├── R ├── application_HS_dataset.R ├── copulaPredict.R ├── demo_BayesGaussCopulaFactor.R ├── demo_CopulaFactorPC.R ├── inferCopulaFactorModel.R ├── plot_CFA_complete.R ├── plot_CFA_incomplete.R ├── plot_causal_continuous.R ├── plot_causal_mixed.R └── rmvCopulaFactorModel.R ├── README.md └── results ├── causal_discovery ├── TPR_FPR_SHD_p10_all.txt ├── TPR_FPR_SHD_p10_all_conti.txt ├── TPR_FPR_SHD_p10_half.txt ├── TPR_FPR_SHD_p4_all.txt ├── TPR_FPR_SHD_p4_all_conti.txt └── TPR_FPR_SHD_p4_half.txt └── factor_analysis ├── HS_MSE.pdf ├── HS_MSE_nonparanormal.pdf ├── MSE_R2_HS.txt ├── k4_mixed_perMissing.txt └── k4_ordinal_complete.txt /R/application_HS_dataset.R: -------------------------------------------------------------------------------- 1 | ################################################################################################## 2 | ## Goal: 1. Learn the parameters of the hypothesised factor structure from the 3 | # 'HolzingerSwineford1939' data provided in Package 'lavaan'; 4 | # 2. Compare BGCF (Bayesian Gaussian copula factor) with MLR (robust maximum likelihood) 5 | # quantitatively with this dataset. 6 | ################################################################################################### 7 | 8 | #### 0. Dependent Packages and Parameter Settings #### 9 | 10 | ## packages 11 | library(caret) 12 | library(lavaan) 13 | library(moments) 14 | source('R/inferCopulaFactorModel.R') 15 | source('R/copulaPredict.R') 16 | 17 | ## parameters 18 | # No. of latent factors 19 | pl <- 3 20 | 21 | 22 | #### 1. Load Data #### 23 | 24 | ## raw data set 25 | data(HolzingerSwineford1939) 26 | 27 | ## select the 9 variables involved 28 | HS9.raw <- dplyr::select(HolzingerSwineford1939, x1:x9) 29 | # sample size 30 | n <- nrow(HS9.raw) 31 | 32 | ## transform the data into substantially nonparanormal and scale each variable to make it comparable 33 | HS9.trans <- data.frame(apply(HS9.raw, 2, function(x) scale(qchisq(rank(x)/(n+1),df=sample(2:8, 1))))) 34 | 35 | ## please choose HS9.raw or HS9.trans 36 | #HS9 <- HS9.raw 37 | HS9 <- HS9.trans 38 | 39 | ## summary of the data set 40 | # VU: No. of unique values of a variable 41 | # p.value: the p-value of normality test 42 | summary.HS9 <- data.frame(VU = apply(HS9, 2, function(x) length(unique(x))), 43 | p.value = apply(HS9, 2, function(x) shapiro.test(x)$p.value), 44 | skewness = skewness(HS9), 45 | kurtosis = kurtosis(HS9)) 46 | # show the summary statistics 47 | summary.HS9 48 | 49 | 50 | ## model description to be used in Method 1 (MLR) 51 | HS.model <- ' visual =~ x1 + x2 + x3 52 | textual =~ x4 + x5 + x6 53 | speed =~ x7 + x8 + x9 ' 54 | 55 | ## sparsity pattern representation of factor loadinds: lambda to be used in Method 2 (BGCF) 56 | lambda <- matrix(0, 9, 3) 57 | lambda[1:3, 1] = lambda[4:6, 2] = lambda[7:9, 3] = 1 58 | 59 | 60 | #### 2. Learn Model Parameters with BGCF #### 61 | 62 | ## inference 63 | HS9.obj <- inferCopulaFactorModel(Y = HS9, Lambda = lambda, nsamp = 1000) 64 | # get Sigma (the correlation matrix over integrated vector) 65 | Sigma <- apply(HS9.obj$Sigma.psamp[,, 501:1000], c(1,2), mean) 66 | # C: correlation matrix over latent factors 67 | C <- Sigma[1:pl, 1:pl] 68 | # Lambda: matrix of factor loadings 69 | Lambda <- round(t(solve(C) %*% Sigma[1:pl, -(1:pl)]), 3) 70 | # D: residual variance 71 | D <- round(Sigma[-(1:pl), -(1:pl)] - Lambda %*% C %*% t(Lambda), 3) 72 | 73 | 74 | #### 3. Perform Prediction (as a regression problem) #### 75 | 76 | 77 | #### Method 1: MLR 78 | 79 | ## help function 80 | lavaanPredict <- function(lav.obj, ind = 9, newData){ 81 | # 82 | # args: 83 | # lav.obj: fitted model 84 | # ind: the index of outcome variable 85 | # newData: new input data 86 | # 87 | # output: 88 | # predicted values 89 | # 90 | S = fitted(lav.obj)$cov 91 | mu = fitted(lav.obj)$mean 92 | p = ncol(S) 93 | b = solve(S[(1:p)[-ind], (1:p)[-ind]], S[(1:p)[-ind],ind]) 94 | b0 = mu[ind] - sum(b * mu[(1:p)[-ind]]) 95 | as.matrix(newData) %*% matrix(b) + b0 96 | } 97 | 98 | ## help function 99 | test.ml <- function(a, HS9){ 100 | # 101 | # args: 102 | # a: the set of index of the train samples 103 | # HS9: the full data set 104 | # 105 | # output: 106 | # MSE and R-squared on the test set 107 | 108 | ## fit the model to training set 109 | model.fit = cfa(HS.model, data = HS9[a,], auto.var = T, auto.cov.lv.x = T, std.lv = T, 110 | meanstructure = TRUE) 111 | ## 112 | p = ncol(HS9) 113 | ## 114 | MSE = numeric(p) 115 | R2 = numeric(p) 116 | 117 | ## take i-th variable as outcome alternately 118 | for(i in 1:p){ 119 | # predicted values 120 | values.pre = lavaanPredict(model.fit, ind = i, HS9[-a,-i]) 121 | # true values 122 | values.true = HS9[-a,i] 123 | # MSE 124 | MSE[i] = mean((values.pre - values.true)^2) 125 | # R squared 126 | R2[i] = 1 - MSE[i]/var(values.true) 127 | } 128 | # return 129 | c(MSE, R2) 130 | } 131 | 132 | ## run MLR 133 | # take the first 200 samples as the training set while the rest as the testing set 134 | result <- test.ml(1:200, HS9 = HS9) 135 | # show result 136 | matrix(result, 9, dimnames = list(paste0('Task', 1:9), c('MSE', 'R-squared'))) 137 | 138 | 139 | #### Method 2 140 | 141 | ## help function 142 | test.cf <- function(a, HS9){ 143 | # 144 | # args: 145 | # a: the set of index of the train samples 146 | # HS9: the full data set 147 | # 148 | # output: 149 | # MSE and R-squared on the test set 150 | 151 | ## train 152 | cop.fac.obj = inferCopulaFactorModel(HS9[a,], odens = 1, Lambda = lambda, nsamp = 500, verb = F) 153 | Sigma = apply(cop.fac.obj$Sigma.psamp[,,101:500], c(1,2), mean) 154 | S = Sigma[4:12, 4:12] 155 | p = ncol(S) 156 | MSE = numeric(p) 157 | R2 = numeric(p) 158 | ## test 159 | for(i in 1:p){ 160 | Y = HS9 161 | Y[-a,i] = NA 162 | pre.obj = copulaPredict(S, Y, nsamp = 500, verb = F, odens = 1) 163 | values.pre = apply(pre.obj$Y.impute[-a, i, 101:500], 1, mean)# 164 | # true values 165 | values.true = HS9[-a,i] 166 | # MSE 167 | MSE[i] = mean((values.pre - values.true)^2) 168 | # R squared 169 | R2[i] = 1 - MSE[i]/var(values.true) 170 | } 171 | # return 172 | c(MSE, R2) 173 | } 174 | 175 | ## run BGCF 176 | # take the first 200 samples as the training set while the rest as the testing set 177 | result <- test.cf(1:200, HS9 = HS9) 178 | # show result 179 | matrix(result, 9, dimnames = list(paste0('Task', 1:9), c('MSE', 'R-squared'))) 180 | 181 | 182 | #### 4. Perform Prediction with Cross-validation #### 183 | 184 | 185 | seed <- 12345 186 | set.seed(seed) 187 | 188 | ## No. of times for k-fold cross-validation 189 | iters = 10 190 | 191 | ## matrix to store results 192 | # dimension: 100 * 18 193 | # columns 1:9, MSE estimates for the 9 tasks 194 | # columns 10:18, R-squared estimates for the 9 tasks 195 | # rows 100 = 10*10, 10 times 10-fold cross-validation 196 | results.ml <- NULL 197 | results.cf <- NULL 198 | 199 | #### perform multiple (iters) k-fold cross-validation 200 | for(i in 1:iters){ 201 | 202 | ## create folds 203 | cv_splits <- createFolds(1:nrow(HS9), k = 10, returnTrain = TRUE) 204 | 205 | ## perform cross validation 206 | # for method 1 207 | cv.ml <- lapply(cv_splits, test.ml, HS9 = HS9) 208 | # for method 2 209 | #cv.cf <- lapply(cv_splits, test.cf, HS9 = HS9) 210 | 211 | ## collect estimates 212 | for(j in 1:length(cv.ml)) results.ml=rbind(results.ml,cv.ml[[j]]) 213 | #for(j in 1:length(cv.cf)) results.cf=rbind(results.cf,cv.cf[[j]]) 214 | 215 | # 216 | print(c('iters:', i)) 217 | } 218 | 219 | #### Show the results 220 | ## the mean over 100 experiments for MLR 221 | matrix(apply(results.ml, 2, mean), 9, dimnames = list(paste0('Task', 1:9), c('MSE', 'R-squared'))) 222 | ## the mean over 100 experiments for BGCF 223 | matrix(apply(results.cf, 2, mean), 9, dimnames = list(paste0('Task', 1:9), c('MSE', 'R-squared'))) 224 | ## 225 | results <- cbind(results.ml, results.cf) 226 | 227 | #### 5. Visualize the Results (Cross-validation) #### 228 | 229 | #### read saved results 230 | # results = read.table(file = 'results/factor_analysis/MSE_R2_HS.txt') 231 | # 1:9, MSE.ml over the 9 variables 232 | # 10:18, R2.ml 233 | # 19:27, MSE.cf 234 | # 28:36, R2.cf 235 | 236 | #### show results in number 237 | ## the mean over 100 experiments (10 * 10) for each variables 238 | mean.each = rbind(MSE.ml = apply(results[, 1:9], 2, mean), MSE.cf = apply(results[, 19:27], 2, mean), 239 | R2.ml = apply(results[, 10:18], 2, mean), R2.cf = apply(results[, 28:36], 2, mean)) 240 | mean.each 241 | ## the standard error of each mean estimate above 242 | mean.se = rbind(MSE.ml = apply(results[, 1:9], 2, sd), MSE.cf = apply(results[, 19:27], 2, sd), 243 | R2.ml = apply(results[, 10:18], 2, sd), R2.cf = apply(results[, 28:36], 2, sd))/sqrt(nrow(results)) 244 | mean.se 245 | ## the mean over all experiments over all variables 246 | apply(mean.each, 1, mean) 247 | 248 | #### plot the results 249 | ## statistical results 250 | stat.results = data.frame(outcome = rep(paste0('Y', 1:9), 2), methods = c(rep('MLR', 9), rep('BGCF', 9)), MSE = c(mean.each[1,], mean.each[2,]), 251 | MSE.se = c(mean.se[1,], mean.se[2,]), R2 = c(mean.each[3,], mean.each[4,]), R2.se = c(mean.se[3,], mean.se[4,])) 252 | ## for plot 253 | pd <- position_dodge(0.9) 254 | ## MSE 255 | MSE.fig = ggplot(stat.results, aes(x = outcome, y = MSE, group = methods, fill = methods)) + coord_cartesian(ylim = c(0.3, 1)) + 256 | geom_bar(stat = 'identity', position = pd) + 257 | geom_point(aes(shape=methods), position=pd) + 258 | xlab('outcome variable') + 259 | geom_errorbar(aes(ymin=MSE-MSE.se, ymax=MSE+MSE.se), width=.2, position=pd) + 260 | theme_bw() + 261 | theme(legend.justification=c(0.99,0.99),legend.position=c(0.99,0.99),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 262 | theme(text = element_text(size=10)) 263 | ## MSE 264 | R2.fig = ggplot(stat.results, aes(x = outcome, y = R2, group = methods, fill = methods)) + #coord_cartesian(ylim = c(0.4, 1.3)) + 265 | geom_bar(stat = 'identity', position = pd) + 266 | geom_point(aes(shape=methods), position=pd) + 267 | ylab('R-squared') + xlab('outcome variable') + 268 | geom_errorbar(aes(ymin=R2-R2.se, ymax=R2+R2.se), width=.2, position=pd) + 269 | theme_bw() + 270 | theme(legend.justification=c(0.99,0.99),legend.position=c(0.99,0.99),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 271 | theme(text = element_text(size=10)) 272 | 273 | #### show figures 274 | ## MSE 275 | MSE.fig 276 | ## R2 277 | R2.fig 278 | 279 | #### save plots into files 280 | ## MSE 281 | pdf(file = 'results/factor_analysis/HS_MSE_nonparanormal.pdf', width = 5, height = 2) 282 | MSE.fig 283 | dev.off() 284 | ## R2 285 | pdf(file = 'results/factor_analysis/HS_R2.pdf', width = 5, height = 2) 286 | R2.fig 287 | dev.off() 288 | -------------------------------------------------------------------------------- /R/copulaPredict.R: -------------------------------------------------------------------------------- 1 | copulaPredict <- function (S, Y, S0 = diag(dim(Y)[2]), n0 = dim(Y)[2] + 2, nsamp = 100, 2 | odens = max(1, round(nsamp/1000)), impute = any(is.na(Y)), 3 | plugin.threshold = 20, plugin.marginal = (apply(Y, 2, function(x) { 4 | length(unique(x)) 5 | }) > plugin.threshold), verb = TRUE) 6 | { 7 | # 8 | # This is a function used to make predictions based on Gaussian copula model 9 | # 10 | # args: 11 | # S: the correlation matrix learned on training set 12 | # Y: training set (both predictors and output) + testing set (only predictors) 13 | # 14 | # return: 15 | # predicted values 16 | # 17 | 18 | ok_S0 <- all(eigen(S0)$val > 0) & dim(S0)[1] == dim(Y)[2] & 19 | dim(S0)[2] == dim(Y)[2] 20 | ok_n0 <- (n0 >= 0) 21 | if (!ok_S0) { 22 | cat("Error: S0 must be a positive definite p x p matrix \n") 23 | } 24 | if (!ok_n0) { 25 | cat("Error: n0 must be positive \n") 26 | } 27 | if (ok_S0 & ok_n0) { 28 | vnames <- colnames(Y) 29 | Y <- as.matrix(Y) 30 | colnames(Y) <- vnames 31 | n <- dim(Y)[1] 32 | p <- dim(Y)[2] 33 | R <- NULL 34 | for (j in 1:p) { 35 | R <- cbind(R, match(Y[, j], sort(unique(Y[, j])))) 36 | } 37 | Rlevels <- apply(R, 2, max, na.rm = TRUE) 38 | Ranks <- apply(Y, 2, rank, ties.method = "average", na.last = "keep") 39 | N <- apply(!is.na(Ranks), 2, sum) 40 | U <- t(t(Ranks)/(N + 1)) 41 | Z <- qnorm(U) 42 | Zfill <- matrix(rnorm(n * p), n, p) 43 | Z[is.na(Y)] <- Zfill[is.na(Y)] 44 | #S <- cov(Z) 45 | Y.pmean <- Y 46 | if (impute) { 47 | Y.pmean <- matrix(0, nrow = n, ncol = p) 48 | } 49 | LPC <- NULL 50 | C.psamp <- array(dim = c(p, p, floor(nsamp/odens))) 51 | Y.imp <- NULL 52 | if (impute) { 53 | Y.imp <- array(dim = c(n, p, floor(nsamp/odens))) 54 | } 55 | dimnames(C.psamp) <- list(colnames(Y), colnames(Y), 56 | 1:floor(nsamp/odens)) 57 | for (ns in 1:nsamp) { 58 | for (j in sample(1:p)) { 59 | Sjc <- S[j, -j] %*% solve(S[-j, -j]) 60 | sdj <- sqrt(S[j, j] - S[j, -j] %*% solve(S[-j, 61 | -j]) %*% S[-j, j]) 62 | muj <- Z[, -j] %*% t(Sjc) 63 | if (!plugin.marginal[j]) { 64 | for (r in 1:Rlevels[j]) { 65 | ir <- (1:n)[R[, j] == r & !is.na(R[, j])] 66 | lb <- suppressWarnings(max(Z[R[, j] == r - 67 | 1, j], na.rm = TRUE)) 68 | ub <- suppressWarnings(min(Z[R[, j] == r + 69 | 1, j], na.rm = TRUE)) 70 | Z[ir, j] <- qnorm(runif(length(ir), pnorm(lb, 71 | muj[ir], sdj), pnorm(ub, muj[ir], sdj)), 72 | muj[ir], sdj) 73 | } 74 | } 75 | ir <- (1:n)[is.na(R[, j])] 76 | Z[ir, j] <- rnorm(length(ir), muj[ir], sdj) #muj[ir]# 77 | } 78 | # relocate the mean to zero 79 | # added by Ruifei Cui 80 | Z = t( (t(Z)-apply(Z,2,mean))) 81 | # S <- solve(rwish(solve(S0 * n0 + t(Z) %*% Z), n0 + 82 | # n)) 83 | if (ns%%odens == 0) { 84 | C <- S/(sqrt(diag(S)) %*% t(sqrt(diag(S)))) 85 | lpc <- ldmvnorm(scale(Z), 86 | C) 87 | LPC <- c(LPC, lpc) 88 | C.psamp[, , ns/odens] <- cor(Z)#C 89 | if (impute) { 90 | Y.imp.s <- Y 91 | for (j in 1:p) { 92 | Y.imp.s[is.na(Y[, j]), j] <- quantile(Y[, 93 | j], pnorm(Z[is.na(Y[, j]), j], 0, sd(Z[,j])), na.rm = TRUE, type = 1) 94 | } 95 | Y.imp[, , ns/odens] <- Y.imp.s 96 | Y.pmean <- ((ns/odens - 1)/(ns/odens)) * Y.pmean + 97 | (1/(ns/odens)) * Y.imp.s 98 | } 99 | } 100 | if (verb == TRUE & (ns%%(odens * 10)) == 0) { 101 | cat(round(100 * ns/nsamp), "percent done ", 102 | date(), "\n") 103 | } 104 | } 105 | G.ps <- list(C.psamp = C.psamp, Y.pmean = Y.pmean, Y.impute = Y.imp, 106 | LPC = LPC) 107 | class(G.ps) <- "psgc" 108 | return(G.ps) 109 | } 110 | } 111 | -------------------------------------------------------------------------------- /R/demo_BayesGaussCopulaFactor.R: -------------------------------------------------------------------------------- 1 | ########################################################################################################################### 2 | # Goal: This is a demo to show how our BGCF approach works. 3 | # Author: Ruifei Cui 4 | ########################################################################################################################### 5 | 6 | 7 | #### 0. Dependencies and Basic Setting #### 8 | 9 | ## dependent functions and packages 10 | source('R/rmvCopulaFactorModel.R') 11 | source('R/inferCopulaFactorModel.R') 12 | library(infotheo) 13 | library(mvtnorm) 14 | library(BDgraph) 15 | library(sbgcop) 16 | 17 | ## parameters 18 | # sample size 19 | n <- 1000 20 | # No. of latent factors 21 | pl <- 4 22 | 23 | 24 | #### 1. Generate Data #### 25 | 26 | ## interfactor correlations (correlation matrix over factors) 27 | set.seed(12345) 28 | R <- matrix(runif(pl^2, 0.2, 0.4), ncol=pl) 29 | R <- (R * lower.tri(R)) + t(R * lower.tri(R)) 30 | diag(R) <- 1 31 | C0 <- R 32 | ## simulate data 33 | data.obj <- rmvCopulaFactorModel(n, sigma = C0, range.indicators = 4, lambda.min = 0.7, lambda.max = 0.7, sd.residual = sqrt(0.51)) 34 | ## factorloading matrix 35 | Lambda0 <- data.obj$Lambda 36 | ## data of response random vector 37 | Z <- data.obj$data 38 | ## data of observed random vector (here all are binary; one could do whatever he or she wants.) 39 | Y <- discretize(Z, nbins = 2) 40 | 41 | 42 | ### 2. Run BGCF Approach #### 43 | 44 | # burn-in 45 | b.in <- 100 46 | # No. of samples 47 | n.samp <- 500 48 | ## inference 49 | cop.fac.obj <- inferCopulaFactorModel(Y, Lambda0, nsamp = n.samp, rand.start = F, odens = 1, verb = T) 50 | # 51 | Sigma.samp <- cop.fac.obj$Sigma.psamp[,,-(1:b.in)] 52 | # get Sigma (the correlation matrix over integrated vector) 53 | Sigma <- apply(Sigma.samp, c(1,2), mean) 54 | # C: correlation matrix over latent factors 55 | C <- Sigma[1:pl, 1:pl] 56 | # Lambda: matrix of factor loadings 57 | Lambda <- round(t(solve(C) %*% Sigma[1:pl, -(1:pl)]), 3) 58 | # D: residual variance 59 | D <- round(Sigma[-(1:pl), -(1:pl)] - Lambda %*% C %*% t(Lambda), 3) 60 | 61 | 62 | #### 3. Convergence Diagnostic #### 63 | 64 | ## Autocorrelation 65 | # for 66 | acf(Sigma.samp[5,3,], plot = T) 67 | 68 | ## Potential Scale Reduction Factor 69 | 70 | 71 | -------------------------------------------------------------------------------- /R/demo_CopulaFactorPC.R: -------------------------------------------------------------------------------- 1 | ###################################################################################### 2 | # This is a demo to show how the Copula Factor PC algorithm works. 3 | # Author: Ruifei Cui 4 | ###################################################################################### 5 | 6 | 7 | #### 0. Dependencies and Parameters #### 8 | 9 | ## dependent packages 10 | library(pcalg) 11 | library(infotheo) 12 | library(BDgraph) 13 | library(sbgcop) 14 | source('R/rmvCopulaFactorModel.R') 15 | source('R/inferCopulaFactorModel.R') 16 | 17 | ## parameters 18 | # No. of factors 19 | pl <- 6 20 | # sample size 21 | n <- 1000 22 | 23 | 24 | #### 1. Simulate Data #### 25 | 26 | ## simulate a DAG 27 | # a random DAG, serving as the true DAG in latent space 28 | g <- randomDAG(pl,2/(pl-1),lB = 0.1,uB=1) 29 | # true CPDAG 30 | g.cpdag <- dag2cpdag(g) 31 | ## generate data 32 | data.obs <- rmvCopulaFactorModel(n, g = g, range.indicators = 4) 33 | # mapping from latents to response variables 34 | Lambda <- (data.obs$Lambda != 0) *1 35 | # data in response space (fully Gaussian) 36 | Z <- data.obs$data 37 | # data in observed space (mixed continuous and ordinal) 38 | p <- ncol(Z) 39 | Y <- Z 40 | for (i in sample(1:p, round(p/2))) { 41 | Y[,i] = matrix(unlist(discretize(Z[,i], nbins = sample(2:5,1))), byrow=FALSE, nrow=n ) 42 | } 43 | 44 | 45 | #### 2. Inference #### 46 | 47 | ## inference 48 | cop.fac.obj <- inferCopulaFactorModel(Y, Lambda = Lambda, nsamp = 1000) 49 | # extract samples of the correlation matrix over latent variables, ignoring the first 500 samples (burn-in) 50 | C.samples <- cop.fac.obj$Sigma.psamp[1:pl, 1:pl, 501:1000] 51 | # the posterior mean 52 | C <- apply(C.samples, c(1,2), mean) 53 | # standard deviations 54 | C.sd <- apply(C.samples, c(1,2), sd) 55 | # effective sample size 56 | C.ess <- ((1-C^2)/C.sd)^2 57 | 58 | #### 3. Causal discovery #### 59 | 60 | ## call the order independent version of the standard PC algorithm 61 | graph.cfpc <- pc(suffStat = list(C = C, n = mean(C.ess[upper.tri(C.ess)])), indepTest = gaussCItest, 62 | alpha = 0.05, p = pl, skel.method = "stable", maj.rule = T, solve.confl = T) 63 | 64 | ## show results 65 | par(mfrow = c(1,2)) 66 | plot(g.cpdag, main = 'True Graph') 67 | plot(graph.cfpc, main = 'Copula Factor PC') 68 | -------------------------------------------------------------------------------- /R/inferCopulaFactorModel.R: -------------------------------------------------------------------------------- 1 | inferCopulaFactorModel <- function (Y, Lambda = diag(ncol(Y)), trueSigma = NULL, nsamp = 100, rand.start = F, 2 | odens = max(1, round(nsamp/1000)), impute = any(is.na(Y)), 3 | plugin.threshold = 20, plugin.marginal = (apply(Y, 2, function(x) { 4 | length(unique(x)) 5 | }) > plugin.threshold), verb = TRUE) 6 | { 7 | # 8 | # This is the main function to perform inference for Gaussian copula factor models. 9 | # 10 | # Args: 11 | # Y, a n by p data matrix 12 | # Lambda, a p by k matrix representing the mapping from factors to observed variables 13 | # nsamp, No. of samples 14 | # For details about the arguements, refer to function 'sbgcop.mcmc' in R package 'sbgcop' 15 | # 16 | # Return: a list that contains samples of the correlation matrix over all variables (factors + observed variables) 17 | # 18 | 19 | require(BDgraph) 20 | library(mvtnorm) 21 | library(sbgcop) 22 | Y <- as.matrix(Y) 23 | vnames <- colnames(Y) 24 | colnames(Y) <- vnames 25 | # sample size 26 | n <- dim(Y)[1] 27 | # No. of observed variables 28 | p <- dim(Y)[2] 29 | 30 | #### handle Lambda and get prior graph G 31 | Lambda = 1 * (Lambda!=0) 32 | # No. of factors 33 | k = ncol(Lambda) 34 | # index of factors with a single indicator 35 | index.1 = which(colSums(Lambda) == 1) 36 | # No. of factors with a single indicator 37 | k1 = length(index.1) 38 | # index of factors with multiple indicators 39 | index.2 = which(colSums(Lambda) > 1) 40 | # No. of factors with multiple indicators 41 | k2 = length(index.2) 42 | ## get the pior graph G 43 | G1 = matrix(1,k,k)-diag(k) 44 | if (k1 == 0) G2 = t(Lambda) else G2 = t(Lambda[-index.1,]) 45 | G3 = matrix(0,p-k1,p-k1) 46 | G = rbind(cbind(G1,G2),cbind(t(G2),G3)) 47 | G[lower.tri(G)] = 0 48 | ## prior parameters for the G-Wishart distribution 49 | # degrees of freedom 50 | n0 = p+k2+1 51 | # scale matrix 52 | S0 = diag(p+k2)/n0 53 | 54 | #### initialize Z, eta, and S 55 | R <- NULL 56 | for (j in 1:p) { 57 | R <- cbind(R, match(Y[, j], sort(unique(Y[, j])))) 58 | } 59 | Rlevels <- apply(R, 2, max, na.rm = TRUE) 60 | Ranks <- apply(Y, 2, rank, ties.method = "average", na.last = "keep") 61 | N <- apply(!is.na(Ranks), 2, sum) 62 | U <- t(t(Ranks)/(N + 1)) 63 | Z <- qnorm(U) 64 | # # handle categorical variable 65 | # Z[, ind.cat] = Y[, ind.cat] 66 | # 67 | Zfill <- matrix(rnorm(n * p), n, p) 68 | Z[is.na(Y)] <- Zfill[is.na(Y)] 69 | # psuedo data of factors with a single indicator 70 | Z1 = eta1 = Z[, index.1] 71 | # psuedo data of response variables 72 | if (k1 == 0) Z2 = Z else Z2 = Z[, -index.1] 73 | # psuedo data of factors with multiple indicators 74 | eta2 = matrix(rnorm(n*k2), n) 75 | eta = cbind(eta1, eta2) 76 | X = cbind(eta, Z2) 77 | # initialize S 78 | if (rand.start){ 79 | S <- solve(rwish(S0*n0, n0 + 1)) 80 | }else{ 81 | S <- cov(X) + S0 82 | } 83 | 84 | #### 85 | Y.pmean <- Y 86 | Z.pmean <- Z2 87 | if (impute) { 88 | Y.pmean <- matrix(0, nrow = n, ncol = p) 89 | } 90 | LPC <- NULL 91 | C.psamp <- array(dim = c(p+k2, p+k2, floor(nsamp/odens))) 92 | Y.imp <- NULL 93 | Z.imp <- array(dim = c(n, p, floor(nsamp/odens))) 94 | if (impute) { 95 | Y.imp <- array(dim = c(n, p, floor(nsamp/odens))) 96 | } 97 | #dimnames(C.psamp) <- list(colnames(Y), colnames(Y), 1:floor(nsamp/odens)) 98 | 99 | #### start of Gibbs sampling scheme 100 | for (ns in 1:nsamp) { 101 | 102 | ## sample Z1 (=eta1) 103 | for (j in index.1) { 104 | # if (!(j %in% ind.cat)){ 105 | ind.tmp = (1:k)[-j] 106 | Sjc <- S[j, ind.tmp] %*% solve(S[ind.tmp, ind.tmp]) 107 | sdj <- sqrt(S[j, j] - Sjc %*% S[ind.tmp, j]) 108 | muj <- X[, ind.tmp] %*% t(Sjc) 109 | if (!plugin.marginal[j]) { 110 | for (r in 1:Rlevels[j]) { 111 | ir <- (1:n)[R[, j] == r & !is.na(R[, j])] 112 | lb <- suppressWarnings(max(X[R[, j] == r - 1, j], na.rm = TRUE)) 113 | ub <- suppressWarnings(min(X[R[, j] == r + 1, j], na.rm = TRUE)) 114 | X[ir, j] <- qnorm(runif(length(ir), pnorm(lb, muj[ir], sdj), pnorm(ub, muj[ir], sdj)), muj[ir], sdj) 115 | } 116 | } 117 | ir <- (1:n)[is.na(R[, j])] 118 | X[ir, j] <- rnorm(length(ir), muj[ir], sdj) 119 | # }else{ 120 | # ir <- (1:n)[is.na(R[, j])] 121 | # X[ir, j] = rnorm(length(ir)) 122 | # } 123 | } 124 | Z1 = eta1 = X[,index.1] 125 | 126 | ## sample Z2 127 | if (k1 == 0) index.tmp = sample(1:p) else index.tmp = sample((1:p)[-index.1]) 128 | if (k2 > 0 ){ 129 | for(j in index.tmp) { 130 | q <- which(Lambda[j,]!=0) 131 | a = S[k2+j, q] / S[q, q] 132 | sdj <- sqrt( S[k2+j,k2+j] - a * S[q,k2+j] ) 133 | muj <- X[,q] * a 134 | if (!plugin.marginal[j]) { 135 | for(r in sort(unique(R[,j]))){ 136 | ir<- (1:n)[R[,j]==r & !is.na(R[, j])] 137 | lb<-suppressWarnings(max( X[ R[,j]r,j+k2],na.rm=T)) 139 | X[ir,j+k2]<-qnorm(runif(length(ir), 140 | pnorm(lb,muj[ir],sdj),pnorm(ub,muj[ir],sdj)),muj[ir],sdj) 141 | } 142 | } 143 | ir <- (1:n)[is.na(R[, j])] 144 | X[ir, j+k2] <- rnorm(length(ir), muj[ir], sdj) 145 | } 146 | Z2 = X[, (k+1):(k2+p)] 147 | 148 | # 149 | Z = cbind(Z1, Z2) 150 | 151 | ## sample eta2 152 | ind.tmp = (1:(p+k2))[-index.2] 153 | A <- S[index.2,ind.tmp] %*% solve(S[ind.tmp,ind.tmp]) 154 | sdj <- S[index.2,index.2] - A %*% S[ind.tmp,index.2] 155 | muj <- X[,ind.tmp] %*% t(A) 156 | X[,index.2] = muj + rmvnorm(n, sigma =sdj) 157 | eta2 = X[,index.2] 158 | 159 | eta = cbind(eta1, eta2) 160 | 161 | ## identification condition: force the first non-zero element 162 | # of each column of Lambda to be positive 163 | for (j in index.2) { 164 | X[,j] = X[,j] * sign(cov(X[,j], X[,k2+which(Lambda[,j] != 0)[1]])) 165 | } 166 | } 167 | 168 | ## relocate the mean to zero 169 | X = t( (t(X)-apply(X,2,mean))) 170 | 171 | ## sample S 172 | P <- rgwish(n = 1, adj.g = G, b = n+n0, D = S0*n0+crossprod(X))[,,1] 173 | S <- solve(P) 174 | S = cov2cor(S) 175 | 176 | if (ns%%odens == 0) { 177 | C <- S#/(sqrt(diag(S)) %*% t(sqrt(diag(S)))) 178 | if (is.null(trueSigma)) 179 | lpc <- ldmvnorm(scale(X), C) 180 | else 181 | lpc <- ldmvnorm(scale(X), trueSigma) 182 | LPC <- c(LPC, lpc) 183 | C.psamp[, , ns/odens] <- C #cor(X)# 184 | if (impute) { 185 | Y.imp.s <- Y 186 | for (j in 1:p) { 187 | Y.imp.s[is.na(Y[, j]), j] <- quantile(Y[,j], 188 | pnorm(Z[is.na(Y[, j]), j], 0, sd(Z[,j])), 189 | na.rm = TRUE, type = 1) 190 | } 191 | Y.imp[, , ns/odens] <- Y.imp.s 192 | Y.pmean <- ((ns/odens - 1)/(ns/odens)) * Y.pmean + (1/(ns/odens)) * Y.imp.s 193 | } 194 | Z.imp[,,ns/odens] = cbind(Z1, Z2) 195 | } 196 | if (verb == TRUE & (ns%%(odens * 10)) == 0) { 197 | cat(round(100 * ns/nsamp), "percent done ", 198 | date(), "\n") 199 | } 200 | } 201 | # 202 | Z.pmean = apply(Z.imp, c(1,2), mean) 203 | 204 | # # 205 | #G.ps <- list(Sigma.psamp = C.psamp, Y.pmean = Y.pmean, Y.impute = Y.imp, Z.pmean = Z.pmean, Z.impute = Z.imp, LPC = LPC) 206 | G.ps <- list(Sigma.psamp = C.psamp) 207 | class(G.ps) <- "psgc" 208 | return(G.ps) 209 | } 210 | -------------------------------------------------------------------------------- /R/plot_CFA_complete.R: -------------------------------------------------------------------------------- 1 | ######################################################################################################## 2 | # Goal: Compare the Bayesian Gaussian copula factor (BGCF) approach, with the diagonally 3 | # weighted least squares (DWLS), and the robust maximum likelihood (MLR) on complete 4 | # ordinal data (4 categories) for learning parameters of CFA models. 5 | # 6 | # Metrics: 1) ARB; 2) ARMSE. 7 | # 8 | # Settings: 1) a correlated 4-factor model with specific parameters where each factor has 4 indicators 9 | # 2) mixed Gaussian and ordinal (4 levels) indicators 10 | # 3) n = {100, 200, 500, 1000} 11 | # 12 | ######################################################################################################## 13 | 14 | #### 0. Load Packages #### 15 | 16 | ## 17 | library(psych) 18 | library(dplyr) 19 | library(ggplot2) 20 | library(gridExtra) 21 | 22 | ## help function 23 | data2stat <- function(data){ 24 | 25 | describe(data) %>% 26 | mutate(ci = qt(0.975,n-1) * se) %>% 27 | mutate(Methods = c(rep('MLR',4), rep('DWLS',4), rep('BGCF',4))) %>% 28 | mutate(Sample.size = as.factor(rep(c(100, 200, 500, 1000), 3))) %>% 29 | dplyr::select(Methods, Sample.size, mean, ci) 30 | } 31 | 32 | 33 | #### 1. Read Data #### 34 | 35 | ## raw data 36 | results = read.table(file = "results/factor_analysis/k4_ordinal_complete.txt") 37 | 38 | #### 2. Plot Figure in PDF #### 39 | pd <- position_dodge(0.9) # move them to the left and right 40 | par(mfrow = c(2,2)) 41 | par(mar=c(3.5,4,2,1.5)) 42 | 43 | #### Figure 1: for interfactor correlations 44 | 45 | ## plot 1: ARB 46 | stat = data2stat(results[,13:24]) 47 | 48 | ARB.corr = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + coord_cartesian(ylim = c(-0.15, 0.15)) + 49 | geom_line() + 50 | geom_point(aes(shape=Methods)) + 51 | geom_hline(yintercept = 0) + 52 | geom_hline(yintercept = 0.05, linetype = "dashed") + 53 | geom_hline(yintercept = -0.05, linetype = "dashed") + 54 | geom_hline(yintercept = 0.1, linetype = "dotted") + 55 | geom_hline(yintercept = -0.1, linetype = "dotted") + 56 | xlab('sample size') + ylab('ARB') + 57 | #geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 58 | theme_bw() + 59 | theme(legend.justification=c(0.99,0.99),legend.position=c(0.99,0.99),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 60 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 61 | 62 | ## plot 2: RMSE 63 | stat = data2stat(results[,25:36]) 64 | 65 | RMSE.corr = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, fill = Methods)) + 66 | geom_bar(position=pd, stat="identity") + 67 | geom_point(aes(shape=Methods), position=pd) + 68 | xlab('sample size') + ylab('RMSE') + 69 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 70 | theme_bw() + 71 | theme(legend.justification=c(0.01,0.01),legend.position=c(0.01,0.01),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 72 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 73 | 74 | ## show Figure 75 | grid.arrange(ARB.corr, RMSE.corr, nrow = 1, ncol = 2) 76 | # ## save Figure 77 | # pdf(file = 'results/factor_analysis/k4_complete_corr.pdf', width = 4.5, height = 1.9) 78 | # grid.arrange(ARB.corr, RMSE.corr, nrow = 1, ncol = 2) 79 | # dev.off() 80 | 81 | 82 | #### Figure 2: for factor loadings 83 | 84 | ## plot 1: ARB 85 | stat = data2stat(results[,37:48]) 86 | 87 | ARB.corr = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + coord_cartesian(ylim = c(-0.15, 0.15)) + 88 | geom_line() + 89 | geom_point(aes(shape=Methods)) + 90 | geom_hline(yintercept = 0) + 91 | geom_hline(yintercept = 0.05, linetype = "dashed") + 92 | geom_hline(yintercept = -0.05, linetype = "dashed") + 93 | geom_hline(yintercept = 0.1, linetype = "dotted") + 94 | geom_hline(yintercept = -0.1, linetype = "dotted") + 95 | xlab('sample size') + ylab('ARB') + 96 | #geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 97 | theme_bw() + 98 | theme(legend.justification=c(0.99,0.99),legend.position=c(0.99,0.99),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 99 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 100 | 101 | ## plot 2: RMSE 102 | stat = data2stat(results[,49:60]) 103 | 104 | RMSE.corr = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, fill = Methods)) + 105 | geom_bar(position=pd, stat="identity") + 106 | geom_point(aes(shape=Methods), position=pd) + 107 | xlab('sample size') + ylab('RMSE') + 108 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 109 | theme_bw() + 110 | theme(legend.justification=c(0.01,0.01),legend.position=c(0.01,0.01),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 111 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 112 | 113 | ## show Figure 114 | grid.arrange(ARB.corr, RMSE.corr, nrow = 1, ncol = 2) 115 | # ## save Figure 116 | # pdf(file = 'results/factor_analysis/k4_complete_loadings.pdf', width = 4.5, height = 1.9) 117 | # grid.arrange(ARB.corr, RMSE.corr, nrow = 1, ncol = 2) 118 | # dev.off() 119 | -------------------------------------------------------------------------------- /R/plot_CFA_incomplete.R: -------------------------------------------------------------------------------- 1 | ######################################################################################################## 2 | # Goal: Compare the Bayesian Gaussian copula factor (BGCF) approach, with the diagonally 3 | # weighted least squares (DWLS), and the full information maximum likelihood (FIML) on mixed 4 | # incomplete for learning parameters of CFA models. 5 | # 6 | # Metrics: 1) ARB; 2) ARMSE. 7 | # 8 | # Settings: 1) a correlated 4-factor model with specific parameters where each factor has 4 indicators 9 | # 2) mixed nonparanormal (df = 8) and ordinal (4 levels) indicators 10 | # 3) n = 500 11 | # 4) percent of missing values = {0, 0.1, 0.2, 0.3} 12 | ######################################################################################################## 13 | 14 | #### 0. Load Packages #### 15 | 16 | ## 17 | library(psych) 18 | library(dplyr) 19 | library(ggplot2) 20 | library(gridExtra) 21 | 22 | ## help function 23 | data2stat <- function(data){ 24 | 25 | describe(data) %>% 26 | mutate(ci = qt(0.975,n-1) * se) %>% 27 | mutate(Methods = c(rep('FIML',4), rep('DWLS',4), rep('BGCF',4))) %>% 28 | mutate(Sample.size = as.factor(rep(c(0, 0.1, 0.2, 0.3) * 100, 3))) %>% 29 | select(Methods, Sample.size, mean, ci) 30 | } 31 | 32 | 33 | 34 | #### 1. Read Data #### 35 | 36 | ## raw data 37 | results = read.table(file = "results/factor_analysis/k4_mixed_perMissing.txt") 38 | 39 | 40 | #### 2. Plot Figure in PDF #### 41 | pd <- position_dodge(0.9) # move them to the left and right 42 | par(mfrow = c(2,2)) 43 | par(mar=c(3.5,4,2,1.5)) 44 | 45 | #### Figure 1: for interfactor correlations 46 | 47 | ## plot 1: ARB 48 | stat = data2stat(results[,13:24]) 49 | 50 | ARB.corr = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + coord_cartesian(ylim = c(-0.15, 0.15)) + 51 | geom_line() + 52 | geom_point(aes(shape=Methods)) + 53 | geom_hline(yintercept = 0) + 54 | geom_hline(yintercept = 0.05, linetype = "dashed") + 55 | geom_hline(yintercept = -0.05, linetype = "dashed") + 56 | geom_hline(yintercept = 0.1, linetype = "dotted") + 57 | geom_hline(yintercept = -0.1, linetype = "dotted") + 58 | xlab('missing percentage') + ylab('ARB') + 59 | #geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 60 | theme_bw() + 61 | theme(legend.justification=c(0.01,0.99),legend.position=c(0.01,0.99),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 62 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 63 | 64 | ## plot 2: RMSE 65 | stat = data2stat(results[,25:36]) 66 | 67 | RMSE.corr = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, fill = Methods)) + 68 | geom_bar(position=pd, stat="identity") + 69 | geom_point(aes(shape=Methods), position=pd) + 70 | xlab('missing percentage') + ylab('RMSE') + 71 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 72 | theme_bw() + 73 | theme(legend.justification=c(0.99,0.01),legend.position=c(0.99,0.01),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 74 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 75 | 76 | ## show Figure 77 | grid.arrange(ARB.corr, RMSE.corr, nrow = 1, ncol = 2) 78 | # ## save Figure 79 | # pdf(file = 'results/factor_analysis/k4_incomplete_corr.pdf', width = 4.5, height = 1.9) 80 | # grid.arrange(ARB.corr, RMSE.corr, nrow = 1, ncol = 2) 81 | # dev.off() 82 | 83 | 84 | #### Figure 2: for factor loadings 85 | 86 | ## plot 1: ARB 87 | stat = data2stat(results[,37:48]) 88 | 89 | ARB.corr = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + coord_cartesian(ylim = c(-0.2, 0.2)) + 90 | geom_line() + 91 | geom_point(aes(shape=Methods)) + 92 | geom_hline(yintercept = 0) + 93 | geom_hline(yintercept = 0.05, linetype = "dashed") + 94 | geom_hline(yintercept = -0.05, linetype = "dashed") + 95 | geom_hline(yintercept = 0.1, linetype = "dotted") + 96 | geom_hline(yintercept = -0.1, linetype = "dotted") + 97 | xlab('missing percentage') + ylab('ARB') + 98 | #geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 99 | theme_bw() + 100 | theme(legend.justification=c(0.01,0.99),legend.position=c(0.01,0.99),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 101 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 102 | 103 | ## plot 2: RMSE 104 | stat = data2stat(results[,49:60]) 105 | 106 | RMSE.corr = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, fill = Methods)) + 107 | geom_bar(position=pd, stat="identity") + 108 | geom_point(aes(shape=Methods), position=pd) + 109 | xlab('missing percentage') + ylab('RMSE') + 110 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 111 | theme_bw() + 112 | theme(legend.justification=c(0.01,0.99),legend.position=c(0.01,0.99),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 113 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 114 | 115 | ## show Figure 116 | grid.arrange(ARB.corr, RMSE.corr, nrow = 1, ncol = 2) 117 | # ## save Figure 118 | # pdf(file = 'results/factor_analysis/k4_incomplete_loadings.pdf', width = 4.5, height = 1.9) 119 | # grid.arrange(ARB.corr, RMSE.corr, nrow = 1, ncol = 2) 120 | # dev.off() 121 | -------------------------------------------------------------------------------- /R/plot_causal_continuous.R: -------------------------------------------------------------------------------- 1 | ################################################################################ 2 | # Goal: Plot the performance of the Copula Factor PC algorithm, the greedy 3 | # step-wise method and fully-integrated method respecively. 4 | # 5 | # Metrics: TPR, FPR, and SHD 6 | # 7 | # Settings: fully Gaussian; 8 | # all factors have multiple indicators; 9 | # k = {4, 10}; 10 | # n = {500, 1000, 2000}. 11 | ################################################################################ 12 | 13 | #### 0. Load Packages #### 14 | 15 | ## 16 | #install.packages("psych") 17 | #install.packages("tikzDevice") 18 | library(psych) 19 | library(tikzDevice) 20 | library(dplyr) 21 | library(psych) 22 | library(ggplot2) 23 | library(gridExtra) 24 | 25 | ## help function 26 | data2stat <- function(data){ 27 | 28 | describe(data) %>% 29 | mutate(ci = qt(0.975,n-1) * se) %>% 30 | mutate(Methods = c(rep('MBPC',3), rep('GSPC',3), rep('CFPC',3))) %>% 31 | mutate(Sample.size = as.factor(rep(c(500,1000,2000),3))) %>% 32 | select(Methods, Sample.size, mean, ci) 33 | } 34 | 35 | 36 | #### 1. Read Data #### 37 | 38 | p4 = read.table("results/causal_discovery/TPR_FPR_SHD_p4_all_conti.txt", header = F) 39 | p10 = read.table("results/causal_discovery/TPR_FPR_SHD_p10_all_conti.txt", header = F) 40 | 41 | # each data frame above is 100 * 27 (dimension) 42 | # 100 means repeated experiments times 43 | 44 | 45 | #### 2. Plot #### 46 | 47 | pd <- position_dodge(0.3) # move them to the left and right 48 | par(mfrow = c(2,2)) 49 | par(mar=c(3.5,4,2,1.5)) 50 | 51 | #### Figure 52 | 53 | ## plot 1: k = 4, TPR 54 | # statistical values 55 | stat = data2stat(p4[,1:9]) 56 | # plot 57 | TPR.k4 = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + coord_cartesian(ylim = c(0, 1)) + 58 | geom_line(position=pd) + 59 | geom_point(aes(shape=Methods), position=pd) + 60 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + xlab('sample size') + ylab('TPR') + ggtitle('TPR (k=4)') + 61 | theme_bw() + 62 | theme(legend.justification=c(0.99,0.01),legend.position=c(0.99,0.01),legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 63 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 64 | 65 | ## plot 2: k = 4, FPR 66 | # statistical values 67 | stat = data2stat(p4[,10:18]) 68 | # plot 69 | FPR.k4 = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + 70 | geom_line(position=pd) + 71 | geom_point(aes(shape=Methods), position=pd) + 72 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + xlab('sample size') + ylab('FPR') + ggtitle('FPR (k=4)') + 73 | theme_bw() + 74 | theme(legend.position='none') + 75 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 76 | 77 | ## plot 3: k = 4, SHD 78 | # statistical values 79 | stat = data2stat(p4[,19:27]) 80 | # plot 81 | SHD.k4 = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + 82 | geom_line(position=pd) + 83 | geom_point(aes(shape=Methods), position=pd) + 84 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + xlab('sample size') + ylab('SHD') + ggtitle('SHD (k=4)') + 85 | theme_bw() + 86 | theme(legend.position='none') + 87 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 88 | 89 | ## plot 4: k = 10, TPR 90 | # statistical values 91 | stat = data2stat(p10[,1:9]) 92 | # plot 93 | TPR.k10 = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + coord_cartesian(ylim = c(0.1, 1)) + 94 | geom_line(position=pd) + 95 | geom_point(aes(shape=Methods), position=pd) + 96 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + xlab('sample size') + ylab('TPR') + ggtitle('TPR (k=10)') + 97 | theme_bw() + 98 | theme(legend.position='none') + 99 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 100 | 101 | ## plot 5: k = 10, FPR 102 | # statistical values 103 | stat = data2stat(p10[,10:18]) 104 | # plot 105 | FPR.k10 = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + 106 | geom_line(position=pd) + 107 | geom_point(aes(shape=Methods), position=pd) + 108 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + xlab('sample size') + ylab('FPR') + ggtitle('FPR (k=10)') + 109 | theme_bw() + 110 | theme(legend.position='none') + 111 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 112 | 113 | ## plot 6: k = 10, SHD 114 | # statistical values 115 | stat = data2stat(p10[,19:27]) 116 | # plot 117 | SHD.k10 = ggplot(stat, aes(x = Sample.size, y = mean, group = Methods, color = Methods)) + 118 | geom_line(position=pd) + 119 | geom_point(aes(shape=Methods), position=pd) + 120 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + xlab('sample size') + ylab('SHD') + ggtitle('SHD (k=10)') + 121 | theme_bw() + 122 | theme(legend.position='none') + 123 | theme(text = element_text(size=8), plot.title = element_text(hjust = 0.5, size = 8)) 124 | 125 | 126 | #### 3. Show and Save the Figure #### 127 | 128 | ## 129 | grid.arrange(TPR.k4, FPR.k4, SHD.k4, TPR.k10, FPR.k10, SHD.k10, nrow = 2, ncol = 3) 130 | 131 | # ## 132 | # pdf(file = 'results/causal_discovery/TFPR_SHD_conti.pdf', width = 7.2, height = 4.05) 133 | # ## arrange 134 | # grid.arrange(TPR.k4, FPR.k4, SHD.k4, TPR.k10, FPR.k10, SHD.k10, nrow = 2, ncol = 3) 135 | # 136 | # dev.off() 137 | 138 | -------------------------------------------------------------------------------- /R/plot_causal_mixed.R: -------------------------------------------------------------------------------- 1 | ############################################################################### 2 | # Goal: Plot the performance of the Copula Factor PC algorithm, the greedy 3 | # step-wise method and fully-integrated method respecively. 4 | # 5 | # Metrics: TPR, FPR, and SHD (we plot three figures for the three metrics) 6 | # 7 | # Settings: Case 1, (4 factors where all have more measurements) 8 | # Case 2, (4 factors where 2 have more measurements while 2 have one) 9 | # Case 3, (4 factors where all have more measurements) 10 | # Case 4, (4 factors where 2 have more measurements while 2 have one) 11 | ############################################################################### 12 | 13 | #### 0. Load Packages #### 14 | 15 | ## 16 | library(psych) 17 | library(dplyr) 18 | library(ggplot2) 19 | library(gridExtra) 20 | 21 | ## help function 22 | data2stat <- function(data){ 23 | stat_data = describe(data) %>% 24 | mutate(ci = qt(0.975,n-1) * se) %>% 25 | mutate(Methods = c(rep('MBPC',3),rep('GSPC',3),rep('CFPC',3))) %>% 26 | mutate(sample_size = as.factor(rep(c(500,1000,2000),3))) %>% 27 | select(Methods, sample_size, mean, ci) 28 | } 29 | 30 | #### 1. Read Data #### 31 | 32 | p4_all = read.table("results/causal_discovery/TPR_FPR_SHD_p4_all.txt", header = F) 33 | p4_half = read.table("results/causal_discovery/TPR_FPR_SHD_p4_half.txt", header = F) 34 | p10_all = read.table("results/causal_discovery/TPR_FPR_SHD_p10_all.txt", header = F) 35 | p10_half = read.table("results/causal_discovery/TPR_FPR_SHD_p10_half.txt", header = F) 36 | 37 | 38 | #### 2. Plot #### 39 | 40 | # 41 | pd <- position_dodge(0.3) # move them to the left and right 42 | 43 | #### Figure 1: TPR 44 | 45 | ## plot 1: for case 1 46 | # statistical values 47 | stat_p4_all = data2stat(p4_all[,1:9]) 48 | # ggplot 49 | TPR_p4_all <- ggplot(stat_p4_all, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + coord_cartesian(ylim = c(0, 1)) + 50 | geom_line(position=pd) + 51 | geom_point(aes(shape=Methods), position=pd) + 52 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 53 | xlab('sample size (n)') + ylab('TPR') +ggtitle('Only multi-indicators (k=4)') + 54 | theme_bw() + 55 | theme(legend.justification=c(0.99,0.01),legend.position=c(0.99,0.01), legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 56 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 57 | 58 | ## plot 2: for case 2 59 | # statistical values 60 | stat_p4_half = data2stat(p4_half[,1:9]) 61 | # ggplot 62 | TPR_p4_half <- ggplot(stat_p4_half, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + coord_cartesian(ylim = c(0, 1)) + 63 | geom_line(position=pd) + 64 | geom_point(aes(shape=Methods), position=pd) + 65 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 66 | xlab('sample size (n)') + ylab('TPR') +ggtitle('Also single indicator (k=4)') + 67 | theme_bw() + theme(legend.position = 'none') + 68 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 69 | 70 | ## plot 3: for case 3 71 | # statistical values 72 | stat_p10_all = data2stat(p10_all[,1:9]) 73 | # ggplot 74 | TPR_p10_all <- ggplot(stat_p10_all, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + coord_cartesian(ylim = c(0, 1)) + 75 | geom_line(position=pd) + 76 | geom_point(aes(shape=Methods), position=pd) + 77 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 78 | xlab('sample size (n)') + ylab('TPR') +ggtitle('Only multi-indicators (k=10)') + 79 | theme_bw() + theme(legend.position = 'none') + 80 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 81 | 82 | ## plot 4: for case 4 83 | # statistical values 84 | stat_p10_half = data2stat(p10_half[,1:9]) 85 | # ggplot 86 | TPR_p10_half <- ggplot(stat_p10_half, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + coord_cartesian(ylim = c(0, 1)) + 87 | geom_line(position=pd) + 88 | geom_point(aes(shape=Methods), position=pd) + 89 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 90 | xlab('sample size (n)') + ylab('TPR') +ggtitle('Also single indicator (k=10)') + 91 | theme_bw() + theme(legend.position = 'none') + 92 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 93 | 94 | ## show Figure 95 | grid.arrange(TPR_p4_all, TPR_p4_half, TPR_p10_all, TPR_p10_half, nrow = 2, ncol = 2) 96 | ## save Figure 97 | pdf(file = 'results/causal_discovery/TPR.pdf', width = 5, height = 4.8) 98 | grid.arrange(TPR_p4_all, TPR_p4_half, TPR_p10_all, TPR_p10_half, nrow = 2, ncol = 2) 99 | dev.off() 100 | 101 | #### Figure 2: FPR 102 | 103 | ## plot 1: for case 1 104 | # statistical values 105 | stat_p4_all = data2stat(p4_all[,10:18]) 106 | # ggplot 107 | TPR_p4_all <- ggplot(stat_p4_all, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + 108 | geom_line(position=pd) + 109 | geom_point(aes(shape=Methods), position=pd) + 110 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 111 | xlab('sample size (n)') + ylab('FPR') +ggtitle('Only multi-indicators (k=4)') + 112 | theme_bw() + 113 | theme(legend.position = 'none') + 114 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 115 | 116 | ## plot 2: for case 2 117 | # statistical values 118 | stat_p4_half = data2stat(p4_half[,10:18]) 119 | # ggplot 120 | TPR_p4_half <- ggplot(stat_p4_half, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + 121 | geom_line(position=pd) + 122 | geom_point(aes(shape=Methods), position=pd) + 123 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 124 | xlab('sample size (n)') + ylab('FPR') +ggtitle('Also single indicator (k=4)') + 125 | theme_bw() + theme(legend.position = 'none') + 126 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 127 | 128 | ## plot 3: for case 3 129 | # statistical values 130 | stat_p10_all = data2stat(p10_all[,10:18]) 131 | # ggplot 132 | TPR_p10_all <- ggplot(stat_p10_all, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + 133 | geom_line(position=pd) + 134 | geom_point(aes(shape=Methods), position=pd) + 135 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 136 | xlab('sample size (n)') + ylab('FPR') +ggtitle('Only multi-indicators (k=10)') + 137 | theme_bw() + theme(legend.position = 'none') + 138 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 139 | 140 | ## plot 4: for case 4 141 | # statistical values 142 | stat_p10_half = data2stat(p10_half[,10:18]) 143 | # ggplot 144 | TPR_p10_half <- ggplot(stat_p10_half, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + 145 | geom_line(position=pd) + 146 | geom_point(aes(shape=Methods), position=pd) + 147 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 148 | xlab('sample size (n)') + ylab('FPR') +ggtitle('Also single indicator (k=10)') + 149 | theme_bw() + theme(legend.position = 'none') + 150 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 151 | 152 | ## show Figure 153 | grid.arrange(TPR_p4_all, TPR_p4_half, TPR_p10_all, TPR_p10_half, nrow = 2, ncol = 2) 154 | # ## save Figure 155 | # pdf(file = 'results/causal_discovery/FPR.pdf', width = 5, height = 4.8) 156 | # grid.arrange(TPR_p4_all, TPR_p4_half, TPR_p10_all, TPR_p10_half, nrow = 2, ncol = 2) 157 | # dev.off() 158 | 159 | #### Figure 3: SHD 160 | 161 | ## plot 1: for case 1 162 | # statistical values 163 | stat_p4_all = data2stat(p4_all[,19:27]) 164 | # ggplot 165 | TPR_p4_all <- ggplot(stat_p4_all, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + coord_cartesian(ylim = c(0, 3.5)) + 166 | geom_line(position=pd) + 167 | geom_point(aes(shape=Methods), position=pd) + 168 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 169 | xlab('sample size (n)') + ylab('SHD') +ggtitle('Only multi-indicators (k=4)') + 170 | theme_bw() + 171 | theme(legend.justification=c(0.01,0.01),legend.position=c(0.01,0.01), legend.title = element_blank(), legend.key.size = unit(0.35, "cm")) + 172 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 173 | 174 | ## plot 2: for case 2 175 | # statistical values 176 | stat_p4_half = data2stat(p4_half[,19:27]) 177 | # ggplot 178 | TPR_p4_half <- ggplot(stat_p4_half, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + 179 | geom_line(position=pd) + 180 | geom_point(aes(shape=Methods), position=pd) + 181 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 182 | xlab('sample size (n)') + ylab('SHD') +ggtitle('Also single indicator (k=4)') + 183 | theme_bw() + theme(legend.position = 'none') + 184 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 185 | 186 | ## plot 3: for case 3 187 | # statistical values 188 | stat_p10_all = data2stat(p10_all[,19:27]) 189 | # ggplot 190 | TPR_p10_all <- ggplot(stat_p10_all, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + 191 | geom_line(position=pd) + 192 | geom_point(aes(shape=Methods), position=pd) + 193 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 194 | xlab('sample size (n)') + ylab('SHD') +ggtitle('Only multi-indicators (k=10)') + 195 | theme_bw() + theme(legend.position = 'none') + 196 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 197 | 198 | ## plot 4: for case 4 199 | # statistical values 200 | stat_p10_half = data2stat(p10_half[,19:27]) 201 | # ggplot 202 | TPR_p10_half <- ggplot(stat_p10_half, aes(x=sample_size, y=mean, group=Methods, color=Methods)) + 203 | geom_line(position=pd) + 204 | geom_point(aes(shape=Methods), position=pd) + 205 | geom_errorbar(aes(ymin=mean-ci, ymax=mean+ci), width=.2, position=pd) + 206 | xlab('sample size (n)') + ylab('SHD') +ggtitle('Also single indicator (k=10)') + 207 | theme_bw() + theme(legend.position = 'none') + 208 | theme(plot.title = element_text(hjust = 0.5, size = 10)) 209 | 210 | ## show Figure 211 | grid.arrange(TPR_p4_all, TPR_p4_half, TPR_p10_all, TPR_p10_half, nrow = 2, ncol = 2) 212 | # ## save Figure 213 | # pdf(file = 'results/causal_discovery/SHD.pdf', width = 5, height = 4.6) 214 | # grid.arrange(TPR_p4_all, TPR_p4_half, TPR_p10_all, TPR_p10_half, nrow = 2, ncol = 2) 215 | # dev.off() 216 | -------------------------------------------------------------------------------- /R/rmvCopulaFactorModel.R: -------------------------------------------------------------------------------- 1 | rmvCopulaFactorModel <-function(n = 1000, g = NULL, sigma = NULL, impurity = 0, range.indicators = 3:10, lambda.min = 0.1, lambda.max = 1, sd.residual = 1) 2 | { 3 | # This function aims to generate data from a Gaussian copula factor model 4 | # given a graph or a covariance matrix in the latent space. 5 | # 6 | # Args: 7 | # n, sample size 8 | # g, a DAG (graphNEL) 9 | # sigma, a covariance matrix 10 | # impurity, No. of impurities of the measurement model 11 | # range.indicators, range of the number of indicators per factor 12 | # lambda.min and lambda.max, the minimum and maximum of factor loadings 13 | # sd.residual, standard deviation of residuals 14 | # 15 | # Return: a list, which contains generated data and ... 16 | # 17 | 18 | library(mvtnorm) 19 | 20 | #### 0. Check inputs and Initialization 21 | ## check input g and sigma 22 | if(!is.null(g)){ 23 | ## pl: the number of latent factors (or variables) 24 | pl = length(g@nodes) 25 | ## sigma: the population covariance matrix 26 | sigma = trueCov(g) 27 | }else if(!is.null(sigma)) 28 | pl = ncol(sigma) 29 | else 30 | stop('Input g and sigma connot be empty simutanously.') 31 | 32 | 33 | ## choose randomly some factors from pl as factors with more (>1) response variables 34 | # the number of factors with more (>1) response variables 35 | pm = round(pl) 36 | index_more = 1:pl#sample(1:pl, pm) 37 | ## choose the number of response variables for each element of index_more from unif(3,10) 38 | #num_res_var = sample(3:10, pm, replace = T)#rep(4, pm)# 39 | ifelse(length(range.indicators) == 1, num_res_var <- rep(range.indicators, pm), num_res_var <- sample(range.indicators, pm, replace = T)) 40 | 41 | ## pr: the number of response variables. 42 | pr = sum(num_res_var) 43 | 44 | 45 | #### 1. Generate normal data in latent sapce 46 | ## d_gauss stands for \eta 47 | d_gauss <- rmvnorm(n, sigma = sigma)#rmvDAG(n,g) 48 | 49 | 50 | #### 2. Generate response data 51 | ## initializing 52 | Y=mat.or.vec(n,pl+pr) 53 | Y[,1:pl] = d_gauss 54 | 55 | ## randomly generate factor loadings (Lamda) from latent factors to response variables 56 | Lamda = matrix(0,pr,pm) 57 | index_res_var = mat.or.vec(pm,1) 58 | for (i in 1:pm) { 59 | index_res_var[i] = sum(num_res_var[1:i]) 60 | } 61 | index_res_var = c(0,index_res_var) 62 | for (i in 1:pm) { 63 | Lamda[(index_res_var[i]+1):index_res_var[i+1],i] = runif(num_res_var[i], min = lambda.min, max = lambda.max) 64 | } 65 | Lamda.pure = Lamda 66 | ## noise 67 | error = matrix(rnorm(pr*n, 0, sd.residual),n,pr) 68 | ## add some impurities 69 | if (impurity > 0){ 70 | # the number of type 1 and 2 impurities 71 | ni.1 = round(impurity) 72 | ni.2 = impurity - ni.1 73 | # type 1: to Lamda 74 | if (ni.1 > 0){ 75 | Lamda[sample(which(Lamda == 0), ni.1)] = runif(ni.1, 0.1, 1) 76 | } 77 | # type 2: to error 78 | if (ni.2 > 0){ 79 | vec = rep(0, pr*(pr-1)/2) 80 | vec[sample(pr*(pr-1)/2, ni.2)] = runif(ni.2) 81 | sigma.error = diag(pr) 82 | sigma.error[upper.tri(sigma.error)] = vec 83 | sigma.error[lower.tri(sigma.error)] = t(sigma.error)[lower.tri(sigma.error)] 84 | error = rmvnorm(n, sigma = sigma.error) 85 | } 86 | } 87 | 88 | 89 | ## generate responsing data 90 | Y[,(pl+1):(pl+pr)] = d_gauss[,index_more] %*% t(Lamda) + error 91 | 92 | 93 | #### 3. Return 94 | list(data = Y[,-(1:pl)], Sigma = sigma, index_more = index_more, Lambda = Lamda.pure) 95 | } -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # CopulaFactorModel 2 | 3 | This project contains the code for our two papers: 4 | 1. Cui, Ruifei, et al. "Learning the Causal Structure of Copula Models with Latent Variables." UAI. 2018. 5 | 2. Cui, R., Bucur, I.G., Groot, P. et al. A novel Bayesian approach for latent variable modeling from mixed data with missing values. Stat Comput 29, 977–993 (2019). https://doi.org/10.1007/s11222-018-09849-7 6 | -------------------------------------------------------------------------------- /results/causal_discovery/TPR_FPR_SHD_p10_all.txt: -------------------------------------------------------------------------------- 1 | 0.0625 0.125 0.25 0.75 0.6875 1 0.6875 0.4375 0.8125 0 0.03448 0.03448 0.13793 0.13793 0.27586 0.03448 0.06897 0.10345 16 17 14 12 11 10 8 14 9 2 | 0.375 0.375 0.875 0.75 0.875 1 0.75 1 0.875 0 0 0.02703 0.05405 0.02703 0.05405 0.02703 0.05405 0 5 5 4 6 2 2 3 7 1 3 | 0 0.625 0.75 0.75 0.875 0.875 0.875 0.875 1 0 0 0.02703 0.05405 0.02703 0.10811 0.02703 0 0.05405 8 5 5 6 7 9 4 1 7 4 | 0.09091 0.45455 0.54545 0.81818 0.90909 1 0.81818 0.81818 0.90909 0 0 0.05882 0.05882 0.08824 0.14706 0.05882 0 0.02941 11 8 12 9 6 10 9 5 5 5 | 0.25 0.5 0.75 0.75 0.75 0.875 0.875 0.875 1 0 0 0 0 0.08108 0 0 0.02703 0.02703 6 4 2 5 8 3 7 8 3 6 | 0 0.55556 0.66667 0.88889 1 1 0.88889 1 1 0 0 0.02778 0.05556 0 0.08333 0.02778 0 0.02778 9 5 4 4 3 3 2 1 3 7 | 0.2 0.3 0.7 0.8 0.6 0.8 0.7 0.9 0.8 0 0.02857 0 0.05714 0.14286 0.08571 0 0.02857 0.02857 8 8 8 8 12 13 8 7 7 8 | 0.09091 0.18182 0.45455 0.63636 1 0.90909 0.72727 0.81818 0.81818 0 0.02941 0 0.05882 0.02941 0.02941 0 0.02941 0 11 10 9 7 3 4 3 3 2 9 | 0.2 0.2 0.7 0.7 0.9 0.9 0.7 0.8 0.9 0 0 0 0.05714 0.02857 0.08571 0 0.02857 0 9 9 8 9 8 6 6 6 6 10 | 0.125 0.375 0.625 0.875 0.875 0.875 0.875 0.875 0.875 0 0 0 0.08108 0.08108 0.13514 0.02703 0 0.05405 8 8 5 5 4 7 3 2 4 11 | 0 0.6 0.6 0.6 0.6 1 0.6 0.8 1 0 0.025 0.025 0.05 0.025 0.05 0.025 0 0 5 4 4 5 6 2 4 4 0 12 | 0.375 0.5 1 0.75 1 1 0.75 0.875 1 0 0 0.02703 0 0.05405 0.05405 0 0.02703 0 6 6 3 4 3 3 4 5 0 13 | 0.07143 0.28571 0.35714 0.57143 0.85714 0.78571 0.64286 0.85714 0.78571 0 0 0 0.03226 0.09677 0.09677 0.03226 0.03226 0.03226 14 12 11 10 5 8 8 4 6 14 | 0.09091 0.45455 0.45455 0.36364 0.72727 0.81818 0.45455 0.54545 0.81818 0 0 0 0 0 0 0 0 0 10 10 9 9 6 2 8 7 3 15 | 0.2 0.6 0.4 0.8 1 1 0.8 1 1 0 0.05 0 0 0 0.05 0 0 0.025 4 6 3 1 0 4 1 0 1 16 | 0.09091 0.45455 0.72727 0.72727 0.90909 0.90909 0.63636 0.72727 0.81818 0 0 0 0.05882 0.11765 0.14706 0 0.02941 0.02941 11 9 6 7 6 7 7 5 5 17 | 0.22222 0.44444 0.66667 0.77778 0.88889 1 0.77778 0.77778 0.88889 0 0 0 0.02778 0.05556 0.08333 0 0.02778 0 8 5 3 6 5 6 2 3 1 18 | 0.33333 0.55556 0.66667 0.77778 0.88889 0.88889 0.77778 0.88889 0.88889 0 0 0 0 0.08333 0.08333 0 0 0 8 5 4 4 7 6 3 4 2 19 | 0 0.27273 0.81818 0.81818 0.90909 0.90909 0.81818 0.90909 0.90909 0 0 0.05882 0.05882 0.05882 0.14706 0 0 0 11 9 8 7 4 7 5 2 2 20 | 0 0.2 0.8 0.8 1 1 0.8 1 1 0 0 0 0.025 0 0.025 0.025 0 0.025 5 5 2 4 0 3 3 0 2 21 | 0.1 0.3 0.6 0.8 0.9 1 0.8 0.9 1 0 0 0 0.08571 0.08571 0.2 0.02857 0 0.02857 9 9 5 6 4 12 6 1 1 22 | 0.22222 0.77778 0.77778 0.88889 0.77778 0.88889 0.77778 0.77778 0.88889 0 0 0.02778 0.02778 0.08333 0.11111 0.02778 0 0 8 3 5 4 8 8 5 4 2 23 | 0.11111 0.44444 0.55556 0.55556 1 1 0.55556 1 1 0.02778 0 0 0.05556 0.02778 0 0 0 0 10 6 4 7 4 1 4 1 3 24 | 0.09091 0.27273 0.54545 0.63636 0.81818 0.81818 0.54545 0.72727 0.72727 0 0 0 0 0.02941 0.05882 0.02941 0 0 10 9 7 4 6 7 6 5 5 25 | 0.11111 0.55556 0.88889 0.88889 1 0.88889 0.88889 0.88889 0.88889 0 0 0 0.02778 0 0.05556 0 0 0 8 4 5 7 7 5 5 1 3 26 | 0.11111 0.33333 0.33333 0.66667 0.77778 0.83333 0.5 0.55556 0.72222 0 0 0.03704 0.07407 0.14815 0.07407 0 0 0 18 14 15 11 11 9 14 11 6 27 | 0.125 0.625 0.875 1 1 1 0.875 1 1 0 0 0 0.02703 0 0.13514 0 0.02703 0 7 4 4 3 0 7 1 4 0 28 | 0 0 0.71429 0.42857 0.71429 0.85714 0.42857 0.71429 0.85714 0 0 0 0 0 0 0.02632 0 0.02632 7 7 4 7 3 1 8 3 2 29 | 0.07692 0.30769 0.38462 0.69231 0.92308 0.84615 0.53846 0.69231 0.69231 0 0 0.03125 0.0625 0 0.0625 0.03125 0 0.03125 13 11 9 9 4 8 9 5 8 30 | 0.08333 0.41667 0.75 0.83333 0.91667 0.91667 0.91667 0.91667 0.91667 0 0 0 0 0.06061 0.0303 0 0 0.0303 12 9 3 3 3 2 1 1 2 31 | 0 0.22222 0.77778 0.66667 0.88889 0.88889 0.66667 0.88889 0.88889 0 0 0 0 0.02778 0.05556 0 0 0.02778 9 9 4 7 2 6 7 4 6 32 | 0.2 0.4 1 1 1 1 1 1 1 0 0 0.025 0.025 0.025 0.075 0.025 0 0 5 4 4 3 1 3 1 0 0 33 | 0 0.41667 0.5 0.75 0.83333 0.91667 0.58333 0.91667 0.91667 0 0 0 0.09091 0.06061 0.12121 0.06061 0 0 12 9 8 10 5 7 12 3 3 34 | 0 0.2 0.8 0.6 1 1 0.4 1 1 0 0 0.025 0 0 0 0 0.025 0.05 5 5 3 3 1 1 3 3 4 35 | 0.125 0.25 0.625 0.875 0.75 0.875 0.875 0.875 0.875 0 0 0 0.02703 0.02703 0.05405 0.02703 0.02703 0 8 8 4 3 3 4 3 2 2 36 | 0 0.46154 0.61538 0.69231 0.84615 0.84615 0.69231 0.76923 0.84615 0 0 0.03125 0.0625 0.09375 0.1875 0 0 0.03125 13 8 8 7 6 10 6 4 5 37 | 0 0.6 0.6 1 1 1 1 1 1 0 0 0 0 0.025 0.025 0 0 0.025 5 2 4 3 5 1 3 3 1 38 | 0.09091 0.54545 0.72727 0.72727 0.72727 0.90909 0.63636 0.72727 0.72727 0 0.02941 0 0 0.02941 0.08824 0 0 0 11 7 6 6 6 5 8 5 5 39 | 0 0.27273 0.27273 0.81818 0.90909 0.72727 0.72727 0.90909 0.81818 0 0 0.02941 0.14706 0.11765 0.17647 0.05882 0 0 11 10 10 11 10 14 9 1 3 40 | 0.42857 0.42857 1 1 1 1 1 1 1 0 0 0.07895 0 0.02632 0.05263 0 0 0.05263 6 7 4 1 2 3 0 0 2 41 | 0 0.375 0.625 0.5 0.875 0.75 0.625 0.875 0.75 0 0 0.02703 0 0 0.05405 0 0 0 8 5 6 4 4 7 3 4 2 42 | 0.18182 0.36364 0.45455 0.81818 0.72727 1 0.81818 0.72727 0.81818 0 0 0.02941 0 0.08824 0.11765 0 0.05882 0.02941 11 8 10 5 11 5 5 9 4 43 | 0.28571 0.5 0.57143 0.71429 0.85714 1 0.71429 0.85714 0.85714 0 0.03226 0 0 0.09677 0.09677 0.03226 0 0 10 12 6 7 9 7 7 4 5 44 | 0.06667 0.26667 0.53333 0.66667 0.66667 0.8 0.53333 0.66667 0.73333 0 0 0 0.03333 0.06667 0.03333 0.03333 0 0 15 13 10 10 13 5 10 9 8 45 | 0 0.28571 0.85714 0.85714 1 1 1 1 1 0 0 0 0 0 0 0 0.02632 0 7 7 1 2 0 0 0 1 0 46 | 0.08333 0.5 0.08333 0.91667 0.91667 1 0.83333 0.91667 0.91667 0 0 0 0.06061 0.09091 0.21212 0 0 0.0303 12 9 12 5 5 7 2 1 4 47 | 0 0.25 0.5 0.875 0.875 1 0.875 1 1 0 0 0 0 0.02703 0.02703 0 0 0 8 7 7 6 7 6 4 5 5 48 | 0 0.4 0.7 0.9 1 1 0.8 0.9 1 0 0 0.02857 0.05714 0.02857 0.11429 0.02857 0 0 10 9 7 4 2 5 4 3 0 49 | 0.3 0.6 0.8 0.9 0.9 0.9 0.8 0.9 0.9 0 0 0 0 0.02857 0.08571 0 0 0.02857 7 5 3 5 7 5 3 4 3 50 | 0.08333 0.41667 0.66667 0.75 0.75 0.83333 0.66667 0.83333 0.83333 0 0 0 0.09091 0.18182 0.24242 0.0303 0.09091 0.06061 12 9 5 9 11 12 5 7 5 51 | 0.23077 0.38462 0.30769 0.76923 0.84615 0.84615 0.76923 0.69231 0.76923 0 0 0.03125 0.09375 0.09375 0.125 0.03125 0 0.03125 12 8 12 8 9 11 5 6 8 52 | 0.1 0.6 0.6 0.7 0.8 0.8 0.6 0.8 0.8 0 0 0 0.05714 0.05714 0.05714 0 0 0 10 8 9 8 5 6 7 5 5 53 | 0.07692 0.38462 0.61538 0.61538 0.84615 0.92308 0.53846 0.84615 0.92308 0 0 0 0.03125 0.0625 0.03125 0 0 0 12 11 5 8 8 8 6 4 7 54 | 0.18182 0.36364 0.54545 0.72727 0.81818 0.90909 0.72727 0.72727 0.90909 0 0.02941 0.02941 0.05882 0.08824 0.11765 0.02941 0.02941 0.02941 9 8 7 10 8 7 7 7 2 55 | 0.2 0.4 0.7 0.8 0.8 0.9 0.8 0.7 0.7 0 0 0 0.08571 0.08571 0.05714 0.02857 0.05714 0 8 7 5 6 8 4 4 7 5 56 | 0.18182 0.63636 0.81818 0.81818 0.90909 1 0.90909 0.90909 0.90909 0 0 0 0.08824 0.02941 0.05882 0.05882 0 0 10 8 6 9 7 4 8 2 2 57 | 0.375 0.625 0.875 0.875 0.875 1 0.875 0.875 1 0 0.02703 0 0 0.02703 0.08108 0 0 0.05405 6 6 1 1 2 3 1 1 6 58 | 0.11111 0 0.66667 0.88889 0.77778 0.88889 0.66667 0.77778 0.77778 0 0 0 0.02778 0.05556 0.02778 0 0.02778 0 8 9 5 4 7 4 3 5 4 59 | 0.0625 0.3125 0.4375 0.6875 0.8125 0.875 0.5625 0.6875 0.75 0 0 0.03448 0.03448 0.03448 0.06897 0.03448 0 0 16 13 14 12 12 8 15 12 8 60 | 0 0.14286 0.85714 0.57143 0.64286 0.78571 0.57143 0.71429 0.71429 0 0 0.06452 0.03226 0.06452 0.06452 0 0 0 14 14 6 12 9 8 9 10 8 61 | 0.2 0.4 0.6 0.7 0.9 0.8 0.7 0.9 0.8 0 0 0 0 0 0 0 0 0.02857 9 8 7 7 3 6 7 2 7 62 | 0 0.44444 0.44444 0.88889 0.88889 1 0.88889 1 1 0 0 0 0 0.02778 0.08333 0.02778 0 0.02778 9 7 6 3 5 4 5 1 3 63 | 0.4 0.8 0.8 0.8 0.9 1 0.7 0.9 1 0 0 0 0 0.02857 0.05714 0 0 0 6 2 2 2 4 5 4 3 2 64 | 0 0.14286 0.42857 0.71429 0.78571 0.92857 0.71429 0.78571 0.92857 0 0 0 0.03226 0.06452 0.06452 0.03226 0 0.03226 14 12 8 12 10 7 9 7 6 65 | 0.2 0.6 0.6 0.6 1 0.8 0.6 1 0.8 0 0 0 0 0.025 0 0 0.025 0.025 5 3 3 3 3 1 3 3 2 66 | 0.16667 0.66667 0.83333 0.83333 0.91667 0.83333 0.75 0.75 0.83333 0 0 0 0.09091 0.09091 0.15152 0.06061 0.0303 0 10 6 7 10 6 7 6 12 4 67 | 0.18182 0.54545 0.63636 0.63636 0.63636 0.81818 0.54545 0.63636 0.81818 0 0 0.05882 0.02941 0.11765 0.17647 0.02941 0.05882 0.05882 11 8 9 9 11 10 8 7 5 68 | 0.09091 0.45455 0.72727 0.90909 0.81818 0.90909 0.81818 0.81818 0.90909 0 0 0.02941 0.05882 0.23529 0.20588 0 0.05882 0 11 7 8 9 16 13 2 4 2 69 | 0.27273 0.36364 0.72727 0.72727 0.81818 0.81818 0.81818 0.81818 0.81818 0 0 0 0.02941 0.02941 0.02941 0 0.02941 0 9 9 5 6 5 8 7 5 4 70 | 0.3 0.3 0.3 0.8 0.9 0.7 0.8 0.8 0.9 0 0 0 0.02857 0.05714 0.05714 0 0 0 9 9 10 3 5 9 3 3 2 71 | 0 0.57143 0.57143 0.85714 0.85714 0.85714 0.85714 0.85714 0.85714 0 0 0 0 0.05263 0.05263 0 0.02632 0 7 6 4 4 5 6 3 4 4 72 | 0.33333 0.55556 0.88889 0.88889 0.88889 1 0.77778 0.88889 0.88889 0 0 0.02778 0.02778 0.08333 0.11111 0 0.02778 0 7 6 4 4 6 7 4 3 1 73 | 0.11111 0.44444 0.33333 0.66667 0.77778 0.88889 0.66667 0.77778 0.88889 0 0 0 0.02778 0.05556 0.05556 0 0.02778 0.02778 9 7 9 8 9 5 7 8 4 74 | 0.375 0.5 0.875 0.875 0.875 1 0.875 0.875 1 0 0 0 0 0 0.05405 0 0 0.02703 6 6 1 1 1 2 2 1 2 75 | 0 0 0.28571 0.57143 0.85714 1 0.42857 0.85714 1 0 0 0 0 0 0.02632 0 0.02632 0 7 7 7 5 3 2 5 4 1 76 | 0 0.09091 0.81818 0.72727 0.90909 1 0.81818 0.72727 1 0 0 0.02941 0.08824 0 0.08824 0.05882 0 0 11 11 5 10 5 7 10 8 3 77 | 0.25 0.25 0.5 0.625 0.875 0.875 0.625 0.875 0.875 0 0 0 0.02703 0.02703 0.02703 0 0 0 8 6 4 6 8 9 6 5 3 78 | 0.15385 0.30769 0.61538 0.76923 0.76923 0.92308 0.69231 0.69231 0.84615 0 0 0 0.0625 0.0625 0.0625 0.03125 0 0.03125 12 11 8 8 7 4 8 5 4 79 | 0.25 0.625 0.625 0.75 1 1 0.75 1 1 0 0 0.02703 0 0.02703 0.05405 0 0 0 6 3 4 2 1 2 2 0 0 80 | 0 0.2 0.5 0.6 0.9 0.8 0.6 0.7 0.8 0 0 0 0.02857 0 0 0 0.02857 0 10 9 8 6 3 4 5 6 4 81 | 0.25 0.33333 0.33333 0.83333 0.58333 0.91667 0.83333 0.58333 1 0 0.0303 0.0303 0.0303 0.06061 0.09091 0.0303 0.0303 0 10 11 11 8 10 8 6 11 3 82 | 0.1 0.4 0.8 0.8 0.9 0.9 0.9 0.8 0.9 0 0 0 0.02857 0.02857 0.05714 0.02857 0 0 10 7 3 6 4 5 4 4 1 83 | 0 0.16667 1 0.66667 1 1 0.66667 1 1 0 0 0 0.02564 0.02564 0.05128 0 0.02564 0 6 5 0 5 4 7 2 6 0 84 | 0.14286 0.5 0.57143 0.85714 0.85714 0.92857 0.71429 0.92857 0.78571 0 0 0.03226 0 0.06452 0.19355 0.06452 0 0 13 11 10 5 8 10 8 3 4 85 | 0 0.18182 0.36364 0.54545 0.72727 1 0.36364 0.63636 0.90909 0 0 0 0.02941 0.02941 0.08824 0 0.02941 0.02941 11 10 9 7 11 8 8 10 5 86 | 0.125 0.375 0 0.5 0.875 0.625 0.625 0.875 0.875 0 0 0 0.02703 0.05405 0.08108 0.02703 0 0.10811 8 5 8 6 5 6 6 3 7 87 | 0.23077 0.46154 0.69231 0.76923 0.84615 0.84615 0.76923 0.84615 0.84615 0 0 0.03125 0.09375 0.09375 0.15625 0 0 0 13 8 5 6 5 7 3 2 2 88 | 0 0.5 0.5 0.5 0.75 0.875 0.625 0.75 0.875 0 0 0.05405 0.02703 0.05405 0.10811 0 0.02703 0 8 4 8 6 4 10 4 3 3 89 | 0 0.15385 0.61538 0.76923 0.84615 0.84615 0.69231 0.76923 0.76923 0 0 0 0.03125 0.03125 0.09375 0 0 0.03125 13 13 5 8 9 10 9 9 11 90 | 0.16667 0.5 0.66667 0.83333 0.83333 1 0.83333 0.83333 1 0 0 0.02564 0 0.02564 0.07692 0 0 0.02564 5 4 5 3 4 4 3 3 2 91 | 0.25 0.58333 0.5 0.75 0.75 0.75 0.58333 0.58333 0.83333 0 0 0 0 0 0.0303 0 0.0303 0 10 7 8 5 5 6 7 8 4 92 | 0.1 0.5 0.3 0.9 0.9 0.8 0.8 0.9 0.9 0 0 0.02857 0.05714 0.08571 0.08571 0 0.02857 0.05714 10 10 10 6 5 7 4 5 10 93 | 0.25 0.5 0.375 0.75 1 0.875 0.625 1 0.875 0 0 0.02703 0 0 0.02703 0 0 0 7 7 8 3 0 2 5 0 1 94 | 0.13333 0.33333 0.33333 0.6 0.66667 0.6 0.53333 0.66667 0.6 0 0 0 0.06667 0.13333 0.13333 0.06667 0 0.1 15 13 15 10 13 13 13 9 12 95 | 0.14286 0.28571 0.57143 0.78571 0.85714 0.85714 0.71429 0.78571 0.78571 0 0 0.03226 0 0.03226 0.03226 0 0 0 14 13 12 8 4 4 7 4 5 96 | 0.33333 0.33333 0.66667 0.88889 0.88889 1 0.66667 0.77778 0.88889 0 0 0 0.05556 0.05556 0.05556 0 0.02778 0 7 8 5 4 4 3 5 3 4 97 | 0.08333 0.25 0.5 0.58333 0.75 0.91667 0.58333 0.66667 0.83333 0 0 0.0303 0.0303 0.06061 0.0303 0 0.0303 0.0303 12 11 9 9 5 5 7 7 5 98 | 0 0.33333 0.83333 0.83333 1 1 0.66667 0.83333 1 0 0 0.02564 0 0.05128 0.02564 0 0.02564 0 6 4 3 2 5 3 3 3 0 99 | 0.22222 0.44444 0.77778 0.77778 0.88889 0.88889 0.77778 0.88889 0.88889 0 0 0.02778 0.02778 0.08333 0.16667 0 0 0.02778 7 6 3 3 5 10 2 2 2 100 | 0.16667 0.83333 0.83333 0.66667 1 1 1 1 1 0 0 0 0.02564 0.02564 0.05128 0.02564 0 0 5 1 1 3 1 2 5 2 0 101 | -------------------------------------------------------------------------------- /results/causal_discovery/TPR_FPR_SHD_p10_all_conti.txt: -------------------------------------------------------------------------------- 1 | 0 0.36364 0.54545 0.54545 0.63636 0.72727 0.54545 0.63636 0.72727 0 0 0 0.05882 0.05882 0.08824 0.02941 0 0 11 8 7 9 8 8 8 7 5 2 | 0.22222 0.44444 0.66667 0.77778 1 1 0.88889 1 1 0 0 0 0.02778 0.02778 0.02778 0 0 0 9 5 3 3 2 2 2 1 0 3 | 0.25 0.5 0.5 0.625 0.625 0.75 0.625 0.625 0.75 0 0 0 0.02703 0.05405 0.05405 0.05405 0 0 8 7 7 6 7 6 10 5 5 4 | 0 0.23529 0.47059 0.64706 0.76471 0.88235 0.41176 0.82353 0.82353 0 0 0 0.07143 0.03571 0.03571 0.07143 0 0 17 17 11 9 6 5 13 4 5 5 | 0.33333 0.66667 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0.88889 0 0 0 0.08333 0.13889 0.11111 0 0 0 6 3 1 11 9 9 3 1 1 6 | 0.5 0.58333 0.5 0.66667 0.58333 0.83333 0.75 0.83333 0.83333 0 0 0 0 0.15152 0.15152 0 0.06061 0.0303 8 8 8 8 12 9 8 6 7 7 | 0.08333 0.5 0.58333 0.66667 0.91667 0.91667 0.75 0.91667 0.83333 0 0 0 0.09091 0 0.12121 0 0 0.0303 12 11 8 12 5 8 6 4 7 8 | 0.35294 0.35294 0.41176 0.58824 0.76471 0.82353 0.52941 0.82353 0.70588 0.03571 0 0 0.10714 0.10714 0.14286 0.03571 0 0 14 12 14 10 7 8 10 3 5 9 | 0.44444 0.66667 0.55556 0.77778 0.88889 1 0.77778 0.88889 1 0 0 0.02778 0.05556 0 0.02778 0.02778 0 0.02778 8 6 9 9 3 3 8 4 4 10 | 0.28571 0.57143 0.42857 0.85714 1 1 0.71429 1 1 0 0 0 0 0.02632 0.02632 0 0.05263 0.05263 6 5 5 3 3 2 4 6 3 11 | 0.625 0.5 0.5 1 1 1 0.875 0.875 1 0 0 0.02703 0.02703 0.05405 0.08108 0.02703 0 0.02703 5 5 6 1 4 3 2 1 1 12 | 0.4 0.6 0.6 0.8 0.8 0.9 0.8 0.8 0.9 0 0 0 0.05714 0.08571 0.08571 0 0 0 9 6 8 5 8 4 4 4 2 13 | 0.33333 0.44444 0.66667 0.88889 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0.05882 0 0.02941 0.02941 10 5 5 2 5 4 3 6 5 66 | 0.66667 0.5 0.33333 0.83333 1 1 0.83333 1 1 0 0.02564 0 0.02564 0.02564 0.07692 0 0 0 4 6 5 2 1 3 1 0 0 67 | 0.33333 0.33333 0.66667 0.88889 1 1 1 1 1 0 0 0 0.05556 0.08333 0.13889 0 0.02778 0 7 7 3 6 5 9 4 2 1 68 | 0.75 0.75 0.875 1 0.875 1 1 1 1 0 0 0 0.02703 0 0.02703 0 0 0 4 4 4 2 2 2 1 0 1 69 | 0.33333 0.5 0.5 0.75 1 1 0.75 0.75 1 0 0 0 0 0.0303 0.06061 0.0303 0 0 11 6 6 4 4 6 9 8 2 70 | 0.5 0.5 0.66667 1 1 1 1 1 1 0.02564 0.02564 0 0 0.05128 0.10256 0 0.02564 0.02564 4 4 4 0 7 6 0 2 1 71 | 0.22222 0.77778 0.77778 0.88889 1 0.77778 0.88889 1 1 0 0 0 0.02778 0 0.02778 0.02778 0 0.05556 9 2 2 4 0 3 3 0 2 72 | 0.4 0.6 0.8 0.8 1 1 0.8 1 1 0 0 0 0.025 0 0.025 0 0.05 0 4 3 1 2 0 1 1 3 0 73 | 0.54545 0.63636 0.72727 0.90909 0.81818 0.81818 0.81818 0.90909 0.81818 0 0 0 0 0.08824 0.02941 0 0 0.02941 9 6 5 4 8 5 4 4 4 74 | 0.46154 0.46154 0.61538 0.69231 0.84615 0.92308 0.61538 0.84615 0.84615 0 0 0 0 0.09375 0.0625 0 0 0 9 9 7 5 7 3 7 4 2 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0.57143 0.85714 1 1 1 1 1 1 0 0 0 0.05263 0 0.05263 0.02632 0 0 6 5 1 5 2 2 4 2 0 85 | 0.36364 0.27273 0.54545 0.72727 0.81818 1 0.63636 0.81818 1 0 0 0.02941 0.02941 0.02941 0.02941 0 0 0 11 10 8 5 3 5 5 4 1 86 | 0.375 0.625 0.75 0.75 1 1 0.875 1 1 0 0 0 0.05405 0.02703 0.08108 0 0 0 6 3 2 6 2 10 3 0 0 87 | 0.23077 0.38462 0.69231 0.76923 0.84615 0.84615 0.76923 0.76923 0.76923 0 0 0 0.0625 0.03125 0.03125 0 0.03125 0 11 10 4 6 4 3 3 4 3 88 | 0.5 0.25 0.875 0.875 0.875 0.875 0.875 0.875 0.875 0 0 0 0.02703 0.08108 0.08108 0 0.02703 0 8 7 2 3 6 6 2 3 3 89 | 0.44444 0.55556 0.66667 0.88889 0.88889 0.88889 0.88889 0.77778 0.88889 0 0 0 0 0.05556 0.02778 0 0.02778 0 7 6 5 2 4 3 2 6 1 90 | 0.22222 0.33333 0.33333 0.77778 1 1 0.77778 0.66667 0.88889 0 0 0 0.02778 0.05556 0.05556 0 0 0 8 8 8 6 5 5 4 3 3 91 | 0.44444 0.55556 0.88889 0.77778 1 1 0.55556 1 1 0 0 0 0 0.05556 0.02778 0 0 0 8 6 2 3 2 1 7 0 0 92 | 0.13333 0.4 0.33333 0.66667 0.73333 0.73333 0.66667 0.73333 0.73333 0.03333 0 0 0.06667 0.13333 0.1 0 0.06667 0 14 11 11 10 13 10 8 8 7 93 | 0.83333 0.5 0.83333 1 1 1 1 1 1 0 0 0 0 0.05128 0.10256 0 0 0.10256 6 4 2 2 3 6 2 2 6 94 | 0.4 0.8 1 0.8 1 1 0.8 1 1 0 0 0 0 0.025 0 0.025 0.05 0.025 3 3 0 3 2 0 4 4 3 95 | 0.375 0.5 1 1 1 1 1 1 1 0 0 0 0 0.05405 0.02703 0 0 0 7 4 1 1 5 4 1 3 1 96 | 0.21429 0.35714 0.57143 0.78571 0.64286 0.78571 0.78571 0.64286 0.71429 0 0.03226 0 0.06452 0.12903 0.12903 0 0 0.03226 12 13 9 8 11 10 6 7 9 97 | 0.07692 0.23077 0.30769 0.76923 0.92308 0.84615 0.69231 0.69231 0.76923 0.03125 0 0 0.09375 0.15625 0.15625 0 0.03125 0 14 12 10 11 13 12 7 8 3 98 | 0.55556 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 1 0 99 | 0.23077 0.53846 0.61538 0.61538 0.84615 0.84615 0.76923 0.84615 0.84615 0 0 0.03125 0.03125 0.03125 0.1875 0.09375 0 0 13 8 10 10 6 10 9 5 3 100 | 0.53846 0.46154 0.53846 0.84615 0.84615 0.84615 0.84615 0.84615 0.84615 0 0 0 0 0.03125 0.125 0.03125 0.03125 0.03125 8 9 9 5 4 7 7 4 4 101 | 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0.83333 0.83333 0.83333 1 0.66667 0.83333 1 0.05128 0 0 0 0 0 0.02564 0.02564 0 6 5 1 3 1 0 5 4 0 16 | 0.33333 0.58333 0 0.75 0.75 0.83333 0.83333 0.75 0.83333 0.0303 0 0 0.0303 0.09091 0.0303 0.06061 0 0 12 8 12 8 9 7 7 4 4 17 | 0.3 0.4 0.5 0.8 1 0.8 0.7 1 0.8 0.02857 0 0 0 0.14286 0.11429 0 0 0 10 8 8 5 6 7 3 0 3 18 | 0.3 0.3 0.7 1 1 1 0.8 1 1 0.02857 0 0 0.02857 0.02857 0.05714 0.02857 0.02857 0 9 8 5 7 5 4 5 5 2 19 | 0.44444 0.55556 0.44444 0.77778 0.88889 1 0.88889 1 1 0 0 0 0 0 0.05556 0 0 0 5 7 8 3 4 2 4 5 0 20 | 0.16667 0.33333 0.33333 0.66667 0.75 0.83333 0.66667 0.75 0.91667 0 0 0.0303 0 0 0.06061 0 0 0.0303 11 9 10 6 5 6 5 5 5 21 | 0.55556 0.33333 0.33333 0.66667 0.88889 1 0.77778 0.88889 1 0 0.05556 0 0.02778 0.08333 0.05556 0.02778 0 0.02778 6 9 6 3 7 4 6 3 4 22 | 0.4 0.3 0.5 1 1 1 0.9 0.9 1 0 0 0.05714 0.02857 0.05714 0 0 0 0 8 8 11 4 8 4 4 4 4 23 | 0.38462 0.38462 0.30769 0.61538 0.76923 0.84615 0.69231 0.69231 0.92308 0 0 0.03125 0.03125 0.09375 0.03125 0.0625 0 0 8 11 13 9 13 5 11 7 7 24 | 0.33333 0.66667 0.77778 1 1 1 0.88889 1 1 0 0.02778 0.02778 0 0.05556 0.02778 0 0 0 7 7 7 4 4 1 1 0 0 25 | 0.23077 0.30769 0.53846 0.61538 0.69231 0.84615 0.84615 0.69231 0.84615 0 0 0 0 0.03125 0.03125 0.03125 0 0 11 11 10 5 6 4 7 5 3 26 | 0.44444 0.44444 0.44444 0.88889 1 1 0.77778 0.88889 1 0 0 0.02778 0.08333 0.02778 0.02778 0.05556 0 0.02778 7 8 8 6 2 1 4 2 1 27 | 0.625 0.625 0.875 0.875 0.875 0.875 0.875 0.875 0.875 0 0 0 0 0.05405 0 0.02703 0.02703 0.05405 4 5 3 3 5 3 7 7 7 28 | 0.5 0.75 0.75 0.75 1 1 0.75 1 1 0 0 0.02439 0 0.04878 0.04878 0.02439 0.04878 0 4 4 5 3 2 3 4 3 0 29 | 0.55556 0.55556 0.44444 0.77778 0.88889 0.88889 0.88889 0.88889 0.88889 0 0 0 0.02778 0 0.02778 0 0.02778 0 5 6 5 5 3 5 4 5 2 30 | 0.36364 0.18182 0.27273 0.81818 0.81818 1 0.72727 0.81818 0.90909 0 0 0 0 0.05882 0.11765 0 0.02941 0.02941 10 11 9 5 8 9 5 5 5 31 | 0.55556 0.33333 0.55556 1 0.88889 0.88889 1 1 1 0 0 0.02778 0.05556 0.05556 0.11111 0.02778 0.05556 0.08333 6 6 7 3 7 4 1 5 5 32 | 0.375 0.5 0.5 0.75 0.875 1 0.75 0.875 1 0 0.02703 0 0 0.02703 0 0.02703 0 0 5 7 5 5 3 6 6 3 4 33 | 0.28571 0.28571 0.42857 1 1 1 1 1 1 0 0 0 0.02632 0.07895 0.10526 0.02632 0.02632 0.05263 7 5 4 1 3 4 1 1 2 34 | 0.25 1 1 1 1 1 1 1 1 0 0 0 0.02703 0.02703 0.05405 0.02703 0 0 6 1 0 1 2 2 2 1 0 35 | 0.27273 0.45455 0.63636 0.72727 0.81818 1 0.81818 0.81818 1 0 0.02941 0 0.02941 0.05882 0.08824 0.02941 0 0.02941 8 9 6 6 5 3 4 3 1 36 | 0.3 0.6 0.4 0.9 1 1 0.9 0.8 1 0 0 0.02857 0.02857 0 0 0 0 0 9 7 8 5 2 4 5 4 4 37 | 0.18182 0.36364 0.36364 0.90909 0.90909 0.90909 0.90909 0.90909 1 0 0 0 0.02941 0.11765 0 0 0.02941 0 10 8 9 8 10 4 6 7 2 38 | 0.23529 0.17647 0.23529 0.58824 0.64706 0.70588 0.64706 0.70588 0.70588 0 0.07143 0.03571 0.03571 0.10714 0.10714 0.07143 0.07143 0.03571 17 18 17 12 17 16 14 9 9 39 | 0.375 0.5 0.5 0.875 0.875 0.875 0.875 0.875 0.875 0.02703 0 0.02703 0 0.02703 0 0 0 0.02703 6 7 6 1 4 1 3 1 2 40 | 0.33333 0.55556 0.77778 0.77778 0.77778 0.88889 0.77778 0.77778 0.88889 0 0.02778 0 0 0.02778 0.02778 0 0.02778 0.08333 9 5 3 6 4 3 4 4 7 41 | 0.5 0.5 0.5 0.66667 1 1 0.66667 0.83333 1 0.02564 0.02564 0.02564 0.05128 0.05128 0 0 0 0.02564 5 4 5 6 3 0 5 0 2 42 | 0.375 0.375 0.375 1 1 1 1 1 1 0 0 0.02703 0 0.02703 0.05405 0.05405 0.02703 0.02703 5 6 6 6 6 3 7 6 2 43 | 0.66667 0.33333 0.33333 0.83333 0.83333 0.83333 0.83333 1 0.83333 0.02564 0.02564 0.02564 0 0 0.07692 0.05128 0 0.02564 3 6 5 1 0 4 3 1 2 44 | 0.18182 0.36364 0.27273 0.72727 0.90909 0.90909 0.81818 0.81818 0.81818 0.02941 0.02941 0 0.02941 0 0.02941 0.02941 0 0 12 10 11 4 3 4 6 1 1 45 | 0.14286 0.42857 0.42857 0.85714 0.85714 0.71429 0.71429 0.71429 0.71429 0.02632 0 0.02632 0 0.05263 0.05263 0.02632 0 0.02632 8 4 6 2 5 5 4 2 4 46 | 0.21429 0.14286 0.28571 0.71429 0.78571 0.85714 0.71429 0.78571 0.85714 0 0 0.03226 0 0.03226 0 0.03226 0 0 14 14 15 6 6 7 9 5 7 47 | 0.55556 0.44444 0.22222 0.88889 0.88889 1 0.88889 0.88889 0.77778 0.02778 0.02778 0 0 0 0.08333 0.05556 0 0 8 7 8 3 2 7 6 2 1 48 | 0.54545 0.54545 0.27273 0.72727 0.81818 0.81818 0.72727 0.72727 0.81818 0 0 0 0.02941 0.02941 0 0 0.02941 0 8 7 11 7 7 4 4 6 4 49 | 0.5 0.5 0.3 1 1 1 1 0.9 1 0 0 0 0.02857 0.02857 0.05714 0 0 0 7 8 8 2 2 2 1 1 0 50 | 0.5 0.66667 0.5 0.83333 1 0.83333 0.83333 1 0.83333 0 0 0.05128 0 0.02564 0.02564 0 0 0.05128 4 3 6 1 1 2 1 0 3 51 | 0.2 0.13333 0.13333 0.66667 0.8 0.8 0.8 0.8 0.86667 0 0.06667 0.03333 0.06667 0.03333 0.03333 0 0.06667 0.06667 15 16 15 13 7 5 10 13 12 52 | 0.09091 0.27273 0.09091 0.72727 0.72727 0.81818 0.72727 0.72727 0.81818 0.02941 0 0 0 0.08824 0.08824 0.02941 0 0 11 9 11 8 10 7 6 7 6 53 | 0.44444 0.55556 0.77778 0.88889 0.88889 0.88889 0.88889 1 0.77778 0 0 0 0 0 0.02778 0.02778 0 0.02778 8 6 2 2 1 3 3 1 6 54 | 0.33333 0.33333 0.25 0.75 0.75 0.83333 0.66667 0.75 0.83333 0.0303 0 0 0.09091 0.12121 0.09091 0 0.06061 0 12 8 10 11 11 8 5 6 2 55 | 0.16667 0.33333 0.5 0.66667 0.75 0.83333 0.83333 0.75 0.91667 0 0 0.0303 0.06061 0.0303 0.09091 0.0303 0 0 10 8 7 9 7 10 5 4 2 56 | 0.44444 0.44444 0.33333 1 1 1 1 1 1 0.02778 0 0 0 0.05556 0.02778 0.02778 0.02778 0.02778 8 8 7 5 8 3 6 8 1 57 | 0.6 0.3 0.4 0.9 0.9 1 0.9 0.8 0.9 0 0 0.02857 0.08571 0.08571 0.11429 0.05714 0.05714 0.05714 7 8 8 10 6 5 9 8 4 58 | 0.66667 0.33333 0.5 1 1 1 0.83333 1 1 0 0 0 0.05128 0.05128 0.10256 0 0 0.02564 2 4 3 5 8 9 2 0 7 59 | 0.2 0.2 0.3 0.6 0.9 1 0.7 0.9 1 0 0 0 0.02857 0.05714 0.08571 0 0.02857 0 9 9 9 8 5 6 8 5 1 60 | 0.54545 0.27273 0.63636 0.81818 0.90909 0.90909 0.81818 0.90909 1 0 0 0.02941 0 0.14706 0.02941 0 0.05882 0 6 10 5 3 8 1 5 7 4 61 | 0.33333 0.5 0.83333 0.66667 0.66667 1 0.66667 0.83333 1 0.05128 0.02564 0.02564 0.02564 0 0.02564 0.02564 0 0.02564 7 5 3 4 2 2 4 3 3 62 | 0.44444 0.33333 0.55556 0.77778 0.66667 0.77778 0.88889 0.77778 0.66667 0 0 0 0.02778 0.08333 0.05556 0 0.08333 0.02778 6 7 4 3 6 6 5 8 4 63 | 0.57143 0.71429 0.71429 0.85714 0.85714 1 0.85714 0.85714 0.85714 0 0 0.05263 0 0 0 0 0.05263 0.07895 6 3 6 2 1 1 1 5 6 64 | 0.3 0.8 0.3 1 1 1 0.9 1 1 0 0 0 0 0 0.02857 0 0 0.02857 9 3 8 3 0 1 1 0 2 65 | 0.66667 0.66667 0.83333 0.83333 0.83333 1 0.83333 0.83333 0.83333 0 0 0 0 0.02564 0.02564 0 0.05128 0.05128 4 4 1 1 5 4 1 5 5 66 | 0.6 0.6 0.4 0.8 0.9 1 0.9 0.8 1 0 0 0.02857 0 0.02857 0 0 0 0.02857 7 7 9 4 9 6 3 7 7 67 | 0.44444 0.55556 0.88889 0.77778 1 1 1 1 1 0 0 0 0 0.02778 0 0 0 0 8 6 7 4 4 4 7 2 2 68 | 0.57143 0.57143 0.57143 1 0.85714 1 1 0.85714 1 0 0 0.02632 0 0 0 0 0.02632 0 4 3 5 0 1 0 0 2 0 69 | 0.41667 0.41667 0.33333 0.91667 0.91667 0.91667 0.91667 0.91667 1 0 0 0 0.06061 0.09091 0.09091 0 0 0.0303 9 10 9 8 5 4 5 2 4 70 | 0.2 0.2 0.26667 0.73333 0.86667 0.8 0.73333 0.8 0.73333 0 0 0 0.06667 0.06667 0.06667 0.06667 0.03333 0.06667 14 14 15 9 8 10 12 7 5 71 | 0.42857 0.71429 1 1 1 1 1 1 1 0.02632 0 0 0.02632 0.02632 0 0 0.02632 0 6 4 0 1 1 0 0 3 0 72 | 0.45455 0.27273 0.54545 0.90909 0.90909 0.90909 0.72727 0.90909 0.90909 0 0 0 0.08824 0.08824 0.11765 0.02941 0.02941 0.02941 9 11 8 9 4 7 5 4 4 73 | 0.57143 0.42857 0.71429 1 1 1 0.71429 1 1 0.02632 0 0 0.07895 0.02632 0 0.02632 0 0 5 6 2 6 2 1 2 1 1 74 | 0.15385 0.30769 0.15385 0.76923 0.76923 0.84615 0.76923 0.92308 0.84615 0.03125 0 0 0 0 0.0625 0.03125 0 0.03125 13 12 13 6 3 6 7 5 5 75 | 0.22222 0.44444 0.22222 0.77778 0.77778 0.88889 0.66667 0.77778 0.77778 0 0 0 0 0 0 0 0 0 8 7 8 5 7 6 4 6 5 76 | 0.375 0.5 0.375 0.5 0.875 0.875 0.625 0.75 0.875 0 0.02703 0 0.05405 0.02703 0.05405 0 0 0.02703 8 9 8 7 6 7 7 5 4 77 | 0.1 0.4 0.2 0.8 0.9 0.9 0.8 0.9 0.9 0.02857 0 0.02857 0.02857 0.05714 0.02857 0.02857 0.02857 0 11 7 9 6 9 6 10 6 5 78 | 0.42857 0.57143 0.57143 0.85714 1 1 0.71429 1 1 0 0 0 0 0 0 0 0 0.02632 4 3 3 2 6 0 1 6 2 79 | 0.5 0.375 0.5 0.875 1 1 0.875 1 1 0 0.02703 0.05405 0.05405 0 0.05405 0.05405 0.02703 0 6 6 6 5 2 3 5 3 0 80 | 0.27273 0.54545 0.45455 0.81818 0.81818 0.81818 0.72727 0.81818 0.81818 0 0 0 0.02941 0.02941 0.02941 0.02941 0 0 9 7 7 5 4 4 6 3 3 81 | 0.05882 0.11765 0.17647 0.64706 0.64706 0.76471 0.64706 0.70588 0.70588 0 0 0.07143 0.03571 0.03571 0.07143 0.03571 0 0 17 17 19 11 12 12 10 10 8 82 | 0.36364 0.63636 0.45455 0.81818 0.90909 0.90909 0.72727 0.90909 0.81818 0.02941 0 0.02941 0.05882 0 0.05882 0 0 0.02941 11 7 9 11 7 7 11 7 9 83 | 0.08333 0.33333 0.5 0.91667 0.91667 0.91667 0.75 0.91667 0.91667 0.0303 0.0303 0 0.0303 0 0.0303 0.06061 0 0.0303 13 10 8 5 4 4 4 2 2 84 | 0.2 0.1 0 0.7 0.9 0.9 0.8 0.8 0.8 0 0.05714 0 0 0.08571 0.05714 0 0.02857 0 9 12 10 5 8 5 6 5 1 85 | 0.09091 0.18182 0.18182 0.54545 0.90909 0.90909 0.54545 0.81818 0.90909 0 0 0 0.02941 0.05882 0.02941 0 0 0.02941 10 11 11 10 4 3 5 2 4 86 | 0.4 0.33333 0.4 0.8 0.8 0.86667 0.8 0.86667 0.86667 0 0 0 0 0 0.03333 0 0 0 13 14 13 5 5 5 6 7 5 87 | 0 0.11765 0 0.58824 0.58824 0.64706 0.58824 0.64706 0.76471 0.03571 0 0 0.03571 0.07143 0.07143 0.07143 0.07143 0.07143 18 17 17 9 12 10 10 13 12 88 | 0.2 0.5 0.4 0.7 0.6 0.9 0.6 0.7 0.8 0 0 0 0.02857 0.02857 0.05714 0.02857 0.02857 0.02857 10 7 9 6 5 4 4 5 2 89 | 0.28571 0.28571 0.35714 0.64286 0.85714 0.78571 0.64286 0.85714 0.78571 0 0 0 0.03226 0.06452 0.03226 0.03226 0.03226 0 12 12 13 8 6 9 9 5 8 90 | 0.2 0 0.2 0.6 0.6 0.6 0.6 0.8 0.8 0 0 0 0.025 0.05 0.05 0.075 0 0 4 5 5 4 4 4 6 3 3 91 | 0.07692 0.15385 0.23077 0.76923 0.92308 0.92308 0.76923 0.92308 0.84615 0 0 0 0 0 0.0625 0.0625 0.03125 0 12 11 10 6 5 4 8 6 2 92 | 0.44444 0.66667 0.44444 0.66667 0.66667 0.77778 0.55556 0.66667 0.88889 0 0 0 0.02778 0.05556 0 0 0.02778 0.02778 8 6 6 8 7 4 5 8 6 93 | 0.5 0.16667 0.5 0.83333 1 1 0.83333 1 1 0 0 0.02564 0.05128 0 0 0 0.02564 0 6 6 5 3 1 0 2 1 0 94 | 0.07692 0.15385 0.23077 0.61538 0.76923 0.84615 0.69231 0.76923 0.84615 0.03125 0 0 0.03125 0.03125 0.15625 0.0625 0.03125 0 14 12 12 5 8 9 7 4 2 95 | 0.45455 0.36364 0.36364 0.72727 0.90909 1 0.81818 0.81818 1 0 0 0.02941 0 0.08824 0.02941 0 0 0 9 8 11 6 6 1 4 4 0 96 | 0.16667 0.83333 0.5 0.83333 0.83333 1 0.83333 0.83333 1 0.02564 0 0.02564 0 0.05128 0.05128 0 0.02564 0.02564 6 2 5 1 5 3 3 3 2 97 | 0.25 0.25 0.125 0.5 0.625 0.75 0.625 0.625 0.875 0 0 0 0.02703 0 0 0.02703 0 0.02703 8 8 8 9 5 3 9 5 4 98 | 0.33333 0.11111 0.22222 0.88889 0.77778 1 0.88889 1 1 0 0 0 0 0.08333 0.05556 0 0.11111 0.05556 7 8 8 2 5 6 1 13 2 99 | 0.18182 0.45455 0.27273 0.72727 0.81818 0.90909 0.81818 0.63636 0.90909 0 0 0 0 0.02941 0 0 0 0 10 7 10 5 6 2 3 2 2 100 | 0.14286 0.21429 0.14286 0.71429 0.92857 1 0.71429 0.78571 1 0.03226 0 0 0 0.06452 0.06452 0 0.03226 0 15 14 14 6 6 3 4 2 0 101 | -------------------------------------------------------------------------------- /results/causal_discovery/TPR_FPR_SHD_p4_all.txt: -------------------------------------------------------------------------------- 1 | 0 0.4 0.8 1 1 1 0.6 1 1 0 0 0 1 1 1 0 0 0 5 3 1 1 1 1 2 3 3 2 | 0.5 0.75 0.75 0.75 0.75 1 1 0.75 1 0 0.5 0 0 0 0 0 0 0 2 3 4 4 2 0 0 2 0 3 | 0.25 0.5 1 1 1 1 0.75 1 1 0 0 0 0 0 0.5 0 0 0 3 4 0 3 4 3 1 0 0 4 | 0.5 0.75 0.75 0.5 0.75 1 0.5 0.75 0.75 0 0.5 0.5 0.5 0.5 0.5 0 0 0 2 4 3 3 3 1 2 1 1 5 | 0.2 0.4 1 0.6 0.8 0.8 0.6 0.6 0.8 0 0 1 0 0 0 0 0 0 5 3 4 3 3 3 3 2 3 6 | 0.25 0.75 0.75 0.5 0.75 1 0.5 0.75 1 0 0 0 0.5 0.5 0 0.5 0 0 3 1 4 4 4 3 4 1 3 7 | 0.2 0.4 0.6 0.6 0.8 1 0.6 0.8 0.6 0 0 0 0 0 0 0 0 0 4 3 4 4 4 0 4 4 2 8 | 0.25 0.75 1 0.75 0.75 0.75 0.75 0.75 0.75 0 0 0.5 0.5 0 0.5 0 0 0 4 2 1 2 2 2 2 2 2 9 | 0.5 0 0.75 0.75 0.75 1 0.5 0.75 1 0 0 0 0 0 0 0 0 0 3 4 3 3 3 0 3 3 0 10 | 0.75 0.75 1 0.75 0.75 0.75 0.75 0.75 0.75 0 0 0 0.5 0.5 0.5 0 0 0 3 1 0 4 5 2 3 1 1 11 | 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 12 | 0.4 1 0.6 0.8 0.6 1 0.8 0.6 0.6 0 0 1 0 0 0 0 0 0 4 0 5 2 3 0 2 3 3 13 | 0.25 0.5 0.75 0.75 1 1 0.5 0.75 1 0 0.5 0 0.5 0 0 0.5 0 0 3 4 4 3 0 2 3 1 1 14 | 0.33333 1 1 0.66667 0.66667 1 0.66667 0.33333 1 0 0.66667 0.33333 0 0 0.33333 0 0 0 2 4 4 1 3 1 1 2 0 15 | 0.75 0.75 0.75 0.75 0.75 0.75 0.75 1 0.75 0 0 0 0.5 0.5 0.5 0 0 0 3 3 3 4 5 5 3 0 1 16 | 0 0.5 0.75 0.75 1 1 0.75 1 1 0 0 0 0 0.5 0 0 0 0 4 2 1 1 4 0 1 0 0 17 | 0.16667 0.66667 0.5 0.83333 0.83333 0.83333 0.66667 0.83333 0.66667 NA NA NA NA NA NA NA NA NA 5 2 3 4 1 1 4 1 4 18 | 0.6 1 1 1 1 0.8 0.6 1 0.8 0 0 0 0 1 1 0 0 0 2 0 0 3 1 2 2 0 3 19 | 0.33333 1 1 1 1 1 1 1 1 0 0.33333 0 0.33333 0 0 0 0 0 2 4 0 1 0 0 0 0 0 20 | 0.5 0.5 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 4 4 6 2 2 2 2 2 2 21 | 0.25 0.75 0.75 0.75 1 1 0.75 0.75 1 0 0 0 0 0.5 0 0 0 0 3 4 1 1 4 0 1 1 0 22 | 0.75 0.5 1 0.75 1 1 0.75 1 1 0 0 0 0 0 0 0 0 0 4 4 0 3 0 0 3 0 0 23 | 0.2 0.4 0.8 0.6 0.8 1 0.6 0.8 0.8 0 0 0 1 1 1 1 0 0 4 3 3 3 4 1 3 5 3 24 | 0.25 0.25 0.5 0.75 0.75 1 0.5 0.75 0.75 0 0.5 0.5 0.5 1 0 0 0 0 3 4 3 4 3 0 4 1 1 25 | 0.25 0 0.75 0.75 0.5 1 0.5 0.5 1 0 0 0 0.5 0.5 0 0.5 0 0 4 4 1 3 4 0 5 4 0 26 | 0.5 0.75 1 1 1 1 0.75 1 1 0 0 1 0.5 0.5 0.5 0 0 0 2 4 4 1 3 3 2 0 0 27 | 0.4 0.4 0.8 0.6 0.8 0.8 0.6 0.8 0.8 0 0 0 0 0 1 0 0 0 3 5 4 2 3 2 2 4 3 28 | 0.5 0.5 1 0.5 1 1 0.5 1 1 0 0 0.25 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 29 | 0 1 1 1 1 1 1 1 1 0 0 0 0 0.33333 0 0 0 0 3 1 0 0 4 0 0 1 0 30 | 0.33333 0.66667 1 0.66667 1 1 1 1 1 0 0 0 0 0.33333 0 0 0 0 3 3 0 1 1 0 1 0 0 31 | 0.4 0.2 0.8 1 0.8 1 0.8 0.8 1 0 0 0 0 1 1 0 0 0 3 4 4 3 2 1 3 1 0 32 | 0.6 0.8 0.6 0.8 1 1 0.6 0.6 1 0 1 0 0 1 1 0 0 0 2 4 2 1 1 1 2 2 0 33 | 0 0.4 1 0.8 1 1 0.8 0.8 0.8 0 0 0 0 0 0 0 0 0 5 3 0 3 5 5 3 3 3 34 | 0.5 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 2 0 2 0 2 2 0 0 35 | 0.33333 1 1 1 1 1 1 1 1 0 0.33333 0 0.33333 0.33333 0.33333 0 0 0 2 1 0 1 1 1 0 0 0 36 | 0.16667 1 0.83333 0.83333 0.83333 0.83333 0.5 0.83333 1 NA NA NA NA NA NA NA NA NA 5 0 4 5 4 4 3 4 0 37 | 0.33333 0.33333 0.66667 1 1 1 1 1 1 0 0 0.33333 0 0 0 0 0 0 2 2 2 0 3 2 0 2 2 38 | 0.2 0.4 0.6 1 1 1 0.8 0.8 0.8 0 0 0 0 0 0 0 0 0 4 5 3 0 3 3 3 3 3 39 | 0.5 0 0.5 0.5 1 1 0.5 1 1 0 0.25 0 0 0 0 0 0 0 2 3 2 2 0 0 2 0 0 40 | 0.2 0.4 0.2 0.8 0.6 0.8 0.8 0.6 0.8 0 0 0 0 1 1 0 0 0 4 3 4 4 3 2 4 2 3 41 | 0.33333 1 0.33333 1 1 1 1 1 1 0 0 0 0.33333 0.33333 0.66667 0 0 0 2 0 2 1 1 2 2 0 0 42 | 0.5 1 1 0.75 0.75 1 0.75 0.75 0.75 0 0.5 0 0 0.5 0.5 0 0 0 2 1 0 1 2 4 1 1 1 43 | 0.5 0.5 1 0.75 1 1 0.75 1 0.75 0 0 0.5 0.5 0.5 0.5 0 0 0 2 2 3 5 4 3 1 0 1 44 | 0 0.25 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 4 3 2 0 0 0 0 0 0 45 | 0.2 0.4 1 0.6 0.8 0.8 0.6 0.6 0.8 0 0 0 0 0 0 0 0 0 4 4 0 4 2 2 4 4 2 46 | 0.25 0.5 1 0.75 0.75 0.75 0.75 0.75 0.75 0 0 0 0 0 0 0 0 0 3 4 4 4 4 1 4 4 1 47 | 0.66667 1 1 1 1 1 1 1 1 0 0.33333 0 0 0.33333 0.33333 0 0 0 3 2 0 0 1 1 0 0 0 48 | 0.33333 0.66667 1 0.33333 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 1 0 2 0 0 0 0 0 49 | 0.5 0.75 0.5 1 1 1 0.75 1 1 0 0 0 0 0 0 0 0 0 4 4 4 2 2 2 2 2 2 50 | 0 0.75 1 0.75 0.75 0.75 0.75 0.75 0.75 0 0 0.5 0 0 0 0 0 0 4 1 4 3 3 1 3 1 1 51 | 0.2 0.4 0.8 0.8 0.8 0.8 0.6 0.8 0.6 0 0 0 1 1 1 0 0 0 4 3 1 2 4 4 2 3 4 52 | 0.4 0.2 0.6 1 1 1 0.6 0.8 0.6 0 0 0 0 0 0 0 0 0 4 4 4 0 0 0 3 2 3 53 | 0.25 0.5 1 0.75 0.75 0.75 0.5 0.75 0.75 0 0.5 1 0 1 1 0 0 0 3 5 2 4 3 4 2 1 1 54 | 0.5 0.75 0.5 0.5 1 1 0.5 0.75 0.75 0 0.5 0 0 0 0 0 0 0 2 2 2 2 3 4 2 4 4 55 | 0.25 0.5 0.5 1 1 1 0.75 1 1 0 0.5 0 0 0 0.5 0 0 0 3 5 2 4 0 1 1 0 0 56 | 0.5 0.5 0.66667 0.66667 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0.5 0.83333 NA NA NA NA NA NA NA NA NA 4 4 4 4 3 4 2 6 4 29 | 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0 0 0 0 0 0 0 0 0 4 4 2 4 4 4 4 4 4 30 | 0.4 0.4 0.6 0.8 0.8 0.8 0.8 0.8 0.8 0 0 0 1 1 1 0 0 0 5 3 2 4 4 2 5 3 3 31 | 0.33333 0.33333 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0.66667 0 0 0 0 0 0 0 0 0 3 3 2 3 3 2 3 3 2 32 | 0.75 0.75 0.75 1 1 1 0.75 1 1 0 0 0 0 0 0.5 0 0 0 1 1 1 0 0 3 1 0 0 33 | 1 1 1 1 1 1 1 1 1 0 0 0 0.2 0 0 0.2 0 0 0 0 0 2 0 0 2 0 0 34 | 1 0.33333 0.66667 0.66667 1 1 1 1 1 0.66667 0.33333 0 0 0 0.33333 0 0 0 3 3 2 2 0 1 0 0 0 35 | 0.66667 0.66667 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 36 | 0.5 0.5 1 1 1 1 1 1 1 0 0.5 0 0 0.5 0.5 0 0 0 2 5 0 0 1 1 0 0 0 37 | 0.33333 0.66667 0.66667 1 1 1 1 1 1 0 0 0 0 0.33333 0.33333 0 0 0 2 1 1 2 3 3 2 2 2 38 | 0.2 0.4 0.4 0.8 1 1 0.6 1 0.8 0 0 0 0 0 1 0 0 0 4 5 3 1 3 1 2 3 1 39 | 0.33333 0.66667 0.66667 1 1 1 1 1 1 0.33333 0 0.33333 0 0 0 0 0 0 4 1 2 1 1 0 1 1 0 40 | 0.4 0.4 0.6 0.8 0.8 1 0.8 0.8 0.8 0 0 0 1 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0.66667 1 1 0.66667 1 1 0 0 0 0 0 0 0 0 0 3 3 1 1 1 1 1 1 1 67 | 0.2 0.4 0.4 0.8 0.8 0.8 0.6 0.6 0.8 0 0 0 0 0 0 0 0 0 4 3 3 4 5 5 2 2 5 68 | 0.75 0.75 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 69 | 0 0.6 0.8 0.8 1 1 0.8 0.8 0.8 0 0 0 0 0 1 0 0 0 5 4 3 4 0 4 3 3 3 70 | 0.5 0.25 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 71 | 0.25 0.5 0.5 0.5 0.75 0.75 0.25 0.75 0.75 0 0 0 0 0 0 0 0 0 3 4 4 4 4 3 3 4 3 72 | 0.5 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 73 | 0.25 0.25 0.5 0.5 0.75 0.75 0.25 0.75 0.75 0 0 0.5 0 0 0 0 0 0 3 3 5 2 3 3 3 3 3 74 | 0.5 0.5 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0 0 0 0 0.5 0.5 0 0 0 2 2 1 1 5 5 1 1 1 75 | 0.5 0.25 0.5 1 1 1 1 1 1 0 0 0 0.5 0.5 1 0 0 0.5 2 3 2 3 1 2 0 0 3 76 | 0.33333 0.5 0.5 0.5 0.66667 0.83333 0.5 0.66667 0.83333 NA NA NA NA NA NA NA NA NA 4 5 5 3 6 4 5 6 4 77 | 0.25 0.5 0.75 1 1 1 1 1 0.75 0 0 0 0 0.5 0.5 0 0 0 3 2 1 0 3 3 0 0 1 78 | 0.33333 0.33333 0.83333 0.83333 0.83333 0.83333 0.66667 0.83333 0.83333 NA NA NA NA NA NA NA NA NA 4 4 4 4 4 4 2 4 4 79 | 0.66667 0.66667 1 1 1 1 1 1 1 0 0 0 0 0.33333 0.33333 0 0 0 1 1 0 0 1 1 0 0 0 80 | 0.25 0.75 0.5 1 1 1 0.75 1 1 0 0 0 0 0 0 0 0 0 3 1 2 4 0 0 3 4 4 81 | 0.25 0.75 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 82 | 0.2 0.2 0.6 0.8 1 1 0.8 1 0.8 0 0 0 0 1 1 0 0 0 4 4 2 1 1 1 1 3 1 83 | 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0.25 0 0 0 0 0 0 0 0 1 0 0 0 84 | 0.6 0.2 0.6 0.8 0.8 0.8 0.8 1 0.8 0 0 0 0 1 1 0 0 0 4 5 3 3 6 6 3 0 3 85 | 0.5 0.25 0.5 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 3 4 3 0 0 0 0 0 0 86 | 0.25 0.5 0.75 0.75 0.75 0.75 0.75 1 1 0 0.5 0 0.5 0 0.5 0 0 0 3 5 1 5 1 5 1 0 0 87 | 0.66667 0.33333 0.66667 0.66667 1 1 0.66667 1 1 0 0 0.33333 0 0 0 0 0 0 1 3 2 1 0 0 1 0 0 88 | 0 0.66667 1 1 1 1 1 1 1 0 0 0 0.33333 0.33333 0 0 0 0 3 1 3 4 1 3 3 0 3 89 | 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0.33333 0 0 0 0 0 0 0 0 1 0 0 0 90 | 0.5 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0 0 0 0 0.5 0.5 0 0 0 2 1 1 1 2 2 1 1 1 91 | 0.66667 0.66667 1 1 1 1 1 1 1 0 0 0 0 0 0.33333 0 0 0 2 2 0 0 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