6,519 research outputs found
Testing probability distributions underlying aggregated data
In this paper, we analyze and study a hybrid model for testing and learning
probability distributions. Here, in addition to samples, the testing algorithm
is provided with one of two different types of oracles to the unknown
distribution over . More precisely, we define both the dual and
cumulative dual access models, in which the algorithm can both sample from
and respectively, for any ,
- query the probability mass (query access); or
- get the total mass of , i.e. (cumulative
access)
These two models, by generalizing the previously studied sampling and query
oracle models, allow us to bypass the strong lower bounds established for a
number of problems in these settings, while capturing several interesting
aspects of these problems -- and providing new insight on the limitations of
the models. Finally, we show that while the testing algorithms can be in most
cases strictly more efficient, some tasks remain hard even with this additional
power
Vickrey Auctions for Irregular Distributions
The classic result of Bulow and Klemperer \cite{BK96} says that in a
single-item auction recruiting one more bidder and running the Vickrey auction
achieves a higher revenue than the optimal auction's revenue on the original
set of bidders, when values are drawn i.i.d. from a regular distribution. We
give a version of Bulow and Klemperer's result in settings where bidders'
values are drawn from non-i.i.d. irregular distributions. We do this by
modeling irregular distributions as some convex combination of regular
distributions. The regular distributions that constitute the irregular
distribution correspond to different population groups in the bidder
population. Drawing a bidder from this collection of population groups is
equivalent to drawing from some convex combination of these regular
distributions. We show that recruiting one extra bidder from each underlying
population group and running the Vickrey auction gives at least half of the
optimal auction's revenue on the original set of bidders
Trade-offs between Selection Complexity and Performance when Searching the Plane without Communication
We consider the ANTS problem [Feinerman et al.] in which a group of agents
collaboratively search for a target in a two-dimensional plane. Because this
problem is inspired by the behavior of biological species, we argue that in
addition to studying the {\em time complexity} of solutions it is also
important to study the {\em selection complexity}, a measure of how likely a
given algorithmic strategy is to arise in nature due to selective pressures. In
more detail, we propose a new selection complexity metric , defined for
algorithm such that , where is
the number of memory bits used by each agent and bounds the fineness of
available probabilities (agents use probabilities of at least ). In
this paper, we study the trade-off between the standard performance metric of
speed-up, which measures how the expected time to find the target improves with
, and our new selection metric.
In particular, consider agents searching for a treasure located at
(unknown) distance from the origin (where is sub-exponential in ).
For this problem, we identify as a crucial threshold for our
selection complexity metric. We first prove a new upper bound that achieves a
near-optimal speed-up of for . In particular, for , the speed-up is
asymptotically optimal. By comparison, the existing results for this problem
[Feinerman et al.] that achieve similar speed-up require . We then show that this threshold is tight by describing a
lower bound showing that if , then
with high probability the target is not found within moves per
agent. Hence, there is a sizable gap to the straightforward
lower bound in this setting.Comment: appears in PODC 201
Robust Coin Flipping
Alice seeks an information-theoretically secure source of private random
data. Unfortunately, she lacks a personal source and must use remote sources
controlled by other parties. Alice wants to simulate a coin flip of specified
bias , as a function of data she receives from sources; she seeks
privacy from any coalition of of them. We show: If , the
bias can be any rational number and nothing else; if , the bias
can be any algebraic number and nothing else. The proof uses projective
varieties, convex geometry, and the probabilistic method. Our results improve
on those laid out by Yao, who asserts one direction of the case in his
seminal paper [Yao82]. We also provide an application to secure multiparty
computation.Comment: 22 pages, 1 figur
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