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DsFeatFreqDistFit.R
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DsFeatFreqDistFit.R
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#' DsFeatFreqDistFit – Dataset Feature-Frequency Distribution Fitting
#' Copyright (C) 2017-2020 Gürol Canbek
#' This file is licensed under
#'
#' GNU Affero General Public License v3.0, GNU AGPLv3
#'
#' This program is free software: you can redistribute it and/or modify
#' it under the terms of the GNU Affero General Public License as published
#' by the Free Software Foundation, either version 3 of the License, or
#' (at your option) any later version.
#'
#' This program is distributed in the hope that it will be useful,
#' but WITHOUT ANY WARRANTY; without even the implied warranty of
#' MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
#' GNU Affero General Public License for more details.
#'
#' You should have received a copy of the GNU Affero General Public License
#' along with this program. If not, see <https://www.gnu.org/licenses/>.
#'
#' See the license file in <https://github.com/gurol/DsFeatFreqDistFit>
#'
#' @author Gürol Canbek, <[email protected]>
#' @references <http://gurol.canbek.com>
#' @keywords distributions, log-normal, power law, Poisson, exponential,
#' data sets, feature frequency
#' @title dsdist - R Scripts for Distribution Fitting Testing
#' @date 11 January 2018
#' @version 1.1
#' @note version history
#' December 2017
#' 1.1 January 2018, Exponential and Poisson fits
#' 1.0 December 2017, The first version
#' @description R scripts for comprehensive set of distribution testing to fit
#' power law, log-normal, exponential, and Poisson statistical distribution
#' into the feature frequency distributions (the truth). A part of dsanalysis
#' (Dataset Analysis)
#' ## libraries
library(ggplot2) # Preinstalled in environment
library(magrittr) # Preinstalled in environment
library(dplyr) # Preinstalled in environment
library(poweRlaw)
source('utils.R', chdir=TRUE)
#' ## Distribution colors
# Power-law Log-Normal Exponent Poisson
cols_dist <- c('#fb8072', '#7f4e2C', '#80b1d3', '#49b960')
col_distpl <- 1
col_distln <- 2
col_distex <- 3
col_distpo <- 4
# Compare distribution Vuon's test statistics sign threshold
sign_threshold <- 0.001
#' ### testLongTailDistributionsHypotheses
#' Test the various long tail distribution fit hypothesis for given truth given
#' as a feature frequencies or counts per class (e.g. 'Positive' or 'Malign')
#' with corresponding feature space names of one or more datasets (ds).
#' **Parameters:**
#' *class_name*: Class identifier (e.g. 'Positive' or 'Malign')
#' *df_feat_freqs_or_counts*: Data frame holding feature frequencies or counts per dataset as a column vector
#' *df_ds_feat_space_names*: Data frame holding feature names per dataset as a column vector
#' *df_ds_sample_sizes*: Data frame holding sample sizes if the feature distribution is given as a frequency (otherwise: default: NULL)
#' *plot_graph_compare_two_dists*: Plot? (default: TRUE)
#' *plot_graph_compare_all_dist*: Plot? (default: TRUE)
#' *plot_graph_likelihood_ratios*: Plot? (default: FALSE)
#' **Return:**
#' none
#' **Details:**
#' Select feature space names in the spreadsheet (hide other columns)
#' `df_ds_feat_space_names <- rclip()`
#' Select feature frequencies or counts in the spreadsheet (hide other columns)
#' `df_feat_freqs_or_counts <- rclip()`
#' Select sampe sizes if frequencies are provided
#' `df_ds_sample_sizes <- rclip(header=FALSE)`
#' ignore warning message: incomplete final line found by readTableHeader on 'pbpaste'
#'
#' You can save the data frames for later use:
#' `save(df_feat_freqs_or_counts, df_ds_feat_space_names, df_ds_sample_sizes, file='Malign.RData')`
#'
#' *See the Examples*
#'
#' **Suggested plot file naming schema:**
#' 6 inch x 8 inch Landscape for Export | Save as PDF...
#' 800 x 600 for Export | Save as Image...
#' Benign_DS0_VuongTest_fitted_powerlaw_vs_lognormal
#' Benign_DS0_VuongTest_fitted_powerlaw_vs_poisson
#' Benign_DS0_VuongTest_fitted_powerlaw_vs_exponential
#' Benign_DS0_VuongTest_powerlaw_vs_fitted_lognormal
#' Benign_DS0_VuongTest_powerlaw_vs_fitted_exponential
#' Benign_DS0_VuongTest_lognormal_vs_fitted_exponential
#' Benign_DS0_fitted_powerlaw_against_others
#' Benign_DS0_fitted_lognormal_against_others
#' Benign_DS0_fitted_exponential_against_others
#' Benign_DS0_bootstrapt_powerlaw_fit
#' Benign_DS0_bootstrapt_lognormal_fit
#' Benign_DS5_bootstrapt_exponential_fit
#' Benign_DS0_LogLikelihoodRatioDistribution_fitted_powerlaw_vs_lognormal
#' Benign_DS0_LogLikelihoodRatioDistribution_powerlaw_vs_fitted_lognormal
#' **Warning:**
#' Unsolved exception when plot_graph_likelihood_ratios=TRUE
#' **Examples:** `testLongTailDistributionsHypotheses('Benign', df_ds_feat_freqs, df_ds_feat_space_names, df_ds_sample_sizes, no_sim_count=50)`
testLongTailDistributionsHypotheses<-function(
class_name, df_feat_freqs_or_counts, df_ds_feat_space_names,
df_ds_sample_sizes=NULL, no_sim_count=NULL,
plot_graph_compare_two_dists=TRUE, plot_graph_compare_all_dist=TRUE,
plot_graph_likelihood_ratios=FALSE
)
{
# Dimensions check
stopifnot(nrow(df_feat_freqs_or_counts) == nrow(df_ds_feat_space_names))
stopifnot(ncol(df_feat_freqs_or_counts) == ncol(df_ds_feat_space_names))
stopifnot(ncol(df_feat_freqs_or_counts) == ncol(df_ds_sample_sizes))
stopifnot(ncol(df_ds_feat_space_names) == ncol(df_ds_sample_sizes))
for (ds in 1:length(df_feat_freqs_or_counts)){
feat_freqs_or_counts <- df_feat_freqs_or_counts[[ds]]
feat_freqs_or_counts <- feat_freqs_or_counts[!is.na(feat_freqs_or_counts)]
feat_space_names <- df_ds_feat_space_names[[ds]]
feat_space_names <- feat_space_names[!is.na(feat_freqs_or_counts)]
if (is.null(df_ds_sample_sizes))
ds_sample_size <- NULL
else
ds_sample_size <- df_ds_sample_sizes[, ds]
ds_name <- gsub('featureFreq', '', colnames(df_feat_freqs_or_counts)[ds])
bs_p <- testLongTailDistributionsHypothesis(
ds_name, class_name, feat_space_names, feat_freqs_or_counts,
ds_sample_size, no_sim_count=no_sim_count,
plot_graph_compare_two_dists=plot_graph_compare_two_dists,
plot_graph_compare_all_dist=plot_graph_compare_all_dist,
plot_graph_likelihood_ratios=plot_graph_likelihood_ratios)
}
}
#' ### testLongTailDistributionsHypothesis
#' Test the various long tail distribution fit hypothesis for given truth given
#' as a feature frequencies or counts for given a class (e.g. 'Positive' or 'Malign')
#' with corresponding feature space names of one dataset (ds).
#' **Parameters:**
#' *ds_name*: Dataset name (e.g. 'DS1')
#' *ds_class_name*: Class identifier (e.g. 'Positive' or 'Malign')
#' *ds_feat_space_names*: Feature names
#' *ds_feat_freqs_or_counts*: Feature frequencies or counts
#' *ds_sample_size*: Sample size if the feature distribution is given as a frequency (otherwise: default: NULL)
#' *threads*: Number of CPU cores (default: extractef from the system)
#' *no_sim_count*: Number of simulation count for bootstrap test (default: NULL)
#' *plot_graph_compare_two_dists*: Plot? (default: TRUE)
#' *plot_graph_compare_all_dist*: Plot? (default: TRUE)
#' *plot_graph_likelihood_ratios*: Plot? (default: FALSE)
#' **Return:**
#' list(bs_power_law, bs_log_normal, bs_exponential) bootstrap objects
#' **Details:**
#'
#' **Examples:** `testLongTailDistributionsHypothesis('DS0', 'Benign', ds_feat_space_names, ds_feat_freqs, 264303, no_sim_count=5)`
testLongTailDistributionsHypothesis<-function(
ds_name, ds_class_name, ds_feat_space_names, ds_feat_freqs_or_counts,
ds_sample_size=NULL, threads=getNumberOfCPUCores(), no_sim_count=NULL,
plot_graph_compare_two_dists=TRUE, plot_graph_compare_all_dist=TRUE,
plot_graph_likelihood_ratios=TRUE)
{
if (all(ds_feat_freqs_or_counts == floor(ds_feat_freqs_or_counts)))
# All elements are integer so the variable holds feature counts
feat_counts <- ds_feat_freqs_or_counts
else
# Elements are fractinal convert into counts by multiplying the frequency
# by dataset sample size
feat_counts <- round(ds_sample_size*ds_feat_freqs_or_counts)
feature_space_size <- length(feat_counts)
# Determine simulation counts
simulation_counts <- 100
if (is.null(no_sim_count)) {
if (ds_sample_size > simulation_counts) {
if (ds_sample_size < 1000)
simulation_counts <- 1000
else if (ds_sample_size < 5000)
simulation_counts <- ds_sample_size
else
simulation_counts <- 5000
}
# else
# simulation_counts <- 100
}
else
simulation_counts <- no_sim_count
xlabel_ds_class <- paste0(ds_name, ' (', ds_class_name, ') feature counts')
# No scientific notation (e.g. 1e+05) in axis in plots
scipen_option <- getOption('scipen')
options(scipen=999)
############ Power-law #######################################################
# (Discrete) Power-law fit? xmin is estimated
fit_power_law <- displ$new(feat_counts)
est <- estimate_xmin(fit_power_law)
fit_power_law$setXmin(est)
est <- estimate_pars(fit_power_law)
fit_power_law$setPars(est)
bs_power_law <- bootstrap_p(fit_power_law, xmax = 1e+06,
threads=threads, no_of_sims=simulation_counts)
# Power-law, bootsptrap parameters
xmin_pl <- fit_power_law$xmin
ntail_pl <- get_ntail(fit_power_law, prop=FALSE)
# (Discrete) Log-Normal fit?
fit_log_normal_with_pl <- dislnorm$new(feat_counts)
# Set Xmin from power-law (they should be the same in both distributions)
# est <- estimate_xmin(fit_log_normal)
fit_log_normal_with_pl$setXmin(xmin_pl)
est <- estimate_pars(fit_log_normal_with_pl)
fit_log_normal_with_pl$setPars(est)
# Vuong's test,
# A likelihood ratio test for model selection
# using the Kullback-Leibler criteria
compdist_pl_vs_ln_with_pl <- compare_distributions(
fit_power_law, fit_log_normal_with_pl)
if (plot_graph_compare_two_dists) {
plot(compdist_pl_vs_ln_with_pl,
col=ifelse(compdist_pl_vs_ln_with_pl$ratio$ratio < -sign_threshold,
cols_dist[col_distln],
ifelse(compdist_pl_vs_ln_with_pl$ratio$ratio > sign_threshold,
cols_dist[col_distpl], 'black')),
main=paste0('Vuong\'s test: Power Law* vs. Log-Normal (',
ds_name, ')'),
xlab=xlabel_ds_class)
}
# (Discrete) Poisson fit?
fit_poisson_with_pl <- dispois$new(feat_counts)
# Set Xmin from power-law (they should be the same in both distributions)
# est <- estimate_xmin(fit_poisson)
fit_poisson_with_pl$setXmin(xmin_pl)
est <- estimate_pars(fit_poisson_with_pl)
fit_poisson_with_pl$setPars(est)
compdist_pl_vs_po_with_pl <- compare_distributions(
fit_power_law, fit_poisson_with_pl)
if (plot_graph_compare_two_dists) {
plot(compdist_pl_vs_po_with_pl,
col=ifelse(compdist_pl_vs_po_with_pl$ratio$ratio < -sign_threshold,
cols_dist[col_distpo],
ifelse(compdist_pl_vs_po_with_pl$ratio$ratio > sign_threshold,
cols_dist[col_distpl], 'black')),
main=paste0('Vuong\'s Test: Power Law* vs. Poisson (', ds_name, ')'),
xlab=xlabel_ds_class)
}
# (Discrete) Exponential fit?
fit_exponential_with_pl <- disexp$new(feat_counts)
# Set Xmin from power-law (they should be the same in both distributions)
# est <- estimate_xmin(fit_exponential)
fit_exponential_with_pl$setXmin(xmin_pl)
est <- estimate_pars(fit_exponential_with_pl)
fit_exponential_with_pl$setPars(est)
compdist_pl_vs_ex_with_pl <- compare_distributions(
fit_power_law, fit_exponential_with_pl)
if (plot_graph_compare_two_dists) {
plot(compdist_pl_vs_ex_with_pl,
col=ifelse(compdist_pl_vs_ex_with_pl$ratio$ratio < -sign_threshold,
cols_dist[col_distex],
ifelse(compdist_pl_vs_ex_with_pl$ratio$ratio > sign_threshold,
cols_dist[col_distpl], 'black')),
main=paste0('Vuong\'s Test: Power Law* vs. Exponential (',
ds_name, ')'),
xlab=xlabel_ds_class)
}
############ Log-Normal ######################################################
# (Discrete) Log-Normal fit ? xmin is estimated
fit_log_normal_only <- dislnorm$new(feat_counts)
est <- estimate_xmin(fit_log_normal_only)
fit_log_normal_only$setXmin(est)
est <- estimate_pars(fit_log_normal_only)
fit_log_normal_only$setPars(est)
bs_log_normal <- bootstrap_p(fit_log_normal_only, xmax = 1e+06,
threads=threads, no_of_sims=simulation_counts)
# Log-Normal, bootsptrap parameters
xmin_ln <- fit_log_normal_only$xmin
ntail_ln <- get_ntail(fit_log_normal_only, prop=FALSE)
# (Discrete) Power-law fit?
fit_power_law_with_ln <- displ$new(feat_counts)
# Set Xmin from Log-Normal (they should be the same in both distributions)
# est <- estimate_xmin(fit_power_law_with_ln)
fit_power_law_with_ln$setXmin(xmin_ln)
est <- estimate_pars(fit_power_law_with_ln)
fit_power_law_with_ln$setPars(est)
# Vuong's test,
# A likelihood ratio test for model selection
# using the Kullback-Leibler criteria
compdist_pl_with_ln_vs_ln <- compare_distributions(
fit_power_law_with_ln, fit_log_normal_only)
if (plot_graph_compare_two_dists) {
plot(compdist_pl_with_ln_vs_ln,
col=ifelse(compdist_pl_with_ln_vs_ln$ratio$ratio < -sign_threshold,
cols_dist[col_distln],
ifelse(compdist_pl_with_ln_vs_ln$ratio$ratio > sign_threshold,
cols_dist[col_distpl], 'black')),
main=paste0('Vuong\'s Test: Power Law vs. Log-Normal* (',
ds_name, ')'),
xlab=xlabel_ds_class)
}
# (Discrete) Poisson fit?
fit_poisson_with_ln <- dispois$new(feat_counts)
# Set Xmin from Log-Normal (they should be the same in both distributions)
# est <- estimate_xmin(fit_poisson_with_ln)
fit_poisson_with_ln$setXmin(xmin_ln)
est <- estimate_pars(fit_poisson_with_ln)
fit_poisson_with_ln$setPars(est)
compdist_po_with_ln_vs_ln <- compare_distributions(
fit_power_law_with_ln, fit_log_normal_only)
if (plot_graph_compare_two_dists) {
plot(compdist_po_with_ln_vs_ln,
col=ifelse(compdist_po_with_ln_vs_ln$ratio$ratio < -sign_threshold,
cols_dist[col_distln],
ifelse(compdist_po_with_ln_vs_ln$ratio$ratio > sign_threshold,
cols_dist[col_distpo], 'black')),
main=paste0('Vuong\'s Test: Poisson vs. Log-Normal* (',
ds_name, ')'),
xlab=xlabel_ds_class)
}
# (Discrete) Exponential fit?
fit_exponential_with_ln <- disexp$new(feat_counts)
# Set Xmin from Log-Normal (they should be the same in both distributions)
# est <- estimate_xmin(fit_exponential_with_ln)
fit_exponential_with_ln$setXmin(xmin_ln)
est <- estimate_pars(fit_exponential_with_ln)
fit_exponential_with_ln$setPars(est)
compdist_ex_with_ln_vs_ln <- compare_distributions(
fit_exponential_with_ln, fit_log_normal_only)
if (plot_graph_compare_two_dists) {
plot(compdist_ex_with_ln_vs_ln,
col=ifelse(compdist_ex_with_ln_vs_ln$ratio$ratio < -sign_threshold,
cols_dist[col_distln],
ifelse(compdist_ex_with_ln_vs_ln$ratio$ratio > sign_threshold,
cols_dist[col_distex], 'black')),
main=paste0('Vuong\'s Test: Exponential vs. Log-Normal* (',
ds_name, ')'),
xlab=xlabel_ds_class)
}
############ Exponential #####################################################
# (Discrete) Exponential fit ? xmin is estimated
fit_exponential_only <- disexp$new(feat_counts)
est <- estimate_xmin(fit_exponential_only)
fit_exponential_only$setXmin(est)
est <- estimate_pars(fit_exponential_only)
fit_exponential_only$setPars(est)
bs_exponential <- bootstrap_p(fit_exponential_only, xmax = 1e+06,
threads=threads, no_of_sims=simulation_counts)
# Exponential, bootsptrap parameters
xmin_ex <- fit_exponential_only$xmin
ntail_ex <- get_ntail(fit_exponential_only, prop=FALSE)
# (Discrete) Power-law fit?
fit_power_law_with_ex <- displ$new(feat_counts)
# Set Xmin from Exponential (they should be the same in both distributions)
# est <- estimate_xmin(fit_power_law_with_ex)
fit_power_law_with_ex$setXmin(xmin_ex)
est <- estimate_pars(fit_power_law_with_ex)
fit_power_law_with_ex$setPars(est)
# Vuong's test,
# A likelihood ratio test for model selection
# using the Kullback-Leibler criteria
compdist_pl_with_ex_vs_ex <- compare_distributions(
fit_power_law_with_ex, fit_exponential_only)
if (plot_graph_compare_two_dists) {
plot(compdist_pl_with_ex_vs_ex,
col=ifelse(compdist_pl_with_ex_vs_ex$ratio$ratio < -sign_threshold,
cols_dist[col_distln],
ifelse(compdist_pl_with_ex_vs_ex$ratio$ratio > sign_threshold,
cols_dist[col_distpl], 'black')),
main=paste0('Vuong\'s Test: Power Law vs. Exponential* (',
ds_name, ')'),
xlab=xlabel_ds_class)
}
# (Discrete) Log-Normal fit?
fit_log_normal_with_ex <- dislnorm$new(feat_counts)
# Set Xmin from Exponential (they should be the same in both distributions)
# est <- estimate_xmin(fit_log_normal_with_ex)
fit_log_normal_with_ex$setXmin(xmin_ex)
est <- estimate_pars(fit_log_normal_with_ex)
fit_log_normal_with_ex$setPars(est)
# Vuong's test,
# A likelihood ratio test for model selection
# using the Kullback-Leibler criteria
compdist_ln_with_ex_vs_ex <- compare_distributions(
fit_log_normal_with_ex, fit_exponential_only)
if (plot_graph_compare_two_dists) {
plot(compdist_ln_with_ex_vs_ex,
col=ifelse(compdist_ln_with_ex_vs_ex$ratio$ratio < -sign_threshold,
cols_dist[col_distln],
ifelse(compdist_ln_with_ex_vs_ex$ratio$ratio > sign_threshold,
cols_dist[col_distpl], 'black')),
main=paste0('Vuong\'s Test: Log-Normal vs. Exponential* (',
ds_name, ')'),
xlab=xlabel_ds_class)
}
# (Discrete) Poisson fit?
fit_poisson_with_ex <- dispois$new(feat_counts)
# Set Xmin from Exponential (they should be the same in both distributions)
# est <- estimate_xmin(fit_poisson_with_ex)
fit_poisson_with_ex$setXmin(xmin_ex)
est <- estimate_pars(fit_poisson_with_ex)
fit_poisson_with_ex$setPars(est)
############ Dump Results ####################################################
ntail_ratio_pl <- get_ntail(fit_power_law, prop=TRUE)
ntail_ratio_ln <- get_ntail(fit_log_normal_only, prop=TRUE)
ntail_ratio_ex <- get_ntail(fit_exponential_only, prop=TRUE)
# pl* vs. ln
if (compdist_pl_vs_ln_with_pl$test_statistic < -sign_threshold)
# Almost equal to double tilda ~
closer_to_the_truth_pl_vs_ln_with_pl <- 'Log-Normal ≈ the truth'
else if (compdist_pl_vs_ln_with_pl$test_statistic > sign_threshold)
closer_to_the_truth_pl_vs_ln_with_pl <- 'no better or worse fit'
else
closer_to_the_truth_pl_vs_ln_with_pl <- 'Power Law ≈ the truth'
# pl vs. ln*
if (compdist_pl_with_ln_vs_ln$test_statistic < -sign_threshold)
# Almost equal to double tilda ~
closer_to_the_truth_pl_with_ln_vs_ln <- 'Log-Normal ≈ the truth'
else if (compdist_pl_with_ln_vs_ln$test_statistic > sign_threshold)
closer_to_the_truth_pl_with_ln_vs_ln <- 'no better or worse fit'
else
closer_to_the_truth_pl_with_ln_vs_ln <- 'Power Law ≈ the truth'
# ex vs. ln*
if (compdist_ex_with_ln_vs_ln$test_statistic < -sign_threshold)
# Almost equal to double tilda ~
closer_to_the_truth_ex_with_ln_vs_ln <- 'Log-Normal ≈ the truth'
else if (compdist_ex_with_ln_vs_ln$test_statistic > sign_threshold)
closer_to_the_truth_ex_with_ln_vs_ln <- 'no better or worse fit'
else
closer_to_the_truth_ex_with_ln_vs_ln <- 'Exponential ≈ the truth'
# pl vs. ex*
if (compdist_pl_with_ex_vs_ex$test_statistic < -sign_threshold)
# Almost equal to double tilda ~
closer_to_the_truth_pl_with_ex_vs_ex <- 'Exponential ≈ the truth'
else if (compdist_pl_vs_ln_with_pl$test_statistic > sign_threshold)
closer_to_the_truth_pl_with_ex_vs_ex <- 'no better or worse fit'
else
closer_to_the_truth_pl_with_ex_vs_ex <- 'Power Law ≈ the truth'
# ln vs. ex*
if (compdist_ln_with_ex_vs_ex$test_statistic < -sign_threshold)
# Almost equal to double tilda ~
closer_to_the_truth_ln_with_ex_vs_ex <- 'Exponential ≈ the truth'
else if (compdist_pl_with_ln_vs_ln$test_statistic > sign_threshold)
closer_to_the_truth_ln_with_ex_vs_ex <- 'no better or worse fit'
else
closer_to_the_truth_ln_with_ex_vs_ex <- 'Log-Normal ≈ the truth'
# See (Clauset, Shalizi, and Newman, 2, pp.2) for typical values
# See (Gillespie, 2015, pp.3) for moments in continous Power Law
if (fit_power_law$pars > 1 && fit_power_law$pars <= 2) {
pl_alpha_type <-
'1 < typical <= 2'
pl_alpha_moments <- 'all moments diverge 1:µ,2:σ2,3:skewness,4:kurtosis'
}
else if (fit_power_law$pars > 2 && fit_power_law$pars <= 3) {
pl_alpha_type <-
'2 < typical <= 3'
pl_alpha_moments <- '1:µ,2:σ2 converge but >2nd moments diverge 3:skewness,4:kurtosis'
}
else {
pl_alpha_type <-
'atypical > 3'
pl_alpha_moments <- '1:µ,2:σ2,3:skewness converge but >α moments diverge 4:kurtosis)'
}
print(paste(
c('Dataset', 'Class', 'Feature count min', 'Feature space size',
# Power-Law fit
'xmin (pl)', 'Parameters (pl)[alpha]', 'Alpha Type', 'Alpha Moments',
'ntail (fitted feature count) (pl)', 'ntail ratio (pl)',
# Power-Law estimation
'Bootstrap p-value (pl)', 'Bootstrap GoF (pl)',
'Bootstrap Simulation Count (pl)', 'Simulation Time (pl)[minute]',
'Package Version', 'GoF Distance Measure',
# Comparison between Power-Law and the other 3 ditributions
'Power Law* vs. Log-Normal: Test Statistics',
'pl* vs. ln: p-value (1-sided)', 'pl* vs. ln: p-value (2-sided)',
'pl* vs. ln: result',
'Power Law* vs. Poisson: Test Statistics',
'pl* vs. po: p-value (1-sided)', 'pl* vs. po: p-value (2-sided)',
'Power Law* vs. Exponential: Test Statistics',
'pl* vs. ex: p-value (1-sided)', 'pl* vs. ex: p-value (2-sided)',
# Log-Normal fit
'xmin (ln)', 'Parameters (ln)[mean]', 'Parameters (ln)[SD]',
'ntail (fitted feature count) (ln)', 'ntail ratio (ln)',
# Log-Normal estimation
'Bootstrap p-value (ln)', 'Bootstrap GoF (ln)',
'Bootstrap Simulation Count (ln)', 'Simulation Time (ln)[minute]',
# Comparison between the other 3 distributions and Log-Normal
'Power Law vs. Log-Normal*: Test Statistics',
'pl vs. ln*: p-value (1-sided)', 'pl vs. ln*: p-value (2-sided)',
'pl vs. ln*: result',
'Poisson vs. Log-Normal*: Test Statistics',
'po vs. ln*: p-value (1-sided)', 'po vs. ln*: p-value (2-sided)',
'Exponential vs. Log-Normal*: Test Statistics',
'ex vs. ln*: p-value (1-sided)', 'ex vs. ln*: p-value (2-sided)',
'ex vs. ln*: result',
# Exponential fit
'xmin (ex)', 'Parameters (ex)[lambda]',
'ntail (fitted feature count) (ex)', 'ntail ratio (ex)',
# Exponential estimation
'Bootstrap p-value (ex)', 'Bootstrap GoF (ex)',
'Bootstrap Simulation Count (ex)', 'Simulation Time (ex)[minute]',
# Comparison between Power-Law and other 2 ditributions
'Power Law vs. Exponential*: Test Statistics',
'pl vs. ex*: p-value (1-sided)', 'pl vs. ex*: p-value (2-sided)',
'pl vs. ex*: result',
'Log-normal vs. Exponential*: Test Statistics',
'ln vs. ex*: p-value (1-sided)', 'ln vs. ex*: p-value (2-sided)',
'ln vs. ex*: result',
'\n'),
collapse='\t'))
print(paste(
ds_name, ds_class_name, min(feat_counts), feature_space_size,
# pl* POWER LAW
xmin_pl, fit_power_law$pars, pl_alpha_type, pl_alpha_moments,
ntail_pl, ntail_ratio_pl,
# pl* bootstrap
bs_power_law$p, bs_power_law$gof,
simulation_counts, bs_power_law$sim_time,
bs_power_law$package_version, bs_power_law$distance,
# pl* vs. ln
compdist_pl_vs_ln_with_pl$test_statistic,
compdist_pl_vs_ln_with_pl$p_one_sided, compdist_pl_vs_ln_with_pl$p_two_sided,
closer_to_the_truth_pl_vs_ln_with_pl,
# pl* vs. po
compdist_pl_vs_po_with_pl$test_statistic,
compdist_pl_vs_po_with_pl$p_one_sided, compdist_pl_vs_po_with_pl$p_two_sided,
# pl* vs. ex
compdist_pl_vs_ex_with_pl$test_statistic,
compdist_pl_vs_ex_with_pl$p_one_sided, compdist_pl_vs_ex_with_pl$p_two_sided,
# ln* LOG-NORMAL
xmin_ln, fit_log_normal_only$pars[1], fit_log_normal_only$pars[2],
ntail_ln, ntail_ratio_ln,
# ln* bootstrap
bs_log_normal$p, bs_log_normal$gof,
simulation_counts, bs_log_normal$sim_time,
# pl vs. ln*
compdist_pl_with_ln_vs_ln$test_statistic,
compdist_pl_with_ln_vs_ln$p_one_sided, compdist_pl_with_ln_vs_ln$p_two_sided,
closer_to_the_truth_pl_with_ln_vs_ln,
# po vs. ln*
compdist_po_with_ln_vs_ln$test_statistic,
compdist_po_with_ln_vs_ln$p_one_sided, compdist_po_with_ln_vs_ln$p_two_sided,
# ex vs. ln*
compdist_ex_with_ln_vs_ln$test_statistic,
compdist_ex_with_ln_vs_ln$p_one_sided, compdist_ex_with_ln_vs_ln$p_two_sided,
closer_to_the_truth_ex_with_ln_vs_ln,
# ex* EXPONENTIAL
xmin_ex, fit_exponential_only$pars[1],
ntail_ex, ntail_ratio_ex,
# exp* bootstrap
bs_exponential$p, bs_exponential$gof,
simulation_counts, bs_exponential$sim_time,
# pl vs. ex*
compdist_pl_with_ex_vs_ex$test_statistic,
compdist_pl_with_ex_vs_ex$p_one_sided, compdist_pl_with_ex_vs_ex$p_two_sided,
closer_to_the_truth_pl_with_ex_vs_ex,
# ln vs. ex*
compdist_ln_with_ex_vs_ex$test_statistic,
compdist_ln_with_ex_vs_ex$p_one_sided, compdist_ln_with_ex_vs_ex$p_two_sided,
closer_to_the_truth_ln_with_ex_vs_ex,
'[Estimation, simulations, and comparisons are completed]\n',
sep='\t'))
# Power-Law fitted and not-fitted features dump
cat(paste('Fitted feature names (Power Law*) [>=xmin]: ',
paste(ds_feat_space_names[feat_counts >= xmin_pl][1:ntail_pl],
collapse=', '), '\n'))
print(paste(
'Not fitted feature names (Power Law*) [<xmin]: ',
paste(
ds_feat_space_names[feat_counts < xmin_pl]
[1:(feature_space_size-ntail_pl)],
collapse=', '), '\n'))
# Log-Normal fitted and not-fitted features dump
print(paste('Fitted feature names (Log-Normal*) [>=xmin]: ',
paste(ds_feat_space_names[feat_counts >= xmin_ln][1:ntail_ln],
collapse=', '), '\n'))
print(paste(
'Not fitted feature names (Log-Normal*) [<xmin]: ',
paste(
ds_feat_space_names[feat_counts < xmin_ln][1:(feature_space_size-ntail_ln)],
collapse=', '), '\n'))
# Exponential fitted and not-fitted features dump
print(paste('Fitted feature names (Exponential*) [>=xmin]: ',
paste(ds_feat_space_names[feat_counts >= xmin_ex][1:ntail_ex],
collapse=', '), '\n'))
print(paste(
'Not fitted feature names (Exponential*) [<xmin]: ',
paste(
ds_feat_space_names[feat_counts < xmin_ex][1:(feature_space_size-ntail_ex)],
collapse=', '), '\n'))
options(scipen=scipen_option)
# return from the function as below for the following error
# Error in grid.Call.graphics(C_setviewport, vp, TRUE) :
# non-finite location and/or size for viewport
# Called from: grid.Call.graphics(C_setviewport, vp, TRUE)
# return(list(bs_power_law, bs_log_normal))
# Plot pl* and other three distributions
if (plot_graph_compare_all_dist) {
plot(fit_power_law,
xlab=xlabel_ds_class,
ylab='Rank',
main=paste0(
'Power Law against other fits for feature distribution of ',
ds_name, ' (', ds_class_name, ')')
# sub = '[Power-Law Fit]')
)
lines(fit_power_law,
col=cols_dist[col_distpl], lty=1, lwd=4)
lines(fit_log_normal_with_pl,
col=cols_dist[col_distln], lty=2, lwd=2)
lines(fit_exponential_with_pl,
col=cols_dist[col_distex], lty=3, lwd=2)
lines(fit_poisson_with_pl,
col=cols_dist[col_distpo], lty=4, lwd=2)
abline(v=xmin_pl, lty=3)
mtext(paste('α:', round(fit_power_law$pars, digits=2),
paste0(' where ', pl_alpha_type,
' \n(', pl_alpha_moments, ')'),
'\nVuong\'s test statistics (pl* vs. ln):',
round(compdist_pl_vs_ln_with_pl$test_statistic, digits=3),
paste0('\n(', closer_to_the_truth_pl_vs_ln_with_pl, ')'),
'\np (1-sided):',
round(compdist_pl_vs_ln_with_pl$p_one_sided, digits=2),
'\np (2-sided):',
round(compdist_pl_vs_ln_with_pl$p_two_sided, digits=2), ' '),
adj=1, line=-6*0.75, side=3, cex=0.75)
mtext(paste0('Xmin:', xmin_pl, ', ntail ratio (X>=Xmin):',
100*round(ntail_ratio_pl, digits=2), "%"),
adj=1-ntail_ratio_pl, side=3, line=0, cex=0.75)
legend(x='bottomleft', box.lty=0, col=cols_dist, lty=1:4, lwd=2,
legend=c('Power Law*', 'Log-Normal', 'Exponential', 'Poisson'))
}
# Plot ln* and other three distributions
if (plot_graph_compare_all_dist) {
plot(fit_log_normal_only,
xlab=xlabel_ds_class,
ylab='Rank',
main=paste0(
'Log-Normal against other fits for feature distribution of ',
ds_name, ' (', ds_class_name, ')')
# sub='[Log-Normal Fit]')
)
lines(fit_power_law_with_ln,
col=cols_dist[col_distpl], lty=1, lwd=2)
lines(fit_log_normal_only,
col=cols_dist[col_distln], lty=2, lwd=4)
lines(fit_exponential_with_ln,
col=cols_dist[col_distex], lty=3, lwd=2)
lines(fit_poisson_with_ln,
col=cols_dist[col_distpo], lty=4, lwd=2)
abline(v=xmin_ln, lty=3)
mtext(paste('µ (mean):', round(fit_log_normal_only$pars[1], digits=2),
', σ (SD):', round(fit_log_normal_only$pars[2], digits=2),
'\nVuong\'s test statistics: (pl vs. ln*)',
round(compdist_pl_with_ln_vs_ln$test_statistic, digits=3),
paste0('\n(', closer_to_the_truth_pl_with_ln_vs_ln, ')'),
'\np (1-sided):',
round(compdist_pl_with_ln_vs_ln$p_one_sided, digits=2),
'\np (2-sided):',
round(compdist_pl_with_ln_vs_ln$p_two_sided, digits=2), ' '),
adj=1, line=-5*0.75, side=3, cex=0.75)
mtext(paste0('Xmin:', xmin_ln, ', ntail ratio (X>=Xmin):',
100*round(ntail_ratio_ln, digits=2), "%"),
adj=1-ntail_ratio_ln, side=3, line=0, cex=0.75)
legend(x='bottomleft', box.lty=0, col=cols_dist, lty=1:4, lwd=2,
legend=c('Power Law', 'Log-Normal*', 'Exponential', 'Poisson'))
}
# Plot ex* and other three distributions
if (plot_graph_compare_all_dist) {
plot(fit_exponential_only,
xlab=xlabel_ds_class,
ylab='Rank',
main=paste0(
'Exponential against other fits for feature distribution of ',
ds_name, ' (', ds_class_name, ')')
# sub='[Exponential Fit]')
)
lines(fit_power_law_with_ex,
col=cols_dist[col_distpl], lty=1, lwd=2)
lines(fit_log_normal_with_ex,
col=cols_dist[col_distln], lty=2, lwd=4)
lines(fit_exponential_only,
col=cols_dist[col_distex], lty=3, lwd=2)
lines(fit_poisson_with_ex,
col=cols_dist[col_distpo], lty=4, lwd=2)
abline(v=xmin_ex, lty=3)
mtext(paste('λ (rate):', round(fit_exponential_only$pars[1], digits=2),
'\nVuong\'s test statistics: (ln vs. ex*)',
round(compdist_ln_with_ex_vs_ex$test_statistic, digits=3),
paste0('\n(', closer_to_the_truth_ln_with_ex_vs_ex, ')'),
'\np (1-sided):',
round(compdist_ln_with_ex_vs_ex$p_one_sided, digits=2),
'\np (2-sided):',
round(compdist_ln_with_ex_vs_ex$p_two_sided, digits=2), ' '),
adj=1, line=-5*0.75, side=3, cex=0.75)
mtext(paste0('Xmin:', xmin_ex, ', ntail ratio (X>=Xmin):',
100*round(ntail_ratio_ex, digits=2), "%"),
adj=1-ntail_ratio_ex, side=3, line=0, cex=0.75)
legend(x='bottomleft', box.lty=0, col=cols_dist, lty=1:4, lwd=2,
legend=c('Power Law', 'Log-Normal', 'Exponential*', 'Poisson'))
}
plot(bs_power_law,
main='bootstrapping hypothesis test: Power Law distribution is plausible?')
plot(bs_log_normal,
main='bootstrapping hypothesis test: Log-Normal distribution is plausible?')
plot(bs_exponential,
main='bootstrapping hypothesis test: Exponential distribution is plausible?')
# reinstall gglot2 (install.packages('ggplot2')) for the following error
# Error in grid.Call.graphics(C_setviewport, vp, TRUE) :
# non-finite location and/or size for viewport
# Called from: grid.Call.graphics(C_setviewport, vp, TRUE)
# Comparison of likelihood ratios per feature
# Based on N. Bertchinger
# https://fias.uni-frankfurt.de/fileadmin/fias/bertschinger/CN/SolutionsWiSe1718_Ex2.pdf
if (plot_graph_likelihood_ratios) {
plotDistributionsLikelyhoodRatios(
xlabel_ds_class, compdist_pl_vs_ln_with_pl,
'Power Law*', 'Log-Normal',
cols_dist[col_distpl], cols_dist[col_distln],
closer_to_the_truth_pl_vs_ln_with_pl)
# print(compdist_pl_vs_ln_with_pl$ratio %>%
# group_by(x, ratio) %>%
# summarize(cnt = n()) %>%
# ggplot(aes(x, ratio, color=ratio < 0, size=cnt)) +
# theme_bw() +
# geom_point(alpha=0.6) +
# # scale_color_discrete(name='Test results for distributions',
# # labels=c('Power Law*', 'Log-Normal')) +
# scale_color_manual(values=c(cols_dist[col_distpl],
# cols_dist[col_distln]),
# name='Vuong\'s test on',
# labels=c('Power Law* vs.', 'Log-Normal')) +
# labs(x=xlabel_ds_class,
# y=paste0('Log-likelihood ratios.',
# ' Test statistics:',
# round(compdist_pl_vs_ln_with_pl$test_statistic, digits=3),
# '\n(', closer_to_the_truth_pl_vs_ln_with_pl, ')',
# ', p (1-sided):',
# round(compdist_pl_vs_ln_with_pl$p_one_sided, digits=2),
# ', p (2-sided):',
# round(compdist_pl_vs_ln_with_pl$p_two_sided, digits=2)),
# size='Count') +
# scale_x_log10())
}
if (plot_graph_likelihood_ratios) {
plotDistributionsLikelyhoodRatios(
xlabel_ds_class, compdist_pl_with_ln_vs_ln,
'Power Law', 'Log-Normal*',
cols_dist[col_distpl], cols_dist[col_distln],
closer_to_the_truth_pl_with_ln_vs_ln)
# print(compdist_pl_with_ln_vs_ln$ratio %>%
# group_by(x, ratio) %>%
# summarize(cnt = n()) %>%
# ggplot(aes(x, ratio, color=ratio < 0, size=cnt)) +
# theme_bw() +
# geom_point(alpha=0.6) +
# scale_color_manual(values=c(cols_dist[col_distpl],
# cols_dist[col_distln]),
# name='Vuong\'s test on',
# labels=c('Power Law vs.', 'Log-Normal*')) +
# labs(x=xlabel_ds_class,
# y=paste0('Log-likelihood ratios.',
# ' Test statistics:',
# round(compdist_pl_with_ln_vs_ln$test_statistic, digits=3),
# '\n(', closer_to_the_truth_pl_with_ln_vs_ln, ')',
# ', p (1-sided):',
# round(compdist_pl_with_ln_vs_ln$p_one_sided, digits=2),
# ', p (2-sided):',
# round(compdist_pl_with_ln_vs_ln$p_two_sided, digits=2)),
# size='Count') +
# scale_x_log10())
}
if (plot_graph_likelihood_ratios) {
plotDistributionsLikelyhoodRatios(
xlabel_ds_class, compdist_ln_with_ex_vs_ex,
'Log-Normal', 'Exponential*',
cols_dist[col_distln], cols_dist[col_distex],
closer_to_the_truth_ln_with_ex_vs_ex)
# print(compdist_ln_with_ex_vs_ex$ratio %>%
# group_by(x, ratio) %>%
# summarize(cnt = n()) %>%
# ggplot(aes(x, ratio, color=ratio < 0, size=cnt)) +
# theme_bw() +
# geom_point(alpha=0.6) +
# scale_color_manual(values=c(cols_dist[col_distln],
# cols_dist[col_distex]),
# name='Vuong\'s test on',
# labels=c('Log-Normal vs.', 'Exponential*')) +
# labs(x=xlabel_ds_class,
# y=paste0('Log-likelihood ratios.',
# ' Test statistics:',
# round(compdist_ln_with_ex_vs_ex$test_statistic,
# digits=3),
# '\n(', closer_to_the_truth_ln_with_ex_vs_ex, ')',
# ', p (1-sided):',
# round(compdist_ln_with_ex_vs_ex$p_one_sided,
# digits=2),
# ', p (2-sided):',
# round(compdist_ln_with_ex_vs_ex$p_two_sided, digits=2)),
# size='Count') +
# scale_x_log10())
}
options(scipen=scipen_option)
return(list(bs_power_law, bs_log_normal, bs_exponential))
}
#' ### plotDistributionsLikelyhoodRatios
#' Plot two compared distributions' log-likelihood ratio tests
#' **Parameters:**
#' *dataset_class*: Class identifier (e.g. 'Positive' or 'Malign')
#' *compdist_dist1_dist2*: Distribution comparison object
#' *dist1_name*: The name of the 1st distribution
#' *dist2_name*: The name of the 2nd distribution
#' *col_dist1*: The color of the 1st distribution
#' *col_dist2*: The color of the 2nd distribution
#' *which_dist_is_closer_the_truth*: Which distribution is closer the truth?
#' **Return:**
#' none
plotDistributionsLikelyhoodRatios <- function(dataset_class,
compdist_dist1_dist2,
dist1_name, dist2_name,
col_dist1, col_dist2,
which_dist_is_closer_the_truth)
{
print(compdist_dist1_dist2$ratio %>%
group_by(x, ratio) %>%
summarize(cnt = n()) %>%
ggplot(aes(x, ratio, color=ratio < 0, size=cnt)) +
theme_bw() +
geom_point(alpha=0.6) +
scale_color_manual(values=c(col_dist1, col_dist2),
name='Vuong\'s test on',
labels=c(paste0(dist1_name, ' vs.'), dist2_name)) +
labs(x=dataset_class,
y=paste0('Log-likelihood ratios.',
' Test statistics:',
round(compdist_dist1_dist2$test_statistic,
digits=3),
'\n(', which_dist_is_closer_the_truth, ')',
', p (1-sided):',
round(compdist_dist1_dist2$p_one_sided,
digits=2),
', p (2-sided):',
round(compdist_dist1_dist2$p_two_sided, digits=2)),
size='Count') +
scale_x_log10())
}
#' ### getCommonFeatures
#' Return the intersection of feature names given as a comma seperated list per dataset (i.e. Copy)
#' **Parameters:**
#' *ds_fit_unfit_features*: Performance metric
#' *split*: Seperator between column values (default: ', ')
#' **Return:**
#' common_features as character vector
#' **Examples:**
# 1) Open datasets.ods file
# 2) Select Features (Permissions) cells in dsdist (fit features) worksheet
# for the following filters
# "Malign" in Class and
# 1 in Plausibility Degree and
# "Fitted (>=xmin)" in Type and
# exclude "NA" rows
# Don't forget to include the first header row cell
# "Features (Permissions)" into your selection
# 3) Copy the selected cells
# 4) Run the following commands
# `malign_fit <- rclip()`
# `malign_fit_common <- getCommonFeatures(malign_fit)`
getCommonFeatures<-function(ds_fit_unfit_features, split=', ')
{
common_features <- character()
ds_count <- nrow(ds_fit_unfit_features)
if (ds_count == 0) {
return(common_features)
}
common_features <- strsplit(ds_fit_unfit_features[1, 1], split=split)[[1]]
for (i in 1:(ds_count-1)) {
features <- strsplit(ds_fit_unfit_features[i+1, 1], split=split)[[1]]
common_features <- intersect(common_features, features)
}
return(common_features)
}