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- W2278157425 abstract "We give the first $tilde{O}(frac{1}{sqrt{T}})$-error online algorithm for reconstructing noisy statistical databases, where $T$ is the number of (online) sample queries received. The algorithm, which requires only $O(log T)$ memory, aims to learn a hidden database-vector $w^{*} in mathbb{R}^{D}$ in order to accurately answer a stream of queries regarding the hidden database, which arrive in an online fashion from some unknown distribution $mathcal{D}$. We assume the distribution $mathcal{D}$ is defined on the neighborhood of a low-dimensional manifold. The presented algorithm runs in $O(dD)$-time per query, where $d$ is the dimensionality of the query-space. Contrary to the classical setting, there is no separate training set that is used by the algorithm to learn the database --- the stream on which the algorithm will be evaluated must also be used to learn the database-vector. The algorithm only has access to a binary oracle $mathcal{O}$ that answers whether a particular linear function of the database-vector plus random noise is larger than a threshold, which is specified by the algorithm. We note that we allow for a significant $O(D)$ amount of noise to be added while other works focused on the low noise $o(sqrt{D})$-setting. For a stream of $T$ queries our algorithm achieves an average error $tilde{O}(frac{1}{sqrt{T}})$ by filtering out random noise, adapting threshold values given to the oracle based on its previous answers and, as a consequence, recovering with high precision a projection of a database-vector $w^{*}$ onto the manifold defining the query-space." @default.
- W2278157425 created "2016-06-24" @default.
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- W2278157425 date "2015-04-05" @default.
- W2278157425 modified "2023-09-27" @default.
- W2278157425 title "An $tilde{O}(frac{1}{sqrt{T}})$-error online algorithm for retrieving heavily perturbated statistical databases in the low-dimensional querying mode." @default.
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