Discriminating Frequency Counts Tables using Higher Criticism

Alon Kipnis

2019-11-05

This package implements an adpatation of the Higher-Criticism (HC) test to discriminate two frequency counts (one-way) tables footnotes1.

The package consists of two main functions: - tables.pvals – for comuting P-values of each feature in the two tables. - HC.vals – for comuting the HC score of the P-values.

A third function tables.HC combines the two functions above so that the HC score of the two tables is obtained using a single function call.

Example:

text1 = "Should I stay or should I go ?"
text2 = "I should stay . I should not go !"
tb1 = table(strsplit(tolower(text1),' '))
tb2 = table(strsplit(tolower(text2),' '))
pv = tables.pval(tb1,tb2)

print(pv$pv)
> [1] 1.0000 1.0000 0.2304 1.0000 1.0000 1.0000     NA 0.1936     NA

print(pv$Var1)
> go i or say should stay you and not

HC.vals(pv$pv)
> $HC
> 0.323954762194625
> $HC.star
> 0.323954762194625
> $p
> 0.2304
> $p.star
> 0.2304

Example 2

n = 1000  #number of features
N = 10*n  #number of observations

seq = seq(1,n)
P = 1 / seq  #sample from Zipf law distribution
P = P / sum(P)
tb1 = data.frame(Feature = seq(1,n),  # sample 1
      Freq = rmultinom(n = 1, prob = P, size = 10*n))

k = 0.1*n # nuber of features to change
seq[sample(seq,k)] <- seq[sample(seq,k)] 
Q = 1 / seq 
Q = Q / sum(Q)  

tb2 = data.frame(Feature = seq(1,n), # sample 2
      Freq = rmultinom(n = 1, prob = Q, size = 10*n))

PV = tables.pval(tb1, tb2)  #compute P-values

HC.vals(PV$pv)  # HC test

# can also test using a single function call
tables.HC(tb1,tb2)

  1. See David Donoho and Alon Kipnis Higher Criticism for Discriminating Word-Frequency Tables and Testing Authorship (2019)↩ī¸Ž