Grim GDP Figures Pile Pressure on Japan Officials.
The GSMA's study highlights that the mobile industry contributed an estimated $177 billion USD1 to the economies of Argentina, Brazil, Chile, Colombia, Ecuador, Mexico, Panama, Peru and Uruguay, representing 3.5 per cent of the region's GDP.
China announced its first quarter GDP growth figures today of 6.1% and most analysts just shrugged.
Congress' inaction on the fiscal cliff could cost US GDP more than 5.
Hollande said that investments wouldn't be taken into account only for countries that respected the 3% deficit-to-GDP ratio.
With debts worth 126 percent of the country's annual economic output, Italy has the second-highest debt-to-GDP ratio in the eurozone, behind only Greece.
Italy has the second-highest debt level as a percentage of its GDP in the eurozone, behind only Greece.
Jamaican GDP Contracted 0.6% in Third Quarter on Mining Decline.
Albany GDP up but jobs lag .
Latvia 's strong economic recovery continues, with GDP increasing 1.7 percent in the third quarter.
MacDonald divided Lick 's $700,000 telescope budget by the US GDP in 1876 and multiplied that number by 2008 GDP.
Unemployment is sliding, home selling and building is rising and GDP reports are expected to be revised upward.
Consumers seen lifting GDP, but pace sluggish.
Disappointing Quarterly GDP Rise Bodes Ill for Emerging Markets' Ability to Boost World Growth.
The latest reading on GDP shows that growth is slowing to a crawl.
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In Section 3, we show the formal connection between testing of generalized differential privacy (GDP) and Lipschitz property testing.
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
In Section 5, we show that Lipschitz testers over the hypergrid domain can be used to test for GDP when the data sets are drawn uniformly from the hypergrid domain.
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
Since, we want to test Lipschitzness efﬁciently with respect to the size of the set S, we will use a relaxed notion of differential privacy called generalized differential privacy (GDP) [BBG+11].
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
The main idea behind GDP is that it allows us to incorporate the randomness over the data generating distribution.
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
The deﬁnition of GDP below is a slight modiﬁcation to the deﬁnition proposed in [BBG+11] and in most natural settings is stronger than [BBG+11].
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
While in both noiseless and natural differential privacy deﬁnitions the randomness is solely over the data generating distribution Dist, in GDP the randomness is both over the data generating distribution and the randomness of the algorithm.
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
At a high-level what GDP says is that there exists a set W of “bad” data sets where (α, γ )-differential privacy condition does not hold.
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
Similarly, it can be shown that under different choices of (α, γ, β ) GDP implies both noiseless privacy and natural differential privacy.
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
As a speciﬁc instantiation of the problem, we study the notion of generalized differential privacy (GDP) (see Deﬁnition 2.2).
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
Roughly speaking, GDP guarantee ensures that the output of Algorithm A when executed on data set D does not depend “too much” on any one entry of D .
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
We refer to the guarantee as (α, γ, β )-Generalized Differential Privacy (or simply (α, γ, β )-GDP).
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
To prove Theorem 3.1, we show a new connection between testing (α, 0, β )-GDP and the problem of testing Lipschitz property.
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
We present an algorithm Atest for testing (α, 0, β )-GDP based on a generalization of Lipschitz tester presented in [JR11].
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
Now let us look at the privacy guarantee of GDP (see Deﬁnition 2.2).
Testing Lipschitz Property over Product Distribution and its Applications to Statistical Data Privacy
Circles indicate countries with GDP per capita < $15000 per year.
Impact of astronomical research from different countries
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