415 research outputs found
Matrix Coherence and the Nystrom Method
The Nystrom method is an efficient technique to speed up large-scale learning
applications by generating low-rank approximations. Crucial to the performance
of this technique is the assumption that a matrix can be well approximated by
working exclusively with a subset of its columns. In this work we relate this
assumption to the concept of matrix coherence and connect matrix coherence to
the performance of the Nystrom method. Making use of related work in the
compressed sensing and the matrix completion literature, we derive novel
coherence-based bounds for the Nystrom method in the low-rank setting. We then
present empirical results that corroborate these theoretical bounds. Finally,
we present more general empirical results for the full-rank setting that
convincingly demonstrate the ability of matrix coherence to measure the degree
to which information can be extracted from a subset of columns
Learning Prices for Repeated Auctions with Strategic Buyers
Inspired by real-time ad exchanges for online display advertising, we
consider the problem of inferring a buyer's value distribution for a good when
the buyer is repeatedly interacting with a seller through a posted-price
mechanism. We model the buyer as a strategic agent, whose goal is to maximize
her long-term surplus, and we are interested in mechanisms that maximize the
seller's long-term revenue. We define the natural notion of strategic regret
--- the lost revenue as measured against a truthful (non-strategic) buyer. We
present seller algorithms that are no-(strategic)-regret when the buyer
discounts her future surplus --- i.e. the buyer prefers showing advertisements
to users sooner rather than later. We also give a lower bound on strategic
regret that increases as the buyer's discounting weakens and shows, in
particular, that any seller algorithm will suffer linear strategic regret if
there is no discounting.Comment: Neural Information Processing Systems (NIPS 2013
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