Loss Bounds and Time Complexity for Speed Priors

04/12/2016
by   Daniel Filan, et al.
0

This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently computable. We propose a variant to the original speed prior (Schmidhuber, 2002), and show that our prior can predict sequences drawn from probability measures that are estimable in polynomial time. Our speed prior is computable in doubly-exponential time, but not in polynomial time. On a polynomial time computable sequence our speed prior is computable in exponential time. We show better upper complexity bounds for Schmidhuber's speed prior under the same conditions, and that it predicts deterministic sequences that are computable in polynomial time; however, we also show that it is not computable in polynomial time, and the question of its predictive properties for stochastic sequences remains open.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/26/2017

Closure of resource-bounded randomness notions under polynomial time permutations

An infinite bit sequence is called recursively random if no computable s...
research
06/13/2022

A Dilemma for Solomonoff Prediction

The framework of Solomonoff prediction assigns prior probability to hypo...
research
08/29/2018

Complexity and mission computability of adaptive computing systems

There is a subset of computational problems that are computable in polyn...
research
03/04/2013

LT^2C^2: A language of thought with Turing-computable Kolmogorov complexity

In this paper, we present a theoretical effort to connect the theory of ...
research
12/13/1999

New Error Bounds for Solomonoff Prediction

Solomonoff sequence prediction is a scheme to predict digits of binary s...
research
05/03/2023

Complexity and Enumeration in Models of Genome Rearrangement

In this paper, we examine the computational complexity of enumeration in...
research
06/19/2019

The Complexity of Online Bribery in Sequential Elections

Prior work on the complexity of bribery assumes that the bribery happens...

Please sign up or login with your details

Forgot password? Click here to reset