examples

Example using the Go Differential Privacy Library

Restaurant

Imagine a fictional restaurant owner named Alice who would like to share business statistics with her visitors. Alice knows when visitors enter the restaurant and how much time and money they spend there. To ensure that visitors' privacy is preserved, Alice decides to use this differential privacy library.

Count visits by hour of the day

In this example, Alice wants to share information with potential clients in order to let them know when the restaurant is most busy.

For this, we will count how many visitors enter the restaurant at every hour of a particular day. For simplicity, assume that a visitor comes to the restaurant at most once a day. Thus, each visitor may only be present at most once in the whole dataset, since the dataset represents a single day of restaurant visits.

The data/day_data.csv file contains visit data for a single day. It includes the visitor’s ID, a timestamp of when the visitor entered the restaurant, the duration of the visitor's visit to the restaurant (in minutes), and the money the visitor spent at the restaurant.

Navigate to examples/go folder, build the codelab code and run it with the scenario=scenario=CountVisitsPerHour argument.

Linux

$ cd examples/go
$ bazel run main/examples -- --scenario=CountVisitsPerHour --input_file=$(pwd)/data/day_data.csv --non_private_output_file=$(pwd)/non_private.csv --private_output_file=$(pwd)/private.csv

Windows

$ cd examples/go
$ bazel run main/examples -- --scenario=CountVisitsPerHour --input_file=%CD%/data/day_data.csv --non_private_output_file=%CD%/non_private.csv --private_output_file=%CD%/private.csv

This triggers the logic of CountVisitsPerHourScenario. It reads the daily statistics and calculates the number of visitors that entered the restaurant every hour of the day. The calculation is done twice, for illustrative purposes:

• First, CountVisitsPerHourScenario computes the raw counts and outputs them to the file from the argument non_private_output_file=<file_name>.
• Next, CountVisitsPerHourScenario calculates private (i.e., anonymized) counts using this differential privacy library and prints them to the file from the argument private_output_file=<file_name>.

The image below illustrates the results. The blue (left) bars represent the counts without anonymization while red (right) bars correspond to the private (or anonymized) counts. Notice that the private counts slightly differ from the non-private counts, though the overall trend is preserved: the restaurant is more busy during lunch and dinner time.

Note that differential privacy involves adding random noise to the actual data and hence, your own results will most likely be slightly different.

Partitions and contributions

We say that the resulting aggregated data is split into partitions. The bar chart for the private and non-private counts each have 15 partitions: one for each hour the restaurant was visited.

More generally, a single partition represents a subset of aggregated data corresponding to a given value of the aggregation criterion. Graphically, a single partition is represented as a bar on the aggregated bar chart.

We say that a visitor contributes to a given partition if their data matches the partition criterion. For example, if a visitor enters between 8 AM and 9 AM, they contribute to the 8 AM partition.

Recall that in the example above, a visitor can enter the restaurant only once per day. This implies the following three contribution bounds.

• Maximum partitions contributed: To how many separate partitions can a visitor contribute? In our example, a visitor can contribute to, at most, only one partition. In other words, there is at most one time-slot when a visitor with a given ID can enter the restaurant.
• Maximum contributed value: What is the maximum value that can be contributed by a visitor to a partition? In our example, the value is the number of visits, so the maximum contributed value is simply 1.
• Maximum contributions per partition: How many times can a visitor contribute to a partition? In our example, a visitor can contribute to a partition at most once. In other words, a visitor can enter the restaurant only once at a given hour.

Why is this important? Differential privacy adjusts the amount of noise to mask the contributions of each visitor. More contributions require more noise.

Next, we will demonstrate how to use the library in scenarios where:

• visitors can contribute to multiple partitions;
• contributed values can be greater than 1; and
• visitors can contribute to a partition multiple times.

Count visits by day of the week

The previous example made some over-simplifying assumptions. Now, let’s have a look at the use-case where visitors can contribute to multiple partitions.

Imagine Alice decides to let visitors know what the busiest days at her restaurant are. For this, she calculates how many people visit the restaurant every day of the week. For simplicity, let’s assume a visitor enters the restaurant at most once a day but may enter multiple days in a single week.

The file data/week_data.csv contains visit data for a week. It includes the visitor’s ID, the visit duration (in minutes), the money spent at the restaurant, and the day of the visit.

Navigate to examples/go folder, build the codelab code and run it with the scenario=CountVisitsPerDay argument.

Linux

$ cd examples/go
$ bazel run main/examples -- --scenario=CountVisitsPerDay --input_file=$(pwd)/data/week_data.csv --non_private_output_file=$(pwd)/non_private.csv --private_output_file=$(pwd)/private.csv

Windows

$ cd examples/go
$ bazel run main/examples -- --scenario=CountVisitsPerDay --input_file=%CD%/data/week_data.csv --non_private_output_file=%CD%/non_private.csv --private_output_file=%CD%/private.csv

This triggers the logic of CountVisitsPerDayScenario. It calculates the number of visitors that entered the restaurant for each day of the week. The calculation is done twice, for illustrative purposes:

• First, CountVisitsPerDayScenario computes raw counts and outputs them to the file from the argument non_private_output_file=<file_name>.
• Next, CountVisitsPerDayScenario calculates private (i.e., anonymized) count using this differential privacy library and prints them to the file from the argument private_output_file=<file_name>.

The results are illustrated in the image below.

Notice that the private values slightly differ from the actual ones, though the overall trend is preserved.

Now, let’s take a closer look at the technical details. Speaking in terms of partitions and contributions, the resulting bar chart has 7 partitions; one for each day of the week. A visitor may enter the restaurant once a day and hence contribute to a partition at most once. A visitor may enter the restaurant several times a week and hence contribute to up to 7 partitions. The code below uses dpagg.Count to calculate the differentially private count of visits for a single day.

const (
    // An upper limit of visits per week for a single person. Visits over this
    // limit will be dropped and ignored in the final statistics.
    //
    // Higher values result into less visits being dropped (and therefore less
    // bias) at the cost of higher noise. A good value should estimate how many
    // times a typical visitor may enter the restaurant per week. Getting
    // this right helps adding optimal amount of noise without losing too much
    // data.
    maxThreeVisitsPerWeek = 3
)

for _, day := range weekDays {
    // Construct dpagg.Count objects, which will be used to calculate DP counts.
    // One Count is created for every work hour.
    dayToDpCount[day], err = dpagg.NewCount(&dpagg.CountOptions{
        Epsilon: ln3,
        // The data was pre-processed so that
        // each visitor may visit the restaurant up to maxThreeVisitsPerWeek times per week.
        // Hence, each visitor may contribute to up to maxThreeVisitsPerWeek daily counts.
        // Note: while the library accepts this limit as a configurable parameter,
        // it doesn't pre-process the data to ensure this limit is respected.
        // It is responsibility of the caller to ensure the data passed to the library
        // is capped for getting the correct privacy guarantee.
        // TODO: Clarify the note above.
        MaxPartitionsContributed: maxThreeVisitsPerWeek,
        Noise:                    noise.Laplace(),
    })
    if err != nil {
        // Handle errors
    }
}

// Pre-process the data set by limiting the number of visits to
// maxThreeVisitsPerWeek per VisitorID.
boundedVisits := boundVisits(weekVisits, maxThreeVisitsPerWeek)
for _, visit := range boundedVisits {
    day := visit.Day
    dayToDpCount[day].Increment()
}

// Run dpagg.Count to calculate a differentially private result
for day, dpCount := range dayToDpCount {
    privateCounts[day], err = dpCount.Result()
    if err != nil {
        // Handle errors
    }
}

Bounding the number of contributed partitions

The parameter MaxPartitionsContributed defines the maximum number of partitions to which a visitor may contribute. One may notice that the value of MaxPartitionsContributed in our example is 3 instead of 7.

Why is that? Differential privacy adds some amount of random noise to hide the contributions of an individual. The more contributions an individual may have, the larger the noise must be. This affects the utility of the data. In order to preserve the data's utility, we made an approximate estimate of how many times a week a person may visit a restaurant on average, and assumed that the value is around 3 instead of scaling the noise by the factor of 7.

We also pre-processed the input data and discarded all exceeding visits. The pre-processing is done by boundVisits(....) in scenarios.go. It is important to keep in mind that the library allows to specify a maximum amount of contributions, but doesn't validate that it is respected.

Sum the revenue per day of the week

The previous example demonstrates how the contributed partitions are bounded. Now, we will demonstrate how individual contributions are clamped. Imagine Alice decides to calculate the sum of the restaurant's revenue per weekday in a differentially private way. For this, she needs to sum the visitors’ daily spending at the restaurant. For simplicity, let’s assume a visitor enters the restaurant at most once a day but may enter multiple times a week (on different days).

The data/week_data.csv file contains visit data for a week. It includes the visitor’s ID, the visit duration (in minutes), the money spent at the restaurant, and the day of the visit.

Navigate to examples/go folder, build the codelab code and run it with the scenario=scenario=SumRevenuePerDay argument.

Linux

$ cd examples/go
$ bazel run main/examples -- --scenario=SumRevenuePerDayScenario --input_file=$(pwd)/data/week_data.csv --non_private_output_file=$(pwd)/non_private.csv --private_output_file=$(pwd)/private.csv

Windows

$ cd examples/go
$ bazel run main/examples -- --scenario=SumRevenuePerDayScenario --input_file=%CD%/data/week_data.csv --non_private_output_file=%CD%/non_private.csv --private_output_file=%CD%/private.csv

This triggers the logic of SumRevenuePerDayScenario. It sums the amount of money visitors spend at the restaurant on each day of the week. The calculation is done twice, for illustrative purposes:

• First,SumRevenuePerDayScenario computes raw sums and outputs them to the file from the argument non_private_output_file=<file_name>.
• Next, SumRevenuePerDayScenario calculates private (i.e., anonymized) sums using this differential privacy library and prints them to file from the argument private_output_file=<file_name>.

The results are illustrated in the image below.

The code below uses dpagg.BoundedSumInt64 to calculate the differentially private sums of the visitors' spending for a single day.

const (
    // TODO: Clarify why we're assuming 4 average visits per week, and why we're calling it a max
    // An estimate of how many times on average a visitor may enter the restaurant per week
    maxFourVisitsPerWeek = 4
    minEurosSpent = 0

    // Maximum amount of money we expect a visitor to spend on a single visit.
    // This limit is used to choose the amount of noise required to "mask"
    // participation of a single user. This is required to ensure that
    // differential privacy guarantees hold for all the users in the dataset,
    // including outliers.
    //
    // Higher limits result into less values being "cut-off" (and therefore less
    // bias) at the cost of higher noise.
    maxEurosSpent = 50
)

for _, day := range weekDays {
    // Construct dpagg.BoundedSumInt64 objects which will be used to calculate DP sums.
    // One dpagg.BoundedSumInt64 is created for every day.
    dayToBoundedSum[day], err = dpagg.NewBoundedSumInt64(&dpagg.BoundedSumInt64Options{
        Epsilon: ln3,
        // The data was pre-processed so that
        // each visitor may visit the restaurant up to maxFourVisitsPerWeek times per week.
        // Hence, each visitor may contribute to up to maxFourVisitsPerWeek daily counts.
        // Note: while the library accepts this limit as a configurable parameter,
        // it doesn't pre-process the data to ensure this limit is respected.
        // It is responsibility of the caller to ensure the data passed to the library
        // is capped for getting the correct privacy guarantee.
        // TODO: Clarify the note above.
        MaxPartitionsContributed: maxFourVisitsPerWeek,
        // No need to pre-process the data: BoundedSumInt64 will clamp the input values.
        Lower: minEurosSpent,
        Upper: maxEurosSpent,
        Noise: noise.Laplace(),
    })
    if err != nil {
        // Handle errors
    }
    privateSums[day] = 0
}

// Pre-process the data set by limiting the number of visits to
// maxFourVisitsPerWeek per VisitorID.
boundedVisits := boundVisits(visits, maxFourVisitsPerWeek)
for _, visit := range boundedVisits {
    dayToBoundedSum[visit.Day].Add(visit.EurosSpent)
}

// Calculate DP result.
for day, boundedSum := range dayToBoundedSum {
    privateSums[day], err = boundedSum.Result()
    if err != nil {
        // Handle errors
    }
}

Clamping individual contributions

The usage of MaxPartitionsContributed in dpagg.BoundedSumInt64 is similar to its usage in dpagg.Count, which is explained in the previous example. This section focuses on the lower and upper bounds. The parameters lower and upper of dpagg.BoundedSumInt64 define the contribution caps. Every input value will be automatically clamped to the specified bounds. In other words, any value that is below lower will be overriden to become the same as lower, and any value greater than upper will be reduced to be the same as upper, so that all values will be within the bounds of lower and upper. This is needed for calculating the sensitivity of the aggregation, and to scale the noise that will be added to the sum accordingly.

Choosing bounds

The lower and upper bounds affect the utility of the sum in two potentially opposing ways: reducing the added noise, and preserving the utility. On the one hand, the added noise is proportional to the maximum of absolute values of the bounds. Thus, the closer the bounds are to zero, the less noise is added. On the other hand, setting the lower and upper bound close to zero may mean that the input values are clamped more aggressively, which can decrease utility as well.

Count visits by certain duration

We will now demonstrate that just adding noise to raw data might be not enough to preserve privacy, and that eliminating some partitions completely may be necessary. This is referred to as thresholding or partition selection.

Imagine Alice wants to know how much time visitors typically spend at the restaurant. Durations of visits can vary greatly. A visitor may be at the restaurant for 31 minutes, while another may stay for a couple of hours. Instead of considering the exact durations, Alice wants to look at the approximate durations, where each visit duration is rounded up to the nearest multiple of 10 minutes. Assume that a visitor may enter the restaurant at most once a day, multiple times a week.

The data/outliers_week_data.csv file contains visit data for a week. It includes the visitor’s ID, the visit duration (in minutes), the money spent at the restaurant, and the day of the visit.

Navigate to examples/go folder, build the codelab code and run it with the scenario=scenario=CountVisitsPerDuration argument.

Linux

$ cd examples/go
$ bazel run main/examples -- --scenario=CountVisitsPerDuration --input_file=$(pwd)/data/outliers_week_data.csv --non_private_output_file=$(pwd)/non_private.csv --private_output_file=$(pwd)/private.csv

Windows

$ cd examples/go
$ bazel run main/examples -- --scenario=CountVisitsPerDuration --input_file=%CD%/data/outliers_week_data.csv --non_private_output_file=%CD%/non_private.csv --private_output_file=%CD%/private.csv

This triggers the logic of CountVisitsPerCertainDurationScenario. It calculates the number of visitors who spent a certain amount of time (per visit) during the week. The calculation is done twice, for illustrative purposes:

• First, CountVisitsPerCertainDurationScenario computes raw counts and outputs them to the file from the argument non_private_output_file=<file_name>.
• Next, CountVisitsPerCertainDurationScenario calculates private (i.e., anonymized) counts using the differential privacy library and prints them to the file from the argument private_output_file=<file_name>.

The results are illustrated in the image below.

Similar to the previous examples, private counts slightly differ from the non-private counts. In addition, some partitions (e.g., 10 minutes and 180 minutes) do not appear in the private statistics. This is because some partitions are dropped due to thresholding.

Let’s take a closer look at the technical details. Speaking in terms of partitions and contributions, the resulting bar-plot for raw counts has 13 partitions and resulting bar-plot for anonymized counts has 11 partitions. Each partition is a visit duration (i.e., the initial set of partitions consists of all visit durations which occurred during the week, rounded up to 10 minutes). A visitor may enter the restaurant at most once a day, multiple times a week. A visitor may spend approximately the same time in each visit (e.g., a fixed-duration lunch break), and hence all their visits over the week may contribute to the same partition.

Using BoundedSum for count

Even though we want to calculate the count of visit durations, we can't use dpagg.Count for that because it can only be used for calculating count of distinct visitors, which is not what we want in this case (i.e., we want to include the fact that the same visitor may be in the restaurant several times a week). Therefore we should use dpagg.BoundedSumInt64.

const (
    // TODO: Clarify why we're assuming 3 average visits per week, and why we're calling it a max
    // An estimate of how many times on average a visitor may enter the
    // restaurant per week
    maxVisitsPerWeek = 4
)

// Pre-process the data set by limiting the number of visits to maxVisitsPerWeek
// per VisitorID.
boundedVisits := boundVisits(weekVisits, maxVisitsPerWeek)

for _, visit := range boundedVisits {
    durationToVisitCount := visitorIDToDurationToVisitCount[visit.VisitorID]
    duration := roundMinutes(visit.MinutesSpent, 10)
    durationToVisitCount[duration]++

    // Recall that each possible visit duration may be represented by a
    // partition. Here, we construct DP PreAggSelectPartition objects for each
    // such duration. PreAggSelectPartition decides whether there are enough
    // visitors in a partition to warrant keeping it, or if there were too few
    // visitors who stayed for that duration, meaning the partition should be
    // dropped.
    //
    // We use epsilon = log(3) / 2 in this example,
    // because we must split epsilon between all the functions that apply
    // differential privacy, which, in this case, is 2 functions:
    // BoundedSumInt64 and PreAggSelectPartition.
    durationToSelectPartition[duration], err = dpagg.NewPreAggSelectPartition(&dpagg.PreAggSelectPartitionOptions{
        Epsilon:                  ln3 / 2,
        Delta:                    0.02,
        MaxPartitionsContributed: maxVisitsPerWeek,
    })
    if err != nil {
        // Handle errors
    }

    // Construct dpagg.BoundedSumInt64 objects, which will be used to calculate DP
    // counts with multiple contributions from a single privacy unit (visitor).
    // One dpagg.BoundedSumInt64 is created for every duration.
    // We use epsilon = log(3) / 2 in this example,
    // because we must split epslion between all the functions that apply differential privacy,
    // which, in this case, is 2 functions: BoundedSumInt64 and PreAggSelectPartition.
    durationToBoundedSum[duration], err = dpagg.NewBoundedSumInt64(&dpagg.BoundedSumInt64Options{
        Epsilon: ln3 / 2,
        MaxPartitionsContributed: maxVisitsPerWeek,
        Lower: 0,
        Upper: maxVisitsPerWeek,
        Noise: noise.Laplace(),
    })
    if err != nil {
        // Handle errors
    }
}

for _, visits := range visitorIDToDurationToVisitCount {
    for duration, totalVisits := range visits {
        durationToBoundedSum[duration].Add(totalVisits)
        // Count distinct visitors for each duration.
        durationToSelectPartition[duration].Increment()
    }
}

// Calculate DP result
for duration, boundedSum := range durationToBoundedSum {
    // Pre-aggregation partition selection.
    // If there are enough visitors within this duration,
    // then it will appear in the result statistics table.
    // Otherwise, the duration's partition is simply dropped and excluded from the result.
    if durationToSelectPartition[duration].ShouldKeepPartition() {
        privateSums[duration], err = boundedSum.Result()
        if err != nil {
            // Handle errors
        }
    }
}

Partition selection

Having too few privacy units (visitors) contributing to a partition, or having too few results in a partition, can put users' privacy at risk, even after adding noise to the data. More precisely, if the set of partitions is not known in advance, the presence of a particular partition in the output can give an attacker information about the users in the dataset. In order to protect against such cases, we need to remove these partitions with too few contributions from the output.

There are 2 approaches for doing this:

• Pre-aggregation partition selection. Drop partitions which do not have a sufficient number of contributing privacy units. Note that these partitions may still be included in other aggregation functions' results, if there are sufficiently many contributing privacy units for that aggregation.
• Post-aggregation partition selection. Apply a threshold to the result of an aggregation. This can be only used with count and sum aggregations. This threshold is independent from the data; it is calculated using given DP parameters. After calculating the statistic (either count or sum) for the partition, if the statistic value is less than the threshold, then the partition will be excluded from the final result.

Note that even though the library has functionality to calculate a threshold and to select partitions, these are not enabled by default. Instead, it is the responsibility of the caller of the library to invoke the provided functions.

// Calculate DP result
for duration, boundedSum := range durationToBoundedSum {
    // Pre-aggregation partition selection.
    // If there are enough visitors within this duration,
    // then it will appear in the result statistics table.
    // Otherwise, the duration's partition is simply dropped and excluded from the result.
    keepPartition := durationToSelectPartition[duration].ShouldKeepPartition()
    if keepPartition {
        privateSums[duration], err = boundedSum.Result()
        if err != nil {
            // Handle errors
        }
    }
}

In this example, we use the Differentially Private Partition Selection method (described in this paper). We use the following parameters: epsilon = log(3) / 2, delta = 0.02, maxPartitionsContributed = 3. The probability of keeping the partition with these parameters is shown on the following chart:

Notice that the probability of keeping the partitions with >= 30 privacy units (visitors) is equal to 1 and the probability of keeping partitions with < 30 privacy units is > 0 and < 1. That means that partitions with >= 30 privacy units will always be kept and other partitions might be either eliminated or kept. Thus, we can say that 30 privacy units is a hard threshold for keeping the partition.

Let's have a closer look to the result bars above. Two partitions were eliminated:

• The partition with visits that lasted approximately 10 minutes was eliminated. There are only 19 visits (from 16 different visitors) with that duration. The probability of keeping this partition is around 50% (see the chart above). This means that each run of the scenario can eliminate the partition or keep it with the same probability. In the bar chart above, we see that it was eliminated.

• The partition visits that lasted approximately 3 hours. Even though there are 38 visits, it doesn't pass the hard threshold, because these visits are from the same 5 people who went to the restaurant every day. Therefore, there are not enough 3-hour visitors to protect their privacy and we should not include their data in the report (i.e., the probability of keeping that partition is too small, see the chart above).

Another interesting observation is that there are 35 visits with duration of 110 minutes. Looking at the dataset, it can be seen that they are all from different visitors. The probability of keeping a partition with 35 privacy units (visitors) is equal to 1 (see the chart above), which is why it isn’t eliminated.