Priorfree Data Acquisition for Accurate Statistical Estimation Yiling

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Prior-free Data Acquisition for Accurate Statistical Estimation Yiling Chen, Shuran Zheng Harvard University June,

Prior-free Data Acquisition for Accurate Statistical Estimation Yiling Chen, Shuran Zheng Harvard University June, 2019

Acquiring data from self-interested individuals to estimate some statistic of a population

Acquiring data from self-interested individuals to estimate some statistic of a population

Problem description A data analyst … • Incur cost to record workout time •

Problem description A data analyst … • Incur cost to record workout time • Cost and data arbitrarily correlated

Model A data analyst •

Model A data analyst •

Problem description •

Problem description •

Previous results: known cost distribution •

Previous results: known cost distribution •

Previous results: known cost distribution •

Previous results: known cost distribution •

Survey mechanisms from Roth and Schoenebeck [2012] • Purchase data with different costs with

Survey mechanisms from Roth and Schoenebeck [2012] • Purchase data with different costs with different probabilities and prices

Previous results: known cost distribution •

Previous results: known cost distribution •

Unknown cost distribution: challenges •

Unknown cost distribution: challenges •

Our contribution • Prior-free mechanism design • Performance matches that of the optimal mechanism,

Our contribution • Prior-free mechanism design • Performance matches that of the optimal mechanism, which knows the true cost distribution, within a constant factor. • Confidence interval estimator

Prior-free mechanisms: algorithm • … …

Prior-free mechanisms: algorithm • … …

Prior-free mechanisms: result •

Prior-free mechanisms: result •

Prior-free mechanisms: proof ideas Step #1: Decompose the variance into per-round ``loss’’

Prior-free mechanisms: proof ideas Step #1: Decompose the variance into per-round ``loss’’

Prior-free mechanisms: proof ideas •

Prior-free mechanisms: proof ideas •

Confidence interval estimator • Allow the estimator to be biased • Ignore some high-cost

Confidence interval estimator • Allow the estimator to be biased • Ignore some high-cost data points • Bias-variance tradeoff • Optimal confidence interval: minimize the worst-case expected length.

ignore? no yes

ignore? no yes

Confidence interval estimator • Characterization of a 2 -approximation of the optimal confidence interval

Confidence interval estimator • Characterization of a 2 -approximation of the optimal confidence interval when the cost distribution is known • Online mechanism that matches the benchmark within a constant factor

Thanks & Questions?

Thanks & Questions?

First estimate the costs •

First estimate the costs •

Questions • Bandits with knapsack (dynamic pricing): • Action space too large • Regret

Questions • Bandits with knapsack (dynamic pricing): • Action space too large • Regret dependent on |A| • Online convex optimization • Put the violation of budget constraint into objective function: cannot be decomposed into per round loss function • Online convex optimization (with long-term budget): unknown budget constraint-> unknown X

ACCURATE PRECISE ACCURATE NOT precise NOT Accurate PRECISEACCURATE PRECISE ACCURATE NOT precise NOT Accurate PRECISE
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