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Metric Relations among Analog Computers
, 1997
"... The recent work on automata whose variables and parameters are real numbers (e.g., Blum, Shub, and Smale, 1989; Koiran, 1993; Bournez and Cosnard, 1996; Siegelmann, 1996; Moore, 1996) has focused largely on questions about computational complexity and tractability. It is also revealing to examine th ..."
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the metric relations that such systems induce on automata via the natural metrics on their parameter spaces. This brings the theory of computational classification closer to theories of learning and statistical modeling which depend on measuring distances between models. With this in mind, I develop a
Informationtheoretic metric learning
 in NIPS 2006 Workshop on Learning to Compare Examples
, 2007
"... We formulate the metric learning problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the Mahalanobis distance function. Via a surprising equivalence, we show that this problem can be solved as a lowrank kernel learning problem. Spe ..."
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Cited by 359 (15 self)
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We formulate the metric learning problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the Mahalanobis distance function. Via a surprising equivalence, we show that this problem can be solved as a lowrank kernel learning problem
Probabilistic Approximation of Metric Spaces and its Algorithmic Applications
 In 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized ..."
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Cited by 351 (32 self)
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algorithms for optimization problems on metric spaces, by relating the randomized performance ratio for any metric space to the randomized performance ratio for a set of "simple" metric spaces. We define a notion of a set of metric spaces that probabilisticallyapproximates another metric space
The Similarity Metric
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2003
"... A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new "normalized information distance", based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class ..."
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Cited by 281 (34 self)
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A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new "normalized information distance", based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class
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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at s 0 and then following π: d π (s) = ∞ t=0 γ t P r {s t = ss 0 , π}. Our first result concerns the gradient of the performance metric with respect to the policy parameter: Theorem 1 (Policy Gradient). For any MDP, in either the averagereward or startstate formulations, Proof: See the appendix
An Explanation of the “Pioneer Effect ” based on QuasiMetric Relativity by
, 2002
"... According to the socalled “quasimetric ” framework developed elsewhere, the cosmic expansion applies directly to gravitationally bound systems. This prediction has a number of observable consequences, none of which are in conflict with observation. In this paper we compare test particle motion in t ..."
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Cited by 2 (0 self)
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According to the socalled “quasimetric ” framework developed elsewhere, the cosmic expansion applies directly to gravitationally bound systems. This prediction has a number of observable consequences, none of which are in conflict with observation. In this paper we compare test particle motion
ON A CLASS OF METRICS RELATED TO GRAPH LAYOUT PROBLEMS
, 2010
"... We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the literature, and also to a class of combinatorial optimization ..."
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We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the literature, and also to a class of combinatorial optimization
A new partmetricrelated inequality chain and an application,” Discrete Dynamics
 in Nature and Society, vol. 2008, Article ID 193872
"... Recommended by Stevo Stevic Partmetricrelated PMR inequality chains are elegant and are useful in the study of difference equations. In this paper, we establish a new PMR inequality chain, which is then applied to show the global asymptotic stability of a class of rational difference equations. ..."
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Cited by 2 (0 self)
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Recommended by Stevo Stevic Partmetricrelated PMR inequality chains are elegant and are useful in the study of difference equations. In this paper, we establish a new PMR inequality chain, which is then applied to show the global asymptotic stability of a class of rational difference equations.
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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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
Results 11  20
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13,638