In terminological/tidy-info-stats: Functions for manipulating information statistics

knitr::opts_chunk$set(
  collapse = TRUE
)

library(infotheo)
library(tidyverse)
#library(ggplot2)
#library(devtools)
library(tidyinfostats)
#devtools::load_all("..")

The infotheo package contains a function to discretise and calculate the mutual information from a data set. Unfortunately it is not somewhat hard to use on tidy data and cannot be used with dbplyr tables without bringing them into memory.

data(USArrests)
dat<-discretize(USArrests)
tidydat = dat %>% mutate(state = rownames(USArrests)) 
tidydat

#computes the MIM (mutual information matrix)

print("Class by class mutual information:")
mutinformation(dat,method= "emp")
mutinformation(dat,method="mm")

print("Murder versus assault mutual information:")
mutinformation(dat[,1],dat[,2])

The first step to a more dplyr friendly mutual information function is to calculate the probabilities of different outcomes. The probabilityFromGroups function counts outcomes defined by the arguments. It returns a complete confusion matrix for each combination of outcome observed.

tidydat %>% probabilitiesFromCooccurrence(vars(Murder),vars(Assault))

Assuming the same discretised data we can calculate MIs for individual combinations using dplyr syntax. This is reiplemented in a way which allows it to be performed in SQL if a dbplyr table is provided

tidydat %>% probabilitiesFromCooccurrence(vars(Murder),vars(Assault)) %>% calculateMultiClassMI() # should be the same as I2

However the more usual situation in tidy data is to not have a matrix as with the USArrests data but a longer format such as the following:

tidydat2 = dat %>% 
        mutate(state = rownames(USArrests)) %>%
        pivot_longer(-state, names_to = "variable", values_to = "level")
tidydat2 %>% head()

And in data from a database you are likely constructing a joint dataset through some sort of join, on a shared field. In this case we will use the same data for both sides

# get a tidy version of the dat data - i.e. 
lhs = tidydat2 %>% rename(variable1=variable, level1=level)
rhs = tidydat2 %>% rename(variable2=variable, level2=level)
tidydat3 =  lhs %>% inner_join(rhs, by="state")

tidydat3 %>% head()

Using this data format it is more natural to group the data by the variables and determine the probabilities is a dplyr friendly way. To prove this is correct we reformat it to the same as the infotheo package

t3 = tidydat3 %>% group_by(variable1,variable2) %>% probabilitiesFromCooccurrence(vars(level1),vars(level2)) %>% calculateMultiClassMI(adjust=FALSE)
t3 %>% pivot_wider(names_from=variable2, values_from=I) # should be the same as I

t4 = tidydat3 %>% group_by(variable1,variable2) %>% probabilitiesFromCooccurrence(vars(level1),vars(level2)) %>% calculateMultiClassMI(adjust=TRUE)
t4 %>% pivot_wider(names_from=variable2, values_from=I) # should be the same as I

TODO: document the binary MI with an example. document the use of the other info stats for plotting ROC curve etc.

terminological/tidy-info-stats documentation built on Nov. 19, 2022, 11:23 p.m.