## 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, Bgy, Bkx, Bgx, seed, xy.explained.variance=0.01, u.explained.variance=0.1){
+simulate_data <- function(N, m, B0, Bxy, Bzx, Bzy, seed, y_explained_variance=0.025, prediction_accuracy=0.73, accuracy_imbalance_difference=0.3){
set.seed(seed)
-
- ## the true value of x
-
- g <- rbinom(N, 1, 0.5)
-
# make w and y dependent
- u <- rnorm(N,0,)
-
- xprime <- Bgx * g + rnorm(N,0,1)
-
- k <- Bkx*xprime + rnorm(N,0,1.5) + 1.1*Bkx*u
-
- x <- as.integer(logistic(scale(xprime)) > 0.5)
+ z <- rbinom(N, 1, 0.5)
+ x <- rbinom(N, 1, Bzx * z + 0.5)
- y <- Bxy * x + Bgy * g + B0 + u + rnorm(N, 0, 1)
+ 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))
+ y <- Bzy * z + Bxy * x + y.epsilon
+
+ df <- data.table(x=x,y=y,z=z)
- df <- data.table(x=x,k=k,y=y,g=g)
-
- w.model <- glm(x ~ k,df, family=binomial(link='logit'))
-
- if( m < N){
+ if(m < N){
df <- df[sample(nrow(df), m), x.obs := x]
} else {
df <- df[, x.obs := x]
}
- df[, x.obs := x.obs]
-
- w <- predict(w.model, df) + rnorm(N, 0, 1)
- ## y = B0 + B1x + e
-
- df[,':='(w=w, w_pred = as.integer(w>0.5),u=u)]
+ ## px <- mean(x)
+ ## 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))
+ print(mean(df$w_pred == df$x))
return(df)
}
-schennach <- function(df){
-
- fwx <- glm(x.obs~w, df, family=binomial(link='logit'))
- df[,xstar_pred := predict(fwx, df)]
- gxt <- lm(y ~ xstar_pred+g, df)
-
-}
-
-
parser <- arg_parser("Simulate data and fit corrected models")
-parser <- add_argument(parser, "--N", default=5000, help="number of observations of w")
-parser <- add_argument(parser, "--m", default=200, help="m the number of ground truth observations")
-parser <- add_argument(parser, "--seed", default=432, help='seed for the rng')
+parser <- add_argument(parser, "--N", default=1400, 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, "--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, "--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)
+
+
args <- parse_args(parser)
B0 <- 0
-Bxy <- 0.2
-Bgy <- 0
-Bkx <- 2
-Bgx <- 0
+Bxy <- 0.3
+Bzy <- args$Bzy
+if(args$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)
-outline <- run_simulation(simulate_data(args$N, args$m, B0, Bxy, Bgy, Bkx, Bgx, args$seed)
- ,list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=args$seed))
+ 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$accuracy_imbalance_difference, error='')
-outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
-if(file.exists(args$outfile)){
- logdata <- read_feather(args$outfile)
- logdata <- rbind(logdata,as.data.table(outline))
-} else {
- logdata <- as.data.table(outline)
-}
+ outline <- run_simulation(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~x+z+y+x:y, truth_formula=x~z)
+
+ outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
+ if(file.exists(args$outfile)){
+ logdata <- read_feather(args$outfile)
+ logdata <- rbind(logdata,as.data.table(outline), fill=TRUE)
+ } else {
+ logdata <- as.data.table(outline)
+ }
-print(outline)
-write_feather(logdata, args$outfile)
-unlock(outfile_lock)
+ print(outline)
+ write_feather(logdata, args$outfile)
+ unlock(outfile_lock)
+}
projects / ml_measurement_error_public.git / blobdiff