Using Fisher information to track stability in multivariate systems

Abstract

With the current proliferation of data, the proficient use of statistical and mining techniques offer substantial benefits to capture useful information from any dataset. As numerous approaches make use of information theory concepts, here, we discuss how Fisher information (FI) can be applied to sustainability science problems and used in data mining applications by analysing patterns in data. FI was developed as a measure of information content in data, and it has been adapted to assess order in complex system behaviour. The main advantage of the approach is the ability to collapse multiple variables into an index that can be used to assess stability and track overall trends in a system, including its regimes and regime shifts. Here, we provide a brief overview of FI theory, followed by a simple step-by-step numerical example on how to compute FI. Furthermore, we introduce an open source Python library that can be freely downloaded from GitHub and we use it in a simple case study to evaluate the evolution of FI for the global-mean temperature from 1880 to 2015. Results indicate significant declines in FI starting in 1978, suggesting a possible regime shift.

Keywords: Fisher information; big data; data mining; information science.

Figure 1.

Illustration of the binning process to calculate FI. Note that binning of the points in table 1 resulted in four states.

Figure 2.

Probability distribution.

Figure 3.

Amplitude of the probability distribution.

Figure 4.

Evolution of (a) global-mean temperature from 1880 to 2015 and (b) FI for global-mean temperature.