<p>The related work I know of is experimental, but a similar setup has been called Learning from Label Proportions: <a href="https://link.springer.com/article/10.1007/s13278-017-0478-6" rel="nofollow noreferrer">https://link.springer.com/article/10.1007/s13278-017-0478-6</a></p>

CC BY-SA 4.0
2019-09-19T04:40:35.487Z
2019-09-19T04:40:35.487Z
Shlomo Engelson Argamon
<p>Let's say we're doing regression over <span class="math-container">$[0,1]^d$</span> -- 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 <span class="math-container">$[0,1]^d$</span> is divided into a grid of cubes with side length <span class="math-container">$\eta$</span>, and rather than seeing the full labeled sample <span class="math-container">$(X_i,Y_i)$</span>, the learner only knows how many points <span class="math-container">$X$</span> fell into each of the grid cubes and the average of their <span class="math-container">$Y$</span> values in that cube.</p>

<p>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?</p>

<machine-learning><lg.learning><st.statistics>
Terminology and references for a learning model
Aryeh
# Terminology and references for a learning model

(Asked by: username_0 on 2019-09-18)

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?

**Tags:** machine-learning, lg.learning, st.statistics


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## 1 answers

### Answer by username_1 on 2019-09-19. Score: 2

The related work I know of is experimental, but a similar setup has been called Learning from Label Proportions: <https://link.springer.com/article/10.1007/s13278-017-0478-6>


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