Algorithmic Data Analytics, Small Data Matters and Correlation versus Causation

This is a review of aspects of the theory of algorithmic information that may contribute to a framework for formulating questions related to complex highly unpredictable systems. We start by contrasting Shannon Entropy and Kolmogorov-Chaitin complexity epitomizing the difference between correlation and causation to then move onto surveying classical results from algorithmic complexity and algorithmic probability, highlighting their deep connection to the study of automata frequency distributions. We end showing how long-range algorithmic predicting models for economic and biological systems may require infinite computation but locally approximated short-range estimations are possible thereby showing how small data can deliver important insights into important features of complex "Big Data".