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In this task, you will be presented with a context from an academic paper and a question separated with a
. You have to answer the question based on the context.

We performed experiments on synthetically generated dataset since it gives us a better control over the distribution of the data. Specifically we compared the gains obtained using our approach versus the variance of the distribution. We created dataset from the following generative process. [H] Generative Process [1] Generate data

Pick k points INLINEFORM0 as domain -1 means and a corresponding set of k points INLINEFORM1 as domain-2 means, and covariance matrices INLINEFORM2

iter INLINEFORM0 upto num INLINEFORM1 samples Sample class INLINEFORM2 Sample INLINEFORM3 Sample INLINEFORM4 Add q and a so sampled to the list of q,a pairs We generated the dataset from the above sampling process with means selected on a 2 dimensional grid of size INLINEFORM5 with variance set as INLINEFORM6 in each dimension.10000 sample points were generated. The parameter INLINEFORM7 of the above algorithm was set to 0.5 and k was set to 9 (since the points could be generated from one of the 9 gaussians with centroids on a INLINEFORM8 grid).
Question: How do they generate the synthetic dataset?
Output:
using generative process