منابع مشابه
Valuations on Log-Concave Functions
A classification of SL(n) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as SL(n) and translation invariant valuations on log-concave functions. 2000 AMS subject classificat...
متن کاملOn the Product of Log-concave Polynomials
A real polynomial is called log-concave if its coefficients form a log-concave sequence. We give a new elementary proof of the fact that a product of log-concave polynomials with nonnegative coefficients and no internal zero coefficients is again log-concave. In addition, we show that if the coefficients of the polynomial ∏ m∈M(x + m) form a monotone sequence where M is a finite multiset of pos...
متن کاملChernoff's density is log-concave.
We show that the density of Z = argmax{W (t) - t2}, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture.
متن کاملNon-parametric log-concave mixtures
Finite mixtures of parametric distributions are often used to model data of which it is known or suspected that there are subpopulations. Instead of a parametric model, a penalized likelihood smoothing algorithm is developed. The penalty is chosen to favor a log-concave result. The standard EM algorithm (“split and fit”) can be used. Theoretical results and applications are presented. © 2006 El...
متن کاملLearning Multivariate Log-concave Distributions
We study the problem of estimating multivariate log-concave probability density functions. We prove the first sample complexity upper bound for learning log-concave densities on Rd, for all d ≥ 1. Prior to our work, no upper bound on the sample complexity of this learning problem was known for the case of d > 3. In more detail, we give an estimator that, for any d ≥ 1 and ǫ > 0, draws Õd ( (1/ǫ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90321-r