Research map / Federated learning and privacy / Differential privacy
Differentially Private Boxplots
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Introduces DPBoxplot, a differentially private boxplot that uses JointExp for the box quartiles/median and the unbounded algorithm for extreme quantiles (whiskers), with noisy outlier counts, and proves optimal location/scale sample complexity and consistency of whiskers and outlier counts.
Problem
Differentially private visualization is underdeveloped, and a differentially private boxplot has not been directly studied; naive boxplots built from a single private quantile algorithm can be inconsistent for extreme quantiles (whiskers).
Approach
Combine JointExp for the box (quartiles and median) with a modified unbounded quantile algorithm for the min/max whisker endpoints, with a buffer parameter and Laplace-noised outlier counts, so location and scale are estimated at optimal sample complexity while skewness and tails remain consistent.
Key results
- DPBoxplot error for all components converges to zero as n grows in all simulated scenarios, and is similar to the non-private boxplot error at epsilon=1.
- Naive boxplots built on JointExp, ApproxQuantile, or PrivateQuantile show poor skewness error on skew and uniform distributions because their whiskers are inconsistent.
- unbounded is consistent for extreme quantiles but performs worse than the other algorithms for estimating scale and location; DPBoxplot combines the best of both.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use JointExp for quartiles and unbounded for extreme quantiles instead of using one quantile algorithm for all boxplot values | DPBoxplot versus naive private boxplots · Simulations: skew-normal and uniform distributions | skewness error | Helped |
| Use unbounded for all quantiles instead of JointExp for quartiles | Naive private boxplot · Simulations: Gaussian data | location and scale error | Hurt |
| Use DPBoxplot instead of naive private boxplots | DPBoxplot · Simulations: normally distributed data at small sample sizes | skewness error | Hurt |
| Use DPBoxplot instead of a non-private sample boxplot | DPBoxplot · Simulations: normal, skew-normal, uniform, beta, and Airbnb distributions | error across location, scale, skewness, and tails | No clear effect |
| Increase the privacy budget | Differentially private boxplot methods · Simulations: privacy budgets ε=0.5 and ε=5 | error | Helped |
| Vary the buffer parameter λₙ among n⁻¹ᐟ², n⁻¹ᐟ⁴, and 1 (ablation) | DPBoxplot and other private boxplot methods · Simulations: sampled distributions | error across location, scale, skewness, and tails | No clear effect |
Surprising findings
- At small sample sizes with normal data, DPBoxplot performs worse than naive methods on the skewness metric because unbounded underestimates the magnitude of the extremes.
Limitations
- Naive JointExp-based whiskers are inconsistent for extreme quantiles unless input bounds match the data support.
- At small sample sizes, DPBoxplot's skewness estimates are worse than naive methods for normal data.
- Case study shows sample-size-driven discrepancies with non-private boxplots, and budget allocation for sequential workflows is unresolved.
Experimental setup
Datasets: 2019 NYC Airbnb listing prices (n=40738 after filtering) simulated normal, skew normal, uniform, beta distributions
Benchmarks: simulated distributions (normal, skew, uniform, beta, airbnb) with n up to 100000 and epsilon in {0.5,1,5,10} NYC Airbnb case study
Metrics: average absolute error in location, scale, skewness, tails v
Baselines: naive private boxplot with JointExp naive private boxplot with ApproxQuantile naive private boxplot with unbounded naive private boxplot with PrivateQuantile non-private sample boxplot
Builds on: JointExp unbounded quantile algorithm PrivateQuantile ApproxQuantile Laplace mechanism
Closest papers by meaning
- Archimedes Meets Privacy: On Privately Estimating Quantiles in High Dimensions Under Minimal Assumptions (NeurIPS 2022 · similarity 0.86)
- Private Statistical Estimation of Many Quantiles (ICML 2023 · similarity 0.85)
- A Simple and Practical Method for Reducing the Disparate Impact of Differential Privacy (AAAI 2024 · similarity 0.84)
- Privacy Profiles for Private Selection (ICML 2024 · similarity 0.84)
- Lightweight Protocols for Distributed Private Quantile Estimation (ICML 2025 · similarity 0.84)
- Differentially Private Equivalence Testing for Continuous Distributions and Applications (NeurIPS 2024 · similarity 0.83)
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