Evaluate utility without opening an unaccounted private-data channel
Separate public benchmarks, private metrics, sampling uncertainty and privacy noise.
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The question for today
What you’ll understand
- Distinguish model postprocessing on public data from a new private metric query.
- Calibrate a bounded accuracy query with an explicit public denominator.
- Interpret a Laplace noise interval without confusing it with population uncertainty.
A privately trained model still needs a useful evaluation, but a raw metric computed on a private holdout is a new information release. Public benchmarks can support development without that access when their inputs and labels are genuinely public. Private evaluation needs its own unit, sensitivity, randomizer and accounting. A good report separates application performance from both ordinary sampling uncertainty and the additional uncertainty introduced by a privacy mechanism.
Specify which data the evaluation accesses
Running an already accounted DP model on public evaluation examples is postprocessing with public information. Querying protected holdout labels is different, even when only one accuracy number is reported. If users appear across training and holdout data, disjoint row splits do not establish disjoint protected populations for user-level accounting. Define whether metrics are per record or per bounded user contribution, and keep the privacy unit consistent with the release claim. Repeatedly inspecting private slices or choosing the best checkpoint from raw metrics is another selection path.
Keep a public development set for ordinary iteration when available and reserve private access for a declared process. The public set may be unrepresentative, so good public performance does not replace deployment-relevant private evidence. Conversely, “private” cannot mean merely hidden from the test author while raw labels are freely queried by the selection system. Version the evaluation data, model artifact, candidate protocol, decoding rules and metric randomizer so a release report describes one reproducible workflow rather than a changing mixture of tests.
Separate privacy noise from population uncertainty
For this Laplace mechanism, the probability that added noise magnitude exceeds radius r is exp(-r/b). Choosing r=b log(1/beta) gives a noise-only coverage probability 1−beta around the released value for the fixed underlying metric. This is a statement about the randomizer, not a confidence interval for future population accuracy. The dataset itself may be a finite, biased or correlated sample, and stochastic generation can introduce additional variation. Those uncertainties need their own design and cannot be folded into the privacy parameter delta.
A beta used in an error-probability statement is not a DP delta. The illustrated Laplace query has delta zero even when a noise interval has only 95% coverage. Clipping a released metric to [0,1] is postprocessing, but interval construction should account for that reporting convention. Do not release an unclipped raw accuracy alongside its privatized version as a convenience; the raw value remains a separate private-data disclosure. Likewise, error bars computed from unsanitized private statistics can themselves need protection.
Report utility and cost under one declared protocol
Publish the protected unit, composed training and evaluation guarantees, fixed denominator assumptions, metric transformation and the uncertainty method. Include important slices only through a valid evaluation and composition plan; many slice queries are not one query merely because they appear in one chart. Evaluate operational metrics such as latency using data paths whose public or private status is explicit too. A model can have lower utility because of clipping, optimization or limited data coverage as well as added noise, so avoid assigning every regression to one parameter.
The sampling lab isolates ordinary iid accuracy variation. Reset and set both p=0.8 and n=100; predict mean 0.8 and variance 0.0016. Separately Reset and set both p=0.8 and n=25; predict mean 0.8 and variance 0.0064. Play highlights exact binomial outcomes instead of running a benchmark. This model contains no private metric query or Laplace noise and cannot compute a privacy guarantee. It helps distinguish finite-sample variability from the separate randomizer interval derived on paper.
Work it through
A private accuracy release has its own noise scale
Use an invented example with 164 correct outcomes and public divisor m₀=200. Each protected evaluation unit contributes one bounded correctness scalar. Release the normalized count with Laplace epsilon_e=0.5. For arithmetic only, suppose the displayed rounded noise is +0.015, and use beta=0.05 for a noise-only interval.
The finite-dataset accuracy is 164/200=0.82. Sensitivity is at most 1/200=0.005, so the Laplace scale is 0.005/0.5=0.01 accuracy units. The scale is not the distribution’s standard deviation, which would be √2 times the scale.
The supplied arithmetic noise produces released value 0.82+0.015=0.835. This illustration does not prescribe a deterministic noise choice for a real mechanism; the actual release must use the stated randomizer.
For beta 0.05, radius is 0.01 log 20≈0.02996. The noise-only 95% interval around the release is approximately [0.80504,0.86496]. It concerns the fixed finite-dataset accuracy and does not establish population coverage or change the query’s pure-DP delta from zero.
The evaluation query has its own pure epsilon 0.5 cost under the declared unit and denominator. Its noise interval and ordinary benchmark uncertainty answer separate questions and must not be called a privacy-budget calculation.
The living notebook
Explore the model
Interactive lab · sampling
Sampling uncertainty is separate from privacy noise
Reset → set p=0.8 and n=100 → predict mean 0.8, variance 0.0016. Separate Reset → set p=0.8 and n=25 → predict variance 0.0064.
- Mean sample proportion
- 0.5
- Sample-mean variance
- 0.0125
- Uniform CDF error bound
- ≤ 0.1062
Exact binomial masses for the mean of n independent Bernoulli trials, compared with normal mass between adjacent half-count boundaries; normal tails outside the finite support remain outside the bars. Playback highlights outcomes, not random samples. The Berry–Esseen bound applies to standardized CDFs, not individual bars or continuity-corrected errors. At p = 0 or 1, normal comparison and that bound are disabled. Normal-CDF evaluation uses a numerical approximation with absolute error below 7.5×10⁻⁸ (at most 1.5×10⁻⁷ per interval, before rounding). Parameter changes pause playback and recompute the model at the current elapsed time. Reset restores both parameters and returns time to zero. Playback starts paused. Adjust either parameter, then choose Play or Step.
Look forThe exact iid binomial sample-mean model has no Laplace randomizer, private dataset or accountant. It illustrates sampling variation only.
Pause & reason
Check your understanding
Your turn
Try it yourself
Use public divisor m₀=100, epsilon_e=0.25 and an invented raw accuracy 0.7. For arithmetic only let noise be -0.02. Find Laplace scale, released value and the beta=0.05 noise-only radius.
Take a moment to make a prediction or work it out on paper. Open a hint when you need one.
Give me a hint
The sensitivity is 0.01. Scale is sensitivity divided by evaluation epsilon, and the radius multiplies that scale by log 20.
Compare with the solution
Scale is 0.01/0.25=0.04. The illustrated release is 0.68. Radius is 0.04 log 20≈0.11983, giving interval approximately [0.56017,0.79983] before any reporting transformation. This is randomizer uncertainty for the fixed query, not a population interval or a delta=0.05 privacy claim.
Keep the idea
Take it with you
- Private evaluation is a separate data access from public benchmarking.
- A public denominator and bounded contribution support an explicit metric sensitivity.
- Utility tail probability, population uncertainty and DP delta are different quantities.
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