## one way to do it is by adding correlation to x.obs and y that isn't in w.
## in other words, the model is missing an important feature of x.obs that's related to y.
-simulate_data <- function(N, m, B0, Bxy, Bzx, Bzy, seed, y_explained_variance=0.025, prediction_accuracy=0.73, accuracy_imbalance_difference=0.3){
+simulate_data <- function(N, m, B0, Bxy, Bzx, Bzy, seed, y_explained_variance=0.025, prediction_accuracy=0.73, y_bias=-0.8,z_bias=0,accuracy_imbalance_difference=0.3){
set.seed(seed)
# make w and y dependent
- z <- rbinom(N, 1, 0.5)
- x <- rbinom(N, 1, Bzx * z + 0.5)
+ z <- rnorm(N,sd=0.5)
+ x <- rbinom(N, 1, plogis(Bzx * z))
y.var.epsilon <- (var(Bzy * z) + var(Bxy *x) + 2*cov(Bzy*z,Bxy*x)) * ((1-y_explained_variance)/y_explained_variance)
y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon))
df <- df[, x.obs := x]
}
- ## px <- mean(x)
+ ## probablity of an error is correlated with y
+ ## pz <- mean(z)
## accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
## # this works because of conditional probability
- ## accuracy_x0 <- prediction_accuracy / (px*(accuracy_imbalance_ratio) + (1-px))
- ## accuracy_x1 <- accuracy_imbalance_ratio * accuracy_x0
-
- ## x0 <- df[x==0]$x
- ## x1 <- df[x==1]$x
- ## nx1 <- nrow(df[x==1])
- ## nx0 <- nrow(df[x==0])
-
- ## yx0 <- df[x==0]$y
- ## yx1 <- df[x==1]$y
-
- # tranform yz0.1 into a logistic distribution with mean accuracy_z0
- ## acc.x0 <- plogis(0.5*scale(yx0) + qlogis(accuracy_x0))
- ## acc.x1 <- plogis(1.5*scale(yx1) + qlogis(accuracy_x1))
-
- ## w0x0 <- (1-x0)**2 + (-1)**(1-x0) * acc.x0
- ## w0x1 <- (1-x1)**2 + (-1)**(1-x1) * acc.x1
- pz <- mean(z)
- accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
-
- # this works because of conditional probability
- accuracy_z0 <- prediction_accuracy / (pz*(accuracy_imbalance_ratio) + (1-pz))
- accuracy_z1 <- accuracy_imbalance_ratio * accuracy_z0
-
- z0x0 <- df[(z==0) & (x==0)]$x
- z0x1 <- df[(z==0) & (x==1)]$x
- z1x0 <- df[(z==1) & (x==0)]$x
- z1x1 <- df[(z==1) & (x==1)]$x
-
- yz0x0 <- df[(z==0) & (x==0)]$y
- yz0x1 <- df[(z==0) & (x==1)]$y
- yz1x0 <- df[(z==1) & (x==0)]$y
- yz1x1 <- df[(z==1) & (x==1)]$y
-
- nz0x0 <- nrow(df[(z==0) & (x==0)])
- nz0x1 <- nrow(df[(z==0) & (x==1)])
- nz1x0 <- nrow(df[(z==1) & (x==0)])
- nz1x1 <- nrow(df[(z==1) & (x==1)])
-
- yz1 <- df[z==1]$y
- yz1 <- df[z==1]$y
-
- # tranform yz0.1 into a logistic distribution with mean accuracy_z0
- acc.z0x0 <- plogis(0.5*scale(yz0x0) + qlogis(accuracy_z0))
- acc.z0x1 <- plogis(0.5*scale(yz0x1) + qlogis(accuracy_z0))
- acc.z1x0 <- plogis(1.5*scale(yz1x0) + qlogis(accuracy_z1))
- acc.z1x1 <- plogis(1.5*scale(yz1x1) + qlogis(accuracy_z1))
-
- w0z0x0 <- (1-z0x0)**2 + (-1)**(1-z0x0) * acc.z0x0
- w0z0x1 <- (1-z0x1)**2 + (-1)**(1-z0x1) * acc.z0x1
- w0z1x0 <- (1-z1x0)**2 + (-1)**(1-z1x0) * acc.z1x0
- w0z1x1 <- (1-z1x1)**2 + (-1)**(1-z1x1) * acc.z1x1
-
- ##perrorz0 <- w0z0*(pyz0)
- ##perrorz1 <- w0z1*(pyz1)
-
- w0z0x0.noisy.odds <- rlogis(nz0x0,qlogis(w0z0x0))
- w0z0x1.noisy.odds <- rlogis(nz0x1,qlogis(w0z0x1))
- w0z1x0.noisy.odds <- rlogis(nz1x0,qlogis(w0z1x0))
- w0z1x1.noisy.odds <- rlogis(nz1x1,qlogis(w0z1x1))
-
- df[(z==0)&(x==0),w:=plogis(w0z0x0.noisy.odds)]
- df[(z==0)&(x==1),w:=plogis(w0z0x1.noisy.odds)]
- df[(z==1)&(x==0),w:=plogis(w0z1x0.noisy.odds)]
- df[(z==1)&(x==1),w:=plogis(w0z1x1.noisy.odds)]
-
- df[,w_pred:=as.integer(w > 0.5)]
- print(mean(df[z==0]$x == df[z==0]$w_pred))
- print(mean(df[z==1]$x == df[z==1]$w_pred))
+ ## accuracy_z0 <- prediction_accuracy / (pz*(accuracy_imbalance_ratio) + (1-pz))
+ ## accuracy_z1 <- accuracy_imbalance_ratio * accuracy_z0
+
+ ## z0x0 <- df[(z==0) & (x==0)]$x
+ ## z0x1 <- df[(z==0) & (x==1)]$x
+ ## z1x0 <- df[(z==1) & (x==0)]$x
+ ## z1x1 <- df[(z==1) & (x==1)]$x
+
+ ## yz0x0 <- df[(z==0) & (x==0)]$y
+ ## yz0x1 <- df[(z==0) & (x==1)]$y
+ ## yz1x0 <- df[(z==1) & (x==0)]$y
+ ## yz1x1 <- df[(z==1) & (x==1)]$y
+
+ ## nz0x0 <- nrow(df[(z==0) & (x==0)])
+ ## nz0x1 <- nrow(df[(z==0) & (x==1)])
+ ## nz1x0 <- nrow(df[(z==1) & (x==0)])
+ ## nz1x1 <- nrow(df[(z==1) & (x==1)])
+
+ ## yz1 <- df[z==1]$y
+ ## yz1 <- df[z==1]$y
+
+ ## # tranform yz0.1 into a logistic distribution with mean accuracy_z0
+ ## acc.z0x0 <- plogis(0.5*scale(yz0x0) + qlogis(accuracy_z0))
+ ## acc.z0x1 <- plogis(0.5*scale(yz0x1) + qlogis(accuracy_z0))
+ ## acc.z1x0 <- plogis(1.5*scale(yz1x0) + qlogis(accuracy_z1))
+ ## acc.z1x1 <- plogis(1.5*scale(yz1x1) + qlogis(accuracy_z1))
+
+ ## w0z0x0 <- (1-z0x0)**2 + (-1)**(1-z0x0) * acc.z0x0
+ ## w0z0x1 <- (1-z0x1)**2 + (-1)**(1-z0x1) * acc.z0x1
+ ## w0z1x0 <- (1-z1x0)**2 + (-1)**(1-z1x0) * acc.z1x0
+ ## w0z1x1 <- (1-z1x1)**2 + (-1)**(1-z1x1) * acc.z1x1
+
+ ## ##perrorz0 <- w0z0*(pyz0)
+ ## ##perrorz1 <- w0z1*(pyz1)
+
+ ## w0z0x0.noisy.odds <- rlogis(nz0x0,qlogis(w0z0x0))
+ ## w0z0x1.noisy.odds <- rlogis(nz0x1,qlogis(w0z0x1))
+ ## w0z1x0.noisy.odds <- rlogis(nz1x0,qlogis(w0z1x0))
+ ## w0z1x1.noisy.odds <- rlogis(nz1x1,qlogis(w0z1x1))
+
+ ## df[(z==0)&(x==0),w:=plogis(w0z0x0.noisy.odds)]
+ ## df[(z==0)&(x==1),w:=plogis(w0z0x1.noisy.odds)]
+ ## df[(z==1)&(x==0),w:=plogis(w0z1x0.noisy.odds)]
+ ## df[(z==1)&(x==1),w:=plogis(w0z1x1.noisy.odds)]
+
+ ## df[,w_pred:=as.integer(w > 0.5)]
+ ## print(mean(df[z==0]$x == df[z==0]$w_pred))
+ ## print(mean(df[z==1]$x == df[z==1]$w_pred))
+ ## print(mean(df$w_pred == df$x))
+
+ resids <- resid(lm(y~x + z))
+ odds.x1 <- qlogis(prediction_accuracy) + y_bias*qlogis(pnorm(resids[x==1])) + z_bias * qlogis(pnorm(z,sd(z)))
+ odds.x0 <- qlogis(prediction_accuracy,lower.tail=F) + y_bias*qlogis(pnorm(resids[x==0])) + z_bias * qlogis(pnorm(z,sd(z)))
+
+ ## acc.x0 <- p.correct[df[,x==0]]
+ ## acc.x1 <- p.correct[df[,x==1]]
+
+ df[x==0,w:=plogis(rlogis(.N,odds.x0))]
+ df[x==1,w:=plogis(rlogis(.N,odds.x1))]
+
+ df[,w_pred := as.integer(w > 0.5)]
+
+
print(mean(df$w_pred == df$x))
+ print(mean(df[y>=0]$w_pred == df[y>=0]$x))
+ print(mean(df[y<=0]$w_pred == df[y<=0]$x))
return(df)
}
parser <- arg_parser("Simulate data and fit corrected models")
-parser <- add_argument(parser, "--N", default=1400, help="number of observations of w")
+parser <- add_argument(parser, "--N", default=5000, help="number of observations of w")
parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
-parser <- add_argument(parser, "--seed", default=50, help='seed for the rng')
+parser <- add_argument(parser, "--seed", default=51, help='seed for the rng')
parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
-parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.01)
-parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73)
+parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.1)
+parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.75)
parser <- add_argument(parser, "--accuracy_imbalance_difference", help='how much more accurate is the predictive model for one class than the other?', default=0.3)
parser <- add_argument(parser, "--Bzx", help='Effect of z on x', default=0.3)
parser <- add_argument(parser, "--Bzy", help='Effect of z on y', default=-0.3)
-
+parser <- add_argument(parser, "--Bxy", help='Effect of z on y', default=0.3)
+parser <- add_argument(parser, "--outcome_formula", help='formula for the outcome variable', default="y~x+z")
+parser <- add_argument(parser, "--proxy_formula", help='formula for the proxy variable', default="w_pred~y*z*x")
+parser <- add_argument(parser, "--y_bias", help='coefficient of y on the probability a classification is correct', default=-0.5)
+parser <- add_argument(parser, "--z_bias", help='coefficient of z on the probability a classification is correct', default=0)
+parser <- add_argument(parser, "--truth_formula", help='formula for the true variable', default="x~z")
args <- parse_args(parser)
B0 <- 0
-Bxy <- 0.3
+Bxy <- args$Bxy
Bzy <- args$Bzy
+Bzx <- args$Bzx
if(args$m < args$N){
- df <- simulate_data(args$N, args$m, B0, Bxy, args$Bzx, Bzy, args$seed, args$y_explained_variance, args$prediction_accuracy, args$accuracy_imbalance_difference)
- result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy, Bzx=args$Bzx, 'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference, error='')
+ df <- simulate_data(args$N, args$m, B0, Bxy, Bzx, Bzy, args$seed, args$y_explained_variance, args$prediction_accuracy, y_bias=args$y_bias)
+
+ ## df.pc <- df[,.(x,y,z,w_pred,w)]
+ ## # df.pc <- df.pc[,err:=x-w_pred]
+ ## pc.df <- pc(suffStat=list(C=cor(df.pc),n=nrow(df.pc)),indepTest=gaussCItest,labels=names(df.pc),alpha=0.05)
+ ## plot(pc.df)
+
+ result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy, Bzx=args$Bzx, 'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference, 'y_bias'=args$y_bias,'outcome_formula'=args$outcome_formula, 'proxy_formula'=args$proxy_formula,truth_formula=args$truth_formula, error='')
- outline <- run_simulation(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~x+z+y+x:y, truth_formula=x~z)
+ outline <- run_simulation(df, result, outcome_formula=as.formula(args$outcome_formula), proxy_formula=as.formula(args$proxy_formula), truth_formula=as.formula(args$truth_formula))
- outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
+
+ outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
if(file.exists(args$outfile)){
logdata <- read_feather(args$outfile)
logdata <- rbind(logdata,as.data.table(outline), fill=TRUE)
projects / ml_measurement_error_public.git / blobdiff