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43
Statistical Behavior and Consistency of Classification Methods based on Convex Risk Minimization
, 2001
"... We study how close the optimal Bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function. The measurement of closeness is characterized by the loss function used in the estimation. ..."
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Cited by 112 (6 self)
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We study how close the optimal Bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function. The measurement of closeness is characterized by the loss function used in the estimation. We show that such a classification scheme can be generally regarded as a (non maximumlikelihood) conditional inclass probability estimate, and we use this analysis to compare various convex loss functions that have appeared in the literature. Furthermore, the theoretical insight allows us to design good loss functions with desirable properties. Another aspect of our analysis is to demonstrate the consistency of certain classification methods using convex risk minimization.
Stability of Data Networks: Stationary and Bursty Models
 OPERATIONS RESEARCH
, 2005
"... This paper studies stability of network models that capture macroscopic features of data communication networks including the Internet. The network model consists of a set of links and a set of possible routes which are fixed subsets of links. A connection is dynamically established along one of ..."
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Cited by 17 (3 self)
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This paper studies stability of network models that capture macroscopic features of data communication networks including the Internet. The network model consists of a set of links and a set of possible routes which are fixed subsets of links. A connection is dynamically established along one of the routes to transmit data as requested, and terminated after the transmission is over. The transmission bandwidth of a link is dynamically allocated, according to specific bandwidth allocation policy, to ongoing connections that traverse the link. A network model is said to be stable under a given bandwidth allocation policy if, roughly, the number of ongoing connections in the network will not blow up over time.
The feedback capacity of the firstorder moving average Gaussian channel. Accepted by
 IEEE Trans. Inform. Theory
, 2006
"... Abstract—Despite numerous bounds and partial results, the feedback capacity of the stationary nonwhite Gaussian additive noise channel has been open, even for the simplest cases such as the firstorder autoregressive Gaussian channel studied by Butman, Tiernan and Schalkwijk, Wolfowitz, Ozarow, and ..."
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Cited by 15 (2 self)
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Abstract—Despite numerous bounds and partial results, the feedback capacity of the stationary nonwhite Gaussian additive noise channel has been open, even for the simplest cases such as the firstorder autoregressive Gaussian channel studied by Butman, Tiernan and Schalkwijk, Wolfowitz, Ozarow, and more recently, Yang, Kavčić, and Tatikonda. Here we consider another simple special case of the stationary firstorder moving average additive Gaussian noise channel and find the feedback capacity in closed form. Specifically, the channel is given by = + =12... where the input satisfies a power constraint and the noise is a firstorder moving average Gaussian process defined by = 1 + 1 with white Gaussian innovations =0 1... We show that the feedback capacity of this channel is. We wish to communicate a message index reliably over the channel. The channel output is causally fed back to the transmitter. We specify a code with the codewords1 satisfying the expected power constraint The proband decoding function ability of error is defined by FB = log 0 where 0 is the unique positive root of the equation
Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with a.c. spectrum, Analysis and PDE
"... Abstract. By combining some ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for OPRL in the a.c. spectral region is implied by convergence of 1 n Kn(x, x) for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials. ..."
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Cited by 14 (6 self)
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Abstract. By combining some ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for OPRL in the a.c. spectral region is implied by convergence of 1 n Kn(x, x) for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials. We then show that these hypotheses are always valid for ergodic Jacobi matrices with a.c. spectrum and prove that the limit of 1 n Kn(x, x) is ρ∞(x)/w(x) where ρ ∞ is the density of zeros and w is the a.c. weight of the spectral measure. 1.
Planar earthmover is not in l1
 In 47th Symposium on Foundations of Computer Science (FOCS
, 2006
"... We show that any L1 embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid {0, 1,..., n} 2 ⊆ R 2 incurs distortion Ω � � log n �. We also use Fourier analytic techniques to construct a simple L1 embedding of this space which has distortion O(lo ..."
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Cited by 12 (2 self)
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We show that any L1 embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid {0, 1,..., n} 2 ⊆ R 2 incurs distortion Ω � � log n �. We also use Fourier analytic techniques to construct a simple L1 embedding of this space which has distortion O(log n). 1
Analysis of Fourier transform valuation formulas and applications
 Applied Mathematical Finance
"... Abstract. The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the ..."
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Cited by 11 (3 self)
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Abstract. The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multidimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in Lévy and stochastic volatility models.
Scaling limits for random fields with longrange dependence. Institut MittagLeffler, The Royal Swedish Academy of Sciences
, 2005
"... This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density λ of the sets grows to infinity and the mean volume ρ of the sets tends to zero. Assuming that the volume distribution has a regularly varying tail with infinite variance, we show tha ..."
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Cited by 11 (2 self)
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This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density λ of the sets grows to infinity and the mean volume ρ of the sets tends to zero. Assuming that the volume distribution has a regularly varying tail with infinite variance, we show that the centered and renormalized random field can have three different limits, depending on the relative speed at which λ and ρ are scaled. If λ grows much faster than ρ shrinks, the limit is Gaussian with longrange dependence, while in the opposite case, the limit is independently scattered with infinite second moments. In a special intermediate scaling regime, there exists a nontrivial limiting random field that is not stable. 1. Introduction. Fractional Brownian
A probabilistic language based on sampling functions
 ACM Transactions on Programming Languages and Systems
, 2006
"... As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages which treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive p ..."
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Cited by 9 (0 self)
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As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages which treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power. This article presents a probabilistic language, called λ○, whose expressive power is beyond discrete distributions. Rich expressiveness of λ ○ is due to its use of sampling functions, that is, mappings from the unit interval (0.0, 1.0] to probability domains, in specifying probability distributions. As such, λ ○ enables programmers to formally express and reason about sampling methods developed in simulation theory. The use of λ ○ is demonstrated with three applications in robotics: robot localization, people tracking, and robotic mapping. All experiments have been carried out with real robots.
Harmonic Analysis Of Fractal Processes Via C*Algebras
 C algebras, Math. Nachr
, 1995
"... . We construct a harmonic analysis of iteration systems which include those which arise from wavelet algorithms based on multiresolutions. While traditional discretizations lead to asymptotic formulas, we argue here for a direct Fourier duality; but it is based on a noncommutative harmonic analysis ..."
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Cited by 8 (6 self)
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. We construct a harmonic analysis of iteration systems which include those which arise from wavelet algorithms based on multiresolutions. While traditional discretizations lead to asymptotic formulas, we argue here for a direct Fourier duality; but it is based on a noncommutative harmonic analysis, specifically on representations of the Cuntz C algebras. With this approach the scaling from the wavelet takes the form of an endomorphism of B (H), H a Hilbert space derived from the lattice of translations. We use this to describe, and to calculate, new invariants for the wavelets. For those iteration systems which arise from wavelets and from Julia sets, we show that the associated endomorphisms are in fact Powers shifts. 1. The Coding Space While automorphisms of measure spaces correspond to dynamical systems with (time) reversal, the irreversible (or dissipative) dynamical systems arise from endomorphisms of the measure space in question. The measure spaces considered here will ...
Asymptotic Minimax Risk for the White Noise Model on the Sphere
 Scandinavian Journal of Statistics
, 1999
"... Estimation of an unknown function on the unit sphere of the Euclidean space is considered. The function is observed in Gaussian continuous time white noise. Uniform norm is chosen as a loss function and exact asymptotic minimax risk is derived extending the result of Korostelev (1993). The exact asy ..."
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Cited by 8 (1 self)
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Estimation of an unknown function on the unit sphere of the Euclidean space is considered. The function is observed in Gaussian continuous time white noise. Uniform norm is chosen as a loss function and exact asymptotic minimax risk is derived extending the result of Korostelev (1993). The exact asymptotic minimax risk is given also for the L 2 loss applying the result of Pinsker (1982). Key Words: asymptotic minimax risk, exact constants in nonparametric smoothing, Gaussian white noise, spherical data, uniform norm. 1 Introduction Let S d = fx 2 R d+1 : kxk = 1g be the unit sphere on the d+1 dimensional Euclidean space, where d 1. Consider the observation of the form dX(x) = f(x)dx + ffldW (x); x 2 S d where ffl ? 0 is the noise size and dW (x) is the Gaussian white noise in S d , that is for measurable sets B;B 1 ; B 2 ae S d , (i) L ( R B dW (x)) = N(0; ¯(B)) where ¯ is the Lebesgue measure of S d , (ii) if B 1 " B 2 = ;, then R B 1 dW (x) and R B 2 dW (x) are indepen...