# Terminology and references for a learning model

Let's say we're doing regression over $$[0,1]^d$$ -- either in the PAC sense with bounded-range agnostic noise or in the more classical-statistics sense with additive Gaussian noise. Suppose further that an additional hindrance stands between the data and the learner: The space $$[0,1]^d$$ is divided into a grid of cubes with side length $$\eta$$, and rather than seeing the full labeled sample $$(X_i,Y_i)$$, the learner only knows how many points $$X$$ fell into each of the grid cubes and the average of their $$Y$$ values in that cube.

Questions: 1. Terminology: Is there a name for this learning setting? "Summary" or "aggregate" statistics come to mind, but I want to be consistent with the known literature. 2. Prior results: Either in the PAC or the the additive-noise setting, is anything known? Efficient algorithms, minimax rates?