Discovery by Minimal Length Encoding: A case study in molecular evolution

Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only single observations are present.We develop a theory how to generate causal graphs explaining similarities between single objects. To this end, we replace the notion of conditional stochastic independence in the causal Markov condition with the vanishing of conditional algorithmic mutual information and describe the corresponding causal inference rules.We explain why a consistent reformulation of causal inference in terms of algorithmic complexity implies a new inference principle that takes into account also the complexity of conditional probability densities, making it possible to select among Markov equivalent causal graphs. This insight provides a theoretical foundation of a heuristic principle proposed in earlier work.We also discuss how to replace Kolmogorov complexity with decidable complexity criteria. This can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions on the underlying distribution. *

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“…The inequality combines ineqs. ( 27) and (28). The last equality follows similar as the equalities in the first line.…”

Section: Lemma 10 (Average Complexity Of Stochastic Maps)mentioning

confidence: 52%

“…We will therefore infer some causal relation (here: common ancestors in the evolution) using the causal principle in Lemma 5 (cf. [28]).…”

Section: Relative Causalitymentioning

confidence: 99%

Causal Inference Using the Algorithmic Markov Condition

Janzing

Schölkopf

2010

IEEE Trans. Inform. Theory

166

237

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“…For example, the compression method has been used to build the evolution tree of mammalian DNA sequences [84]. It has also used to discover new sub-families of Alu-sequences [85,86]. Hence, the main purpose of using compression methods in these cases are not to reduce the storage size, rather they are used to discover the hidden relationship among the sequences, such as whether they are coming from the same family tree.…”

Section: Reference-based Dna Compression Methods For Partially Similamentioning

confidence: 99%

Application of signal processing for DNA sequence compression

Law

2019

IET signal process.

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Due to the advancement of high-throughput sequencing technologies, it is now feasible for sequencing individual genomes in a fast and affordable manner. With the significant increase in the number of individual genomes, compression methods are needed to reduce pressure on data storage as well as enable effective data distribution and management. The compression methods can generally be divided into two classes, namely reference-free methods and reference-based methods. In reference-free methods, redundancies within the target DNA sequence to be compressed are explored. In reference-based methods, redundancies between the target DNA sequence and other reference sequences are identified to achieve compression. This type of method is applicable to population sequences which are highly similar to each other and have a small number of mismatches. Some of the methods can also be applied to partially similar sequences such as chromosome sequences or sequences having evolutionary relationship. The authors highlight recent developments in these methods. In the comparative study, the authors' simulation results reveal that the selection of a reference sequence is a crucial factor affecting the compression performance. Use of multiple number of reference sequences and enhancement strategies such as reference rewriting are important to achieve a large compression gain. (a) Short segment of the chromosome 19 of the human Homo sapiens genome, (b) Its lossless encoded representation with 'A' represented as '00', 'T' as '11', 'C' as '01' and 'G' as '10', (c) Resultant segment after the first referencing instruction is applied

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