A Note on A Priori Forecasting and Simplicity Bias in Time Series

Dingle, Kamaludin; Rafiq, Kamal,; Hamzi, Boumediene

doi:10.48550/arxiv.2203.05391

Cited by 3 publications

(7 citation statements)

References 34 publications

(58 reference statements)

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“…The work here has focussed on discrete geometries, configurations, or sequences, such as binary strings, discrete graphs, branching patters, and lattice shapes. However, continuous curves, functions and shapes can be discretised often quite easily [23,35], and because of this the arguments presented here apply to a wide array of shapes and geometries.…”

Section: Discussionmentioning

confidence: 99%

Optima and Simplicity in Nature

Dingle¹

2022

Preprint

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Why are simple, regular, and symmetric shapes common in nature? Many natural shapes arise as solutions to energy minimisation or other optimisation problems, but is there a general relation between optima and simple, regular shapes and geometries? Here we argue from algorithmic information theory that for objective functions common in nature --- based on physics and engineering laws --- optimal geometries will be simple, regular, and symmetric. Further, we derive a null model prediction that if a given geometry is an optimal solution for one natural objective function, then it is a priori more likely to be optimal or close to optimal for another objective function.

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Section: Discussionmentioning

confidence: 99%

Optima and Simplicity in Nature

Dingle¹

2022

Preprint

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“…For example, the parameters of a large ordinary differential equation system are not usually understood as an 'algorithm' for the solution profile, nonetheless the upper bound has been shown to predict the probability of outputs in such systems [9,27]. Even more distant from a computer running a program, the upper bound has been shown to work well in predicting natural time series patterns [8] for which both the notion of program and computer is much less clearly defined.…”

Section: Discussionmentioning

confidence: 99%

“…[7]. (b) Time series data taken from the World Bank Open Data project (https://data.worldbank.org), which have been discretised to binary strings (of length 16 bits) while studying SB [8]. (c) Computationally predicted [24] RNA secondary structures obtained from randomly sampling 1 million sequences of length L = 35 nucleotides.…”

Section: A Low Complexity Low Probability Behaviour Is Very Commonmentioning

confidence: 99%

“…The authors of ref. [8] invoked algorithmic probability and the upper bound in Eq. ( 3) to make predictions about natural time series data taken from the World Bank Open Data project (the example time series data set described above was taken from their study).…”

Section: Time Series Predictionmentioning

confidence: 99%

“…The maps studied are: (a) A finite state transducer (FST) with data taken from ref. [7]; (b) time series patterns from the World Bank Open Data, with data taken from [8]; (c) computationally predicted RNA secondary structures from 1 million randomly sampled input sequences; and (d) discretised polynomials curves generated with x ∈(0,1) and random coefficients, data taken from [9].…”

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confidence: 99%

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Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications

Alaskandarani¹,

Dingle²

2022

Preprint

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Developing new ways to estimate probabilities can be valuable for science, statistics, and engineering. By considering the information content of different output patterns, recent work invoking algorithmic information theory has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam's razor, machine learning, and password guessing.

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Predicting phenotype transition probabilities via conditional algorithmic probability approximations

Dingle

Novev

Ahnert

et al. 2022

Preprint

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Unravelling the structure of genotype-phenotype (GP) maps is an important problem in biology. Recently, arguments inspired by algorithmic information theory (AIT) and Kolmogorov complexity have been invoked to uncover simplicity bias in GP maps, an exponentially decaying upper bound in phenotype probability with increasing phenotype descriptional complexity. This means that phenotypes with very many genotypes assigned via the GP map must be simple, while complex phenotypes must have few genotypes assigned. Here we use similar arguments to bound the probability P(x → y) that phenotype x, upon random genetic mutation, transitions to phenotype y. The bound is P(x → y)≲ 2−aK˜(y|x)−b, where K˜(y|x) is the estimated conditional complexity of y given x, quantifying how much extra information is required to make y given access to x. This upper bound is related to the conditional form of algorithmic probability from AIT. We demonstrate the practical applicability of our derived bound by predicting phenotype transition probabilities (and other related quantities) in simulations of RNA and protein secondary structures. Our work contributes to a general mathematical understanding of GP maps, and also facilitates the prediction of transition probabilities directly from examining phenotype themselves, without utilising detailed knowledge of the GP map.

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A Note on A Priori Forecasting and Simplicity Bias in Time Series

Cited by 3 publications

References 34 publications

Optima and Simplicity in Nature

Optima and Simplicity in Nature

Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications

Predicting phenotype transition probabilities via conditional algorithmic probability approximations

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