Semi-Finite Length Analysis for Information Theoretic Tasks

11/01/2018
by   Masahito Hayashi, et al.
0

We focus on the optimal value for various information-theoretical tasks. There are several studies for the asymptotic expansion for these optimal values up to the order √(n) or n. However, these expansions have errors of the order o(√(n)) or o( n), which does not goes to zero asymptotically. To resolve this problem, we derive the asymptotic expansion up to the constant order for upper and lower bounds of these optimal values. While the expansions of upper and lower bonds do not match, they clarify the ranges of these optimal values, whose errors go to zero asymptotically.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/04/2018

Improved Bounds on Lossless Source Coding and Guessing Moments via Rényi Measures

This paper provides upper and lower bounds on the optimal guessing momen...
research
03/31/2020

Information-Theoretic Lower Bounds for Zero-Order Stochastic Gradient Estimation

In this paper we analyze the necessary number of samples to estimate the...
research
07/23/2022

A New Approach to Drifting Games, Based on Asymptotically Optimal Potentials

We develop a new approach to drifting games, a class of two-person games...
research
01/05/2023

Optimal lower bounds for Quantum Learning via Information Theory

Although a concept class may be learnt more efficiently using quantum sa...
research
11/02/2021

Nearly Optimal Algorithms for Level Set Estimation

The level set estimation problem seeks to find all points in a domain X ...
research
06/23/2023

Precise Asymptotic Generalization for Multiclass Classification with Overparameterized Linear Models

We study the asymptotic generalization of an overparameterized linear mo...
research
09/18/2021

A Tighter Upper Bound of the Expansion Factor for Universal Coding of Integers and Its Code Constructions

In entropy coding, universal coding of integers (UCI) is a binary univer...

Please sign up or login with your details

Forgot password? Click here to reset