The Geometry of Logconcave Functions and an O∗(n3) Sampling Algorithm
نویسندگان
چکیده
The class of logconcave functions in Rn is a common generalization of Gaussians and of indicator functions of convex sets. Motivated by the problem of sampling from a logconcave density function, we study their geometry and introduce a technique for “smoothing” them out. This leads to an efficient sampling algorithm (by a random walk) with no assumptions on the local smoothness of the density function. After appropriate preprocessing, the algorithm produces a point from approximately the right distribution in time O∗(n4), and in amortized time O∗(n3) if many sample points are needed (where the asterisk indicates that dependence on the error parameter and factors of log n are not shown).
منابع مشابه
The geometry of logconcave functions and sampling algorithms
The class of logconcave functions in R is a common generalization of Gaussians and of indicator functions of convex sets. Motivated by the problem of sampling from a logconcave density function, we study their geometry and introduce a technique for “smoothing” them out. These results are applied to analyze two efficient algorithms for sampling from a logconcave distribution in n dimensions, wit...
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