Rejection sampling from shape-constrained distributions in sublinear time

05/29/2021
by   Sinho Chewi, et al.
0

We consider the task of generating exact samples from a target distribution, known up to normalization, over a finite alphabet. The classical algorithm for this task is rejection sampling, and although it has been used in practice for decades, there is surprisingly little study of its fundamental limitations. In this work, we study the query complexity of rejection sampling in a minimax framework for various classes of discrete distributions. Our results provide new algorithms for sampling whose complexity scales sublinearly with the alphabet size. When applied to adversarial bandits, we show that a slight modification of the Exp3 algorithm reduces the per-iteration complexity from 𝒪(K) to 𝒪(log^2 K), where K is the number of arms.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/09/2022

Sampling an Edge in Sublinear Time Exactly and Optimally

Sampling edges from a graph in sublinear time is a fundamental problem a...
05/31/2019

Exact sampling of determinantal point processes with sublinear time preprocessing

We study the complexity of sampling from a distribution over all index s...
10/12/2022

Quantum Algorithms for Sampling Log-Concave Distributions and Estimating Normalizing Constants

Given a convex function fℝ^d→ℝ, the problem of sampling from a distribut...
08/15/2022

Nesterov smoothing for sampling without smoothness

We study the problem of sampling from a target distribution in ℝ^d whose...
02/10/2021

On the Suboptimality of Thompson Sampling in High Dimensions

In this paper we consider Thompson Sampling for combinatorial semi-bandi...
10/31/2022

A Faster Sampler for Discrete Determinantal Point Processes

Discrete Determinantal Point Processes (DPPs) have a wide array of poten...
12/12/2017

Dynamic Discrete Tomography

We consider the problem of reconstructing the paths of a set of points o...

Please sign up or login with your details

Forgot password? Click here to reset