r-statistics.co by Selva Prabhakaran

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Synthetic Data Generation in R: Protect Privacy While Testing Models

Synthetic data looks and behaves like real data but contains no actual individuals. It lets you share datasets, test models, and develop code without exposing sensitive information — all while preserving the statistical relationships your analysis depends on.

You need to share a dataset with a collaborator, but it contains patient records. You want to test a machine learning pipeline, but the real data is locked behind an NDA. You're teaching a class and need realistic examples without privacy risks. Synthetic data solves all of these problems.

Why Synthetic Data?

Use Case Problem Solution
Sharing with collaborators Real data has PII Share synthetic copy
Testing code/pipelines No access to production data Generate realistic test data
Teaching & tutorials Need realistic examples Create privacy-safe datasets
Augmenting small datasets Not enough training data Synthesize additional records
Open science Can't share raw data Release synthetic version
Development & QA Need many test scenarios Generate edge cases

Method 1: Parametric Simulation

Generate data from known distributions that match the real data's properties.

# Step 1: Analyze real data properties cat("=== Real Data Properties (mtcars) ===\n") cat(sprintf("MPG: mean=%.1f, sd=%.1f\n", mean(mtcars$mpg), sd(mtcars$mpg))) cat(sprintf("HP: mean=%.1f, sd=%.1f\n", mean(mtcars$hp), sd(mtcars$hp))) cat(sprintf("WT: mean=%.2f, sd=%.2f\n", mean(mtcars$wt), sd(mtcars$wt))) cat(sprintf("Correlation (mpg, wt): %.3f\n", cor(mtcars$mpg, mtcars$wt))) # Step 2: Generate synthetic data preserving these properties set.seed(42) n_synth <- 100 # Use multivariate normal to preserve correlations real_means <- colMeans(mtcars[, c("mpg","hp","wt")]) real_cov <- cov(mtcars[, c("mpg","hp","wt")]) # Cholesky decomposition for correlated normals L <- chol(real_cov) z <- matrix(rnorm(n_synth * 3), ncol = 3) synth_data <- z %*% L + matrix(real_means, n_synth, 3, byrow = TRUE) synth_df <- as.data.frame(synth_data) names(synth_df) <- c("mpg","hp","wt") # Enforce realistic constraints synth_df$mpg <- pmax(synth_df$mpg, 8) synth_df$hp <- pmax(round(synth_df$hp), 50) synth_df$wt <- pmax(synth_df$wt, 1.5) cat("\n=== Synthetic Data Properties ===\n") cat(sprintf("MPG: mean=%.1f, sd=%.1f\n", mean(synth_df$mpg), sd(synth_df$mpg))) cat(sprintf("HP: mean=%.1f, sd=%.1f\n", mean(synth_df$hp), sd(synth_df$hp))) cat(sprintf("WT: mean=%.2f, sd=%.2f\n", mean(synth_df$wt), sd(synth_df$wt))) cat(sprintf("Correlation (mpg, wt): %.3f\n", cor(synth_df$mpg, synth_df$wt)))


  






Method 2: CART-Based Synthesis (synthpop approach)



The synthpop package uses classification and regression trees to model the conditional distributions in your data. Here's the concept implemented manually.





  


    
# Simplified CART-based synthesis concept
set.seed(42)

# Original data
original <- data.frame(
  age = sample(20:70, 200, replace = TRUE),
  income = NA,
  education = sample(c("HS","BA","MA","PhD"), 200, replace = TRUE,
                     prob = c(0.3, 0.4, 0.2, 0.1))
)
# Income depends on age and education (realistic relationships)
edu_bonus <- c(HS = 0, BA = 15000, MA = 25000, PhD = 35000)
original$income <- 20000 + 500 * original$age +
                   edu_bonus[original$education] +
                   rnorm(200, 0, 10000)

cat("=== Original Data Summary ===\n")
cat(sprintf("N = %d\n", nrow(original)))
cat(sprintf("Mean income: $%.0f\n", mean(original$income)))
cat(sprintf("Income by education:\n"))
print(round(tapply(original$income, original$education, mean)))

# Synthesize: model each variable conditionally
# Variable 1: age (sample from empirical distribution)
synth_age <- sample(original$age, 200, replace = TRUE)

# Variable 2: education (conditional on age - use original proportions per age group)
age_group <- cut(synth_age, c(0,35,50,80), labels = c("young","mid","senior"))
synth_edu <- character(200)
for (ag in levels(age_group)) {
  mask_synth <- age_group == ag
  orig_mask <- cut(original$age, c(0,35,50,80), labels = c("young","mid","senior")) == ag
  probs <- prop.table(table(original$education[orig_mask]))
  synth_edu[mask_synth] <- sample(names(probs), sum(mask_synth), replace = TRUE, prob = probs)
}

# Variable 3: income (conditional on age and education)
model <- lm(income ~ age + education, data = original)
synth_income <- predict(model, data.frame(age = synth_age, education = synth_edu)) +
                rnorm(200, 0, summary(model)$sigma)

synthetic <- data.frame(age = synth_age, income = synth_income, education = synth_edu)

cat("\n=== Synthetic Data Summary ===\n")
cat(sprintf("N = %d\n", nrow(synthetic)))
cat(sprintf("Mean income: $%.0f\n", mean(synthetic$income)))
cat(sprintf("Income by education:\n"))
print(round(tapply(synthetic$income, synthetic$education, mean)))


    


      

      

    


    


  






Method 3: Bootstrap-Based Synthesis



Simple and effective for many use cases: sample with replacement and add noise.





  


    
# Bootstrap + noise synthesis
set.seed(42)

# Start with real data
real <- mtcars[, c("mpg", "cyl", "hp", "wt")]

# Bootstrap sample
n_synth <- 50
boot_idx <- sample(1:nrow(real), n_synth, replace = TRUE)
synth <- real[boot_idx, ]
rownames(synth) <- NULL

# Add noise to continuous variables (not to categorical)
noise_level <- 0.1  # 10% of SD
synth$mpg <- synth$mpg + rnorm(n_synth, 0, noise_level * sd(real$mpg))
synth$hp <- round(synth$hp + rnorm(n_synth, 0, noise_level * sd(real$hp)))
synth$wt <- synth$wt + rnorm(n_synth, 0, noise_level * sd(real$wt))

cat("=== Bootstrap + Noise Synthesis ===\n")
cat("Real data:\n")
print(round(sapply(real, function(x) c(mean=mean(x), sd=sd(x))), 2))
cat("\nSynthetic data:\n")
print(round(sapply(synth, function(x) c(mean=mean(x), sd=sd(x))), 2))


    


      

      

    


    


  






Measuring Utility: Is the Synthetic Data Good Enough?



Synthetic data is useful only if it preserves the statistical properties you need. Here's how to measure that.





  


    
# Utility comparison
set.seed(42)

# Fit the same model on real and synthetic data
real_model <- lm(mpg ~ hp + wt, data = mtcars)
synth_model <- lm(mpg ~ hp + wt, data = synth)

cat("=== Utility Comparison ===\n")
cat("\nReal data model coefficients:\n")
print(round(coef(real_model), 4))
cat("\nSynthetic data model coefficients:\n")
print(round(coef(synth_model), 4))

# Compare distributions
cat("\n--- Distribution Comparison ---\n")
for (var in c("mpg", "hp", "wt")) {
  ks <- ks.test(real[[var]], synth[[var]])
  cat(sprintf("%s: KS statistic = %.3f, p = %.3f %s\n",
      var, ks$statistic, ks$p.value,
      ifelse(ks$p.value > 0.05, "(similar)", "(different!)")))
}


    


      

      

    


    


  






Privacy Check: Is the Synthetic Data Safe?





  


    
# Check for identity disclosure risk
# If a synthetic record exactly matches a real record, that's a risk

check_disclosure <- function(real, synth, tolerance = 0.01) {
  matches <- 0
  for (i in 1:nrow(synth)) {
    for (j in 1:nrow(real)) {
      diffs <- abs(as.numeric(synth[i,]) - as.numeric(real[j,]))
      ranges <- apply(real, 2, function(x) diff(range(x)))
      rel_diffs <- diffs / ranges
      if (all(rel_diffs < tolerance)) {
        matches <- matches + 1
        break
      }
    }
  }
  matches
}

cat("=== Privacy Risk Assessment ===\n")
# Use numeric columns only
real_num <- mtcars[, c("mpg","hp","wt")]
synth_num <- synth[, c("mpg","hp","wt")]

n_matches <- check_disclosure(real_num, synth_num, tolerance = 0.05)
cat(sprintf("Records within 5%% of a real record: %d of %d (%.1f%%)\n",
    n_matches, nrow(synth_num), 100 * n_matches/nrow(synth_num)))

cat("\nGuidelines:\n")
cat("  < 5% close matches: Low risk\n")
cat("  5-20% close matches: Moderate risk, add more noise\n")
cat("  > 20% close matches: High risk, regenerate with more perturbation\n")


    


      

      

    


    


  






Using synthpop





  


    
# synthpop package usage (conceptual)
cat("=== synthpop Package ===\n\n")
cat('library(synthpop)\n\n')
cat('# Generate synthetic data\n')
cat('synth_obj <- syn(original_data, method = "cart")\n\n')
cat('# Extract the synthetic dataset\n')
cat('synthetic_data <- synth_obj$syn\n\n')
cat('# Compare distributions\n')
cat('compare(synth_obj, original_data)\n\n')
cat('# Utility metrics\n')
cat('utility.gen(synth_obj, original_data)\n\n')
cat('Available methods:\n')
cat('  "cart"    - Classification and Regression Trees (default)\n')
cat('  "norm"    - Normal linear regression\n')
cat('  "logreg"  - Logistic regression (for binary)\n')
cat('  "polyreg" - Polytomous regression (for categorical)\n')
cat('  "sample"  - Random sampling from observed values\n')


    


      

      

    


    


  






Summary: Choosing a Synthesis Method







Method
Complexity
Privacy
Utility
Best For






Parametric
Low
Medium
Medium
Known distributions




Bootstrap + noise
Low
Low-medium
High
Quick prototyping




CART (synthpop)
Medium
Medium-high
High
General purpose




Copula-based
Medium
Medium-high
High
Complex dependencies




GAN-based
High
High
Very high
Complex multimodal data




Differential privacy
High
Very high
Lower
Formal guarantees needed







FAQ



Can synthetic data completely replace real data for model training? For testing and development, yes. For final model training, usually no — synthetic data may miss rare patterns, outliers, or subtle interactions. Use synthetic data for development and privacy-safe sharing, but validate final models on real data.



How much noise should I add? Enough to prevent re-identification but not so much that utility is destroyed. Start with 5-10% of the variable's standard deviation and check both utility metrics (KS test, coefficient comparison) and privacy metrics (close-match percentage). Adjust iteratively.



Is synthpop the only R package for synthetic data? No. Other options include simPop (for complex survey data), simstudy (for clinical trial simulation), fabricatr (for social science), and MICE (imputation-based synthesis). Choose based on your data type and use case.



What's Next




        


        
      


      

        

        
© 2016- Selva Prabhakaran.
          This work is licensed under the Creative Commons License.