem relaxes the independence assumption, allowing for an arbitrary dependence structure among the vertices, modeled by a Bayesian Netork DAG .
The
We have contributed to complexity improvements on all three steps of this reduction. We have also contributed the first known algorithm for identifying causal structure in the mixture setting.