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• W2987620614 abstract "Consider a query-based data acquisition problem that aims to recover the values of $k$ binary variables from parity (XOR) measurements of chosen subsets of the variables. Assume the response model where only a randomly selected subset of the measurements is received. We propose a method for designing a sequence of queries so that the variables can be identified with high probability using as few ($n$) measurements as possible. We define the query difficulty $bar{d}$ as the average size of the query subsets and the sample complexity $n$ as the minimum number of measurements required to attain a given recovery accuracy. We obtain fundamental trade-offs between recovery accuracy, query difficulty, and sample complexity. In particular, the necessary and sufficient sample complexity required for recovering all $k$ variables with high probability is $n = c_0 max{k, (k log k)/bar{d}}$ and the sample complexity for recovering a fixed proportion $(1-delta)k$ of the variables for $delta=o(1)$ is $n = c_1max{k, (k log(1/delta))/bar{d}}$, where $c_0, c_1>0$." @default.
• W2987620614 created "2019-11-22" @default.
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• W2987620614 date "2018-09-04" @default.
• W2987620614 modified "2023-09-25" @default.
• W2987620614 title "Parity Queries for Binary Classification" @default.
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• W2987620614 hasPublicationYear "2018" @default.
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