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I am considering the following hypothetical situation: I have a time series of data. In general, 'the public' should have access to features of this data. However, making the time series available would constitute a privacy leak. I am considering making a moving average available instead.

Can anyone recommend either some literature on this, or some alternative methods?

I understand that this is a case by case question. However, I think there should be a general answer available along the following lines:

1) Privacy leaks occur because you can match up the time stamp to an individual, by using outside information.

2) Therefore, you want to make it so that each window aggregates the data of several individuals. (The data is of a form where the mean is a meaningful quantity.)

There are of course ways to break this privacy, if one is sufficiently determined. I think in this case no one is. So I'm looking for literature that deals with some real world case studies, if possible.

(This situation is hypothetical. I do not have access to the data. I am 'the public' that wants the data, and I want to suggest a reasonable approach for aggregation.)

I also asked this question over on cross validated: https://stats.stackexchange.com/questions/324204/privacy-through-moving-averages

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The key question is how we can allow the public to make useful queries to a dataset without revealing private information.

The field of Differential Privacy deals with answering just that.

The key concept is to track a user's queries and the information revealed and add uncertainty to the answers to guarantee privacy.

For example, a broad query like "what is the rate of cancer in Europe?" could have an answer of with "1% +/- .1%", whereas "what is the rate of cancer for the population of men aged 72 living at my neighbours's address?" would give an answer of "50% +/- 50%": we do not want to reveal whether a specific individual has cancer or not.

Differential privacy gives users an information budget and tracks the queries, results and information revealed. The more you ask, or the closer you get to personal information the less specific the answer. At one point the information budget is exhausted and can query no more. You end up with nothing more than "your neighbour has cancer with probability p=0.5 +/- 0.5".

This also guards against constructing a clever sequence of queries to pin down the answer like in the children's game of "20 questions". For example, you might try to ask questions like "what is the rate of men of cancer for men of age 72 in this city?", "what is the rate of cancer for men of height 182 cm at age 72?", "what is the height distribution of men with my cancer in my street?" etc. until you can deduce whether your 182 cm tall, 72 year old, male neighbour has cancer or not.

Differential Privacy guarantees that such strategies will never work (under certain assumptions).

Moving Averages

With this background, your example of only publishing the moving average seems quite reasonable. Differential Privacy can be used to calculate how long or short the moving average needs to be on your dataset in order to provide the best possible information while preserving privacy.

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  • $\begingroup$ Thanks! Do you have a preferred reference for differential privacy? $\endgroup$ – Lorenzo Najt Jan 24 '18 at 4:40
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Depending on what you're working with here, one approach that might work would be to "jitter" the data. In other words: add noise. Your concern seems to be about people getting recognized from specific timestamp values, so jitter those. depending on the data, you could end up with new timestamps that don't align with any individuals in the data at all while minimally affecting the public's ability to draw inferences from the data.

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