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Results 1 - 10
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279
BAYESIAN MULTIPLE TESTING UNDER SPARSITY FOR POLYNOMIAL-TAILED DISTRIBUTIONS
"... Abstract: This paper considers Bayesian multiple testing under sparsity for polynomial-tailed distributions satisfying a monotone likelihood ratio prop-erty. Included in this class of distributions are the Student’s t, the Pareto, and many other distributions. We prove some general asymptotic optima ..."
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Abstract: This paper considers Bayesian multiple testing under sparsity for polynomial-tailed distributions satisfying a monotone likelihood ratio prop-erty. Included in this class of distributions are the Student’s t, the Pareto, and many other distributions. We prove some general asymptotic
The limiting process of N-particle branching random walk with polynomial tails
, 2013
"... We consider a system of N particles on the real line that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the positive reals and 3) only the N right-most particles are retaine ..."
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– in the case where the displacement distribution admits exponential moments. Here, we consider the case of displacements with regularly varying tails, where the relevant space and time scales are markedly different. We characterize the behavior of the system for two distinct asymptotic regimes. First, we prove
Support-vector machines for histogram-based image classification
- IEEE Transactions on Neural Networks
, 1999
"... Abstract — Traditional classification approaches generalize poorly on image classification tasks, because of the high dimensionality of the feature space. This paper shows that support vector machines (SVM’s) can generalize well on difficult image classification problems where the only features are ..."
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Cited by 229 (1 self)
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are high dimensional histograms. Heavy-tailed RBF kernels of the form K(x;y) = e jx y j with a 1 and b 2 are evaluated on the classification of images extracted from the Corel stock photo collection and shown to far outperform traditional polynomial or Gaussian radial basis function (RBF) kernels
On the head and the tail of the colored Jones polynomial
- Compos. Math
"... Abstract. The colored Jones polynomial is a function JK: N − → Z[t, t −1] associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of JK(n) are independent of n when n is sufficiently large. Computation ..."
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Cited by 14 (2 self)
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Abstract. The colored Jones polynomial is a function JK: N − → Z[t, t −1] associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of JK(n) are independent of n when n is sufficiently large. Computation
Methods to Distinguish Between Polynomial and Exponential Tails
"... ABSTRACT. Two methods to distinguish between polynomial and exponential tails are introduced. The methods are based on the properties of the residual coefficient of variation for the exponential and non-exponential distributions. A graphical method, called a CV-plot, shows departures from exponenti ..."
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ABSTRACT. Two methods to distinguish between polynomial and exponential tails are introduced. The methods are based on the properties of the residual coefficient of variation for the exponential and non-exponential distributions. A graphical method, called a CV-plot, shows departures from
UPPER TAILS AND INDEPENDENCE POLYNOMIALS IN RANDOM GRAPHS
"... Abstract. The upper tail problem in the Erdős-Rényi random graph G ∼ Gn,p asks to estimate the probability that the number of copies of a graph H in G exceeds its expectation by a factor 1 + δ. Chatterjee and Dembo (2014) showed that in the sparse regime of p → 0 as n→ ∞ with p ≥ n−α for an explic ..."
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and any fixed δ> 0, the upper tail probability is exp[−(cH(δ) + o(1))n2p ∆ log(1/p)], where ∆ is the maximum degree of H. As it turns out, the leading order constant in the large deviation rate function, cH(δ), is governed by the independence polynomial of H, defined as PH(x) = iH(k)x k where i
THE POLYNOMIAL LOWER TAIL RANDOM CONDUCTANCES MODEL
, 2013
"... We study the decay of the return probabilities of continuous time random walks among i.i.d. random conductances of power-law tail near 0 with exponent γ> 0. For any γ> 1 4, we show that the decay of the quenched return probabilities actually is standard, i.e. of order t−d/2. ..."
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We study the decay of the return probabilities of continuous time random walks among i.i.d. random conductances of power-law tail near 0 with exponent γ> 0. For any γ> 1 4, we show that the decay of the quenched return probabilities actually is standard, i.e. of order t−d/2.
Rogers–Ramanujan type identities and the head and tail of the colored Jones polynomial
"... Abstract. We study the head and tail of the colored Jones polynomial while focusing mainly on alternating links. Various ways to compute the colored Jones polynomial for a given link give rise to combinatorial identities for those power series. We further show that the head and tail functions only d ..."
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Cited by 10 (1 self)
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Abstract. We study the head and tail of the colored Jones polynomial while focusing mainly on alternating links. Various ways to compute the colored Jones polynomial for a given link give rise to combinatorial identities for those power series. We further show that the head and tail functions only
On the tail of jones polynomials of closed braids with a full twist
"... For a closed n–braid with a full positive twist and with ` negative crossings, 0 ≤ ` ≤ n, we determine the first n−`+1 terms of the Jones polynomial VL(t). We show that VL(t) satisfies a braid index constraint, which is a gap of length at least n− ` between the first two nonzero coefficients of (1 ..."
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Cited by 4 (0 self)
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For a closed n–braid with a full positive twist and with ` negative crossings, 0 ≤ ` ≤ n, we determine the first n−`+1 terms of the Jones polynomial VL(t). We show that VL(t) satisfies a braid index constraint, which is a gap of length at least n− ` between the first two nonzero coefficients of (1
Results 1 - 10
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279
