Physics

Systems biology

Inference

Mathematics

Biology

Principle of maximum entropy

Entropy (arrow of time)

Data mining

Statistics

Machine learning

Engineering

Artificial intelligence

Programming language

Data science

Soundness

Computer science

Management science

Quantum mechanics

Computational biology

Theoretical computer science

Information theory

Heliyon

A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of 'entropy', and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data.

An introduction to the maximum entropy approach and its application to inference problems in biology