Adaptive Greedy Rejection Sampling

by   Gergely Flamich, et al.

We consider channel simulation protocols between two communicating parties, Alice and Bob. First, Alice receives a target distribution Q, unknown to Bob. Then, she employs a shared coding distribution P to send the minimum amount of information to Bob so that he can simulate a single sample X ∼ Q. For discrete distributions, Harsha et al. (2009) developed a well-known channel simulation protocol – greedy rejection sampling (GRS) – with a bound of D_KL[Q ‖ P] + 2ln(D_KL[Q ‖ P] + 1) + 𝒪(1) on the expected codelength of the protocol. In this paper, we extend the definition of GRS to general probability spaces and allow it to adapt its proposal distribution after each step. We call this new procedure Adaptive GRS (AGRS) and prove its correctness. Furthermore, we prove the surprising result that the expected runtime of GRS is exactly exp(D_∞[Q ‖ P]), where D_∞[Q ‖ P] denotes the Rényi ∞-divergence. We then apply AGRS to Gaussian channel simulation problems. We show that the expected runtime of GRS is infinite when averaged over target distributions and propose a solution that trades off a slight increase in the coding cost for a finite runtime. Finally, we describe a specific instance of AGRS for 1D Gaussian channels inspired by hybrid coding. We conjecture and demonstrate empirically that the runtime of AGRS is 𝒪(D_KL[Q ‖ P]) in this case.


page 1

page 2

page 3

page 4


Fast Relative Entropy Coding with A* coding

Relative entropy coding (REC) algorithms encode a sample from a target d...

Greedy Poisson Rejection Sampling

One-shot channel simulation is a fundamental data compression problem co...

Notes on the runtime of A* sampling

The challenge of simulating random variables is a central problem in Sta...

Remote Sampling with Applications to General Entanglement Simulation

We show how to sample exactly discrete probability distributions whose d...

On the expected runtime of multiple testing algorithms with bounded error

Consider the testing of multiple hypotheses in the setting where the p-v...

Adaptive Policies for Sequential Sampling under Incomplete Information and a Cost Constraint

We consider the problem of sequential sampling from a finite number of i...

Algorithms for the Communication of Samples

We consider the problem of reverse channel coding, that is, how to simul...

Please sign up or login with your details

Forgot password? Click here to reset