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2,158
Metric Convergence in Social Network Sampling
"... While enabling new research questions and methodologies, the massive size of social media platforms also poses a significant issue for the analysis of these networks. In order to deal with this data volume, researchers typically turn to samples of these graph structures to conduct their analysis. Th ..."
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. This however raises the question about the representativeness of such limited crawls, and the amount of data necessary to come to stable predictions about the underlying systems. This paper analyzes the convergence of six commonly used topological metrics as a function of the crawling method and sample size
Metrics Convergence; Aligning Metrics With Organizational Goals Metrics Convergence: Aligning Metrics to Better Achieve Organizational Goals
"... There is virtually universal agreement that proper metrics are a key to achieving organizational goals. The irony is: it is hard to determine which metric(s) are best! But without metrics, we can’t sense the health of the organization. There may not be a pulse. This problem is further exacerbated b ..."
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There is virtually universal agreement that proper metrics are a key to achieving organizational goals. The irony is: it is hard to determine which metric(s) are best! But without metrics, we can’t sense the health of the organization. There may not be a pulse. This problem is further exacerbated
Policy gradient methods for reinforcement learning with function approximation.
 In NIPS,
, 1999
"... Abstract Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly repres ..."
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Cited by 439 (20 self)
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that the gradient can be written in a form suitable for estimation from experience aided by an approximate actionvalue or advantage function. Using this result, we prove for the first time that a version of policy iteration with arbitrary differentiable function approximation is convergent to a locally optimal
On the geometry of metric measure spaces
 II, ACTA MATH
, 2004
"... We introduce and analyze lower (’Ricci’) curvature bounds Curv(M, d,m) ≥ K for metric measure spaces (M, d,m). Our definition is based on convexity properties of the relative entropy Ent(.m) regarded as a function on the L2Wasserstein space of probability measures on the metric space (M, d). Amo ..."
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Cited by 247 (9 self)
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spaces with doubling constant ≤ C is closed under Dconvergence. Moreover, the family of normalized metric measure spaces with doubling constant ≤ C and radius ≤ R is compact under Dconvergence.
An analysis of BGP convergence properties
 In SIGCOMM
"... The Border Gateway Protocol (BGP) is the de facto interdomain routing protocol used to exchange reachability information between Autonomous Systems in the global Internet. BGP is a pathvector protocol that allows each Autonomous System to override distancebased metrics with policybased metrics wh ..."
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Cited by 236 (14 self)
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The Border Gateway Protocol (BGP) is the de facto interdomain routing protocol used to exchange reachability information between Autonomous Systems in the global Internet. BGP is a pathvector protocol that allows each Autonomous System to override distancebased metrics with policybased metrics
On choosing and bounding probability metrics
 INTERNAT. STATIST. REV.
, 2002
"... When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a mea ..."
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Cited by 153 (2 self)
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When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a
The Variational Formulation of the FokkerPlanck Equation
 SIAM J. Math. Anal
, 1999
"... The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper, ..."
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Cited by 282 (22 self)
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, we are concerned with FokkerPlanck equations for which the drift term is given by the gradient of a potential. For a broad class of potentials, we construct a timediscrete, iterative variational scheme whose solutions converge to the solution of the FokkerPlanck equation. The major novelty
The Stable Paths Problem and Interdomain Routing
 IEEE/ACM Transactions on Networking
, 2002
"... Abstract—Dynamic routing protocols such as RIP and OSPF essentially implement distributed algorithms for solving the shortest paths problem. The border gateway protocol (BGP) is currently the only interdomain routing protocol deployed in the Internet. BGP does not solve a shortest paths problem sinc ..."
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Cited by 262 (11 self)
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since any interdomain protocol is required to allow policybased metrics to override distancebased metrics and enable autonomous systems to independently define their routing policies with little or no global coordination. It is then natural to ask if BGP can be viewed as a distributed algorithm
CONVERGENCE
"... Recall the notion of convergence of sequences in metric spaces. In any set X, a sequence in X is just a mapping a mapping x: Z + → X, n ↦ → xn. If X is endowed with a metric d, a sequence x in X is said to converge to an element x of X if for all ɛ> 0, there exists an N = N(ɛ) such that for all n ..."
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Cited by 1 (1 self)
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Recall the notion of convergence of sequences in metric spaces. In any set X, a sequence in X is just a mapping a mapping x: Z + → X, n ↦ → xn. If X is endowed with a metric d, a sequence x in X is said to converge to an element x of X if for all ɛ> 0, there exists an N = N(ɛ) such that for all
InformationTheoretic Determination of Minimax Rates of Convergence
 Ann. Stat
, 1997
"... In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain informationtheoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence. ..."
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Cited by 151 (24 self)
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In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain informationtheoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.
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